Inference procedure has parameters:
Ice fuel: 200
Timeout: 60s
Convolution: left


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}
}
definition:
{
(leq, P:
{() -> leq([a, y])
() -> leq([b, b])
(leq([b, a])) -> BOT}
)
(insert, F:
{() -> insert([x, nil, cons(x, nil)])
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)])
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))])}
(insert([_uo, _vo, _wo]) /\ insert([_uo, _vo, _xo])) -> eq_eltlist([_wo, _xo])
)
(sort, F:
{() -> sort([nil, nil])
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo])}
(sort([_ap, _bp]) /\ sort([_ap, _cp])) -> eq_eltlist([_bp, _cp])
)
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)])}
(append([_ep, _fp, _gp]) /\ append([_ep, _fp, _hp])) -> eq_eltlist([_gp, _hp])
)
(reverse, F:
{() -> reverse([nil, nil])
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp])}
(reverse([_kp, _lp]) /\ reverse([_kp, _mp])) -> eq_eltlist([_lp, _mp])
)
}

properties:
{(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp])}


over-approximation: {append, insert, reverse, sort}
under-approximation: {leq}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
() -> reverse([nil, nil]) -> 0
() -> sort([nil, nil]) -> 0
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 0
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 0
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 0
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 0
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 0
(leq([b, a])) -> BOT -> 0
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 0
}


Solving took 63.826920 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3899, q_gen_3900, q_gen_3901, q_gen_3911, q_gen_3912, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3925, q_gen_3926, q_gen_3927, q_gen_3932, q_gen_3933, q_gen_3934, q_gen_3941, q_gen_3942, q_gen_3943, q_gen_3952, q_gen_3953, q_gen_3954, q_gen_3955, q_gen_3956, q_gen_3957, q_gen_3966, q_gen_3967, q_gen_3971, q_gen_3981, q_gen_3982, q_gen_3983, q_gen_3985, q_gen_3986, q_gen_3994, q_gen_3995, q_gen_3996, q_gen_3997, q_gen_3998, q_gen_4000, q_gen_4001, q_gen_4002, q_gen_4003, q_gen_4009, q_gen_4010, q_gen_4011, q_gen_4012, q_gen_4016, q_gen_4017, q_gen_4018, q_gen_4021, q_gen_4022, q_gen_4023, q_gen_4024, q_gen_4029, q_gen_4030, q_gen_4031, q_gen_4032, q_gen_4033, q_gen_4034, q_gen_4040, q_gen_4041, q_gen_4042, q_gen_4043, q_gen_4044, q_gen_4045, q_gen_4049, q_gen_4055, q_gen_4056, q_gen_4057, q_gen_4058, q_gen_4059, q_gen_4060, q_gen_4061, q_gen_4062, q_gen_4063, q_gen_4072, q_gen_4073, q_gen_4074, q_gen_4075, q_gen_4079, q_gen_4080, q_gen_4081, q_gen_4089, q_gen_4090},
Q_f={},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<a>() -> q_gen_3954
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3900
<a, a>() -> q_gen_3901
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3954, q_gen_3914) -> q_gen_3957
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3986
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3995
<b, a>() -> q_gen_3998
<a, b>() -> q_gen_4003
<cons, cons>(q_gen_3895, q_gen_3957) -> q_gen_4011
<cons, cons>(q_gen_3901, q_gen_3900) -> q_gen_4030
<cons, cons>(q_gen_3901, q_gen_3957) -> q_gen_4033
<cons, cons>(q_gen_4003, q_gen_3957) -> q_gen_4044
<cons, cons>(q_gen_3895, q_gen_4057) -> q_gen_4056
<cons, cons>(q_gen_3901, q_gen_4058) -> q_gen_4057
<cons, cons>(q_gen_3901, q_gen_3995) -> q_gen_4058
<cons, cons>(q_gen_4003, q_gen_4062) -> q_gen_4061
<cons, cons>(q_gen_3901, q_gen_4063) -> q_gen_4062
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_4063
<nil, nil, nil>() -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<nil, cons, cons>(q_gen_3901, q_gen_3900) -> q_gen_3899
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3911
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3912
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3901, q_gen_3894) -> q_gen_3925
<cons, nil, cons>(q_gen_3895, q_gen_3900) -> q_gen_3926
<nil, cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3927
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3932
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<cons, cons, cons>(q_gen_3942, q_gen_3913) -> q_gen_3941
<a, b, a>() -> q_gen_3942
<cons, cons, cons>(q_gen_3942, q_gen_3893) -> q_gen_3943
<cons, cons, cons>(q_gen_3955, q_gen_3953) -> q_gen_3952
<nil, nil, cons>(q_gen_3954, q_gen_3914) -> q_gen_3953
<b, a, b>() -> q_gen_3955
<nil, cons, cons>(q_gen_3895, q_gen_3957) -> q_gen_3956
<cons, cons, cons>(q_gen_3967, q_gen_3953) -> q_gen_3966
<a, a, a>() -> q_gen_3967
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3971
<cons, cons, cons>(q_gen_3942, q_gen_3982) -> q_gen_3981
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3982
<nil, cons, cons>(q_gen_3895, q_gen_3986) -> q_gen_3985
<nil, cons, cons>(q_gen_3901, q_gen_3995) -> q_gen_3994
<cons, cons, cons>(q_gen_3955, q_gen_3997) -> q_gen_3996
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3997
<nil, cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_4000
<cons, cons, cons>(q_gen_3942, q_gen_4002) -> q_gen_4001
<nil, cons, cons>(q_gen_4003, q_gen_3957) -> q_gen_4002
<cons, nil, cons>(q_gen_3895, q_gen_3957) -> q_gen_4009
<cons, nil, cons>(q_gen_3895, q_gen_4011) -> q_gen_4010
<nil, cons, cons>(q_gen_4003, q_gen_3894) -> q_gen_4012
<cons, cons, cons>(q_gen_3967, q_gen_4009) -> q_gen_4016
<cons, cons, cons>(q_gen_3916, q_gen_4018) -> q_gen_4017
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_4018
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_4021
<cons, cons, cons>(q_gen_3942, q_gen_4023) -> q_gen_4022
<cons, cons, cons>(q_gen_3916, q_gen_3982) -> q_gen_4023
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_4024
<nil, cons, cons>(q_gen_3895, q_gen_4030) -> q_gen_4029
<cons, cons, cons>(q_gen_3942, q_gen_4032) -> q_gen_4031
<nil, cons, cons>(q_gen_4003, q_gen_4033) -> q_gen_4032
<nil, cons, cons>(q_gen_4003, q_gen_3933) -> q_gen_4034
<cons, cons, cons>(q_gen_3955, q_gen_4041) -> q_gen_4040
<cons, nil, cons>(q_gen_4003, q_gen_3957) -> q_gen_4041
<cons, cons, cons>(q_gen_3967, q_gen_4043) -> q_gen_4042
<cons, nil, cons>(q_gen_3895, q_gen_4044) -> q_gen_4043
<cons, cons, cons>(q_gen_3967, q_gen_3884) -> q_gen_4045
<cons, nil, cons>(q_gen_3895, q_gen_3986) -> q_gen_4049
<nil, cons, cons>(q_gen_3895, q_gen_4056) -> q_gen_4055
<cons, cons, cons>(q_gen_3942, q_gen_4060) -> q_gen_4059
<nil, cons, cons>(q_gen_3895, q_gen_4061) -> q_gen_4060
<cons, cons, cons>(q_gen_3955, q_gen_3899) -> q_gen_4072
<cons, cons, cons>(q_gen_3955, q_gen_4074) -> q_gen_4073
<cons, cons, cons>(q_gen_3955, q_gen_4075) -> q_gen_4074
<nil, cons, cons>(q_gen_3901, q_gen_3957) -> q_gen_4075
<cons, cons, cons>(q_gen_3916, q_gen_4080) -> q_gen_4079
<nil, nil, cons>(q_gen_3954, q_gen_3983) -> q_gen_4080
<cons, cons, cons>(q_gen_3916, q_gen_3953) -> q_gen_4081
<cons, cons, cons>(q_gen_3916, q_gen_4009) -> q_gen_4089
<cons, cons, cons>(q_gen_3942, q_gen_4010) -> q_gen_4090
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3885, q_gen_3886, q_gen_3887, q_gen_3891, q_gen_3892, q_gen_3897, q_gen_3898, q_gen_3902, q_gen_3903, q_gen_3904, q_gen_3907, q_gen_3908, q_gen_3909, q_gen_3910, q_gen_3919, q_gen_3920, q_gen_3921, q_gen_3922, q_gen_3930, q_gen_3939, q_gen_3949, q_gen_3950, q_gen_3962, q_gen_3963, q_gen_3964, q_gen_3965, q_gen_3968, q_gen_3974, q_gen_3975, q_gen_3979, q_gen_3980, q_gen_3990, q_gen_3991, q_gen_3992, q_gen_4026, q_gen_4027, q_gen_4037, q_gen_4038, q_gen_4070, q_gen_4078, q_gen_4087},
Q_f={},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<b, a>() -> q_gen_3903
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3910
<cons, cons>(q_gen_3921, q_gen_3908) -> q_gen_3920
<a, b>() -> q_gen_3921
<cons, cons>(q_gen_3892, q_gen_3965) -> q_gen_3964
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3965
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3980
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3991
<cons, cons>(q_gen_3921, q_gen_3886) -> q_gen_4027
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_4038
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3885
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3891
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3897
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3902
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3907
<b, cons, cons>(q_gen_3892, q_gen_3910) -> q_gen_3909
<b, cons, cons>(q_gen_3887, q_gen_3920) -> q_gen_3919
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3930
<b, cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3939
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3949
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3950
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3962
<a, cons, cons>(q_gen_3892, q_gen_3964) -> q_gen_3963
<b, cons, cons>(q_gen_3892, q_gen_3965) -> q_gen_3968
<a, cons, cons>(q_gen_3892, q_gen_3965) -> q_gen_3974
<b, cons, cons>(q_gen_3903, q_gen_3965) -> q_gen_3975
<b, cons, cons>(q_gen_3892, q_gen_3980) -> q_gen_3979
<b, cons, cons>(q_gen_3887, q_gen_3991) -> q_gen_3990
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3992
<b, cons, cons>(q_gen_3903, q_gen_4027) -> q_gen_4026
<b, cons, cons>(q_gen_3903, q_gen_4038) -> q_gen_4037
<a, cons, cons>(q_gen_3921, q_gen_3920) -> q_gen_4070
<b, cons, cons>(q_gen_3892, q_gen_4027) -> q_gen_4078
<a, cons, cons>(q_gen_3892, q_gen_4027) -> q_gen_4087
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3880, q_gen_3890, q_gen_3896},
Q_f={},
Delta=
{
<b, b>() -> q_gen_3879
<a, b>() -> q_gen_3880
<b, a>() -> q_gen_3890
<a, a>() -> q_gen_3896
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3928, q_gen_3929, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3944, q_gen_3945, q_gen_3946, q_gen_3947, q_gen_3948, q_gen_3958, q_gen_3959, q_gen_3960, q_gen_3969, q_gen_3972, q_gen_3973, q_gen_3984, q_gen_3987, q_gen_3988, q_gen_3989, q_gen_4004, q_gen_4005, q_gen_4006, q_gen_4007, q_gen_4013, q_gen_4019, q_gen_4020, q_gen_4025, q_gen_4035, q_gen_4046, q_gen_4050, q_gen_4051, q_gen_4052, q_gen_4064, q_gen_4065, q_gen_4066, q_gen_4067, q_gen_4068, q_gen_4076, q_gen_4082, q_gen_4083, q_gen_4084},
Q_f={},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<a>() -> q_gen_3960
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3989
<cons>(q_gen_3960, q_gen_3937) -> q_gen_4068
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3928
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<cons, cons>(q_gen_3929, q_gen_3936) -> q_gen_3944
<cons, cons>(q_gen_3948, q_gen_3946) -> q_gen_3945
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3946
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3948
<cons, cons>(q_gen_3918, q_gen_3959) -> q_gen_3958
<nil, cons>(q_gen_3960, q_gen_3937) -> q_gen_3959
<cons, cons>(q_gen_3947, q_gen_3946) -> q_gen_3969
<cons, cons>(q_gen_3918, q_gen_3973) -> q_gen_3972
<cons, nil>(q_gen_3960, q_gen_3937) -> q_gen_3973
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3984
<cons, cons>(q_gen_3918, q_gen_3988) -> q_gen_3987
<nil, cons>(q_gen_3938, q_gen_3989) -> q_gen_3988
<cons, cons>(q_gen_3948, q_gen_4005) -> q_gen_4004
<cons, cons>(q_gen_3947, q_gen_3936) -> q_gen_4005
<cons, cons>(q_gen_3918, q_gen_4007) -> q_gen_4006
<nil, cons>(q_gen_3960, q_gen_3989) -> q_gen_4007
<cons, cons>(q_gen_3918, q_gen_3984) -> q_gen_4013
<cons, cons>(q_gen_3918, q_gen_3944) -> q_gen_4019
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_4020
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_4025
<cons, cons>(q_gen_3948, q_gen_3936) -> q_gen_4035
<cons, cons>(q_gen_3929, q_gen_3973) -> q_gen_4046
<cons, cons>(q_gen_3929, q_gen_3928) -> q_gen_4050
<cons, cons>(q_gen_3929, q_gen_4052) -> q_gen_4051
<cons, cons>(q_gen_3929, q_gen_3917) -> q_gen_4052
<cons, cons>(q_gen_3948, q_gen_4065) -> q_gen_4064
<cons, cons>(q_gen_3947, q_gen_3973) -> q_gen_4065
<cons, cons>(q_gen_3948, q_gen_4067) -> q_gen_4066
<cons, nil>(q_gen_3938, q_gen_4068) -> q_gen_4067
<cons, cons>(q_gen_3948, q_gen_3973) -> q_gen_4076
<cons, cons>(q_gen_3918, q_gen_4020) -> q_gen_4082
<cons, cons>(q_gen_3929, q_gen_4084) -> q_gen_4083
<cons, cons>(q_gen_3929, q_gen_3959) -> q_gen_4084
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3923, q_gen_3924, q_gen_3931, q_gen_3940, q_gen_3951, q_gen_3961, q_gen_3970, q_gen_3976, q_gen_3977, q_gen_3978, q_gen_3993, q_gen_3999, q_gen_4008, q_gen_4014, q_gen_4015, q_gen_4028, q_gen_4036, q_gen_4039, q_gen_4047, q_gen_4048, q_gen_4053, q_gen_4054, q_gen_4069, q_gen_4071, q_gen_4077, q_gen_4085, q_gen_4086, q_gen_4088},
Q_f={},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3931
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3940
<cons, cons>(q_gen_3906, q_gen_3923) -> q_gen_3951
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3961
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3970
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3976
<cons, cons>(q_gen_3924, q_gen_3978) -> q_gen_3977
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3978
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3993
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3999
<cons, cons>(q_gen_3889, q_gen_3993) -> q_gen_4008
<cons, cons>(q_gen_4015, q_gen_3877) -> q_gen_4014
<a, a>() -> q_gen_4015
<cons, cons>(q_gen_3924, q_gen_3993) -> q_gen_4028
<cons, cons>(q_gen_4015, q_gen_3888) -> q_gen_4036
<cons, cons>(q_gen_3924, q_gen_3961) -> q_gen_4039
<cons, cons>(q_gen_4015, q_gen_3923) -> q_gen_4047
<cons, cons>(q_gen_3924, q_gen_4036) -> q_gen_4048
<cons, cons>(q_gen_4015, q_gen_3993) -> q_gen_4053
<cons, cons>(q_gen_3906, q_gen_3993) -> q_gen_4054
<cons, cons>(q_gen_3889, q_gen_3999) -> q_gen_4069
<cons, cons>(q_gen_3906, q_gen_3951) -> q_gen_4071
<cons, cons>(q_gen_3889, q_gen_4014) -> q_gen_4077
<cons, cons>(q_gen_3906, q_gen_3970) -> q_gen_4085
<cons, cons>(q_gen_4015, q_gen_4014) -> q_gen_4086
<cons, cons>(q_gen_4015, q_gen_3970) -> q_gen_4088
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.016836 s (model generation: 0.015936,  model checking: 0.000900):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
() -> reverse([nil, nil]) -> 0
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 1
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 1
}
Sat witness: Found: (() -> sort([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.010834 s (model generation: 0.010750,  model checking: 0.000084):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877},
Q_f={q_gen_3877},
Delta=
{
<nil, nil>() -> q_gen_3877
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 1
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 1
}
Sat witness: Found: (() -> reverse([nil, nil]), {

})

-------------------------------------------
Step 2, which took 0.012400 s (model generation: 0.012354,  model checking: 0.000046):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877},
Q_f={q_gen_3877},
Delta=
{
<nil, nil>() -> q_gen_3877
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 1
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 1
}
Sat witness: Found: (() -> leq([b, b]), {

})

-------------------------------------------
Step 3, which took 0.009025 s (model generation: 0.008972,  model checking: 0.000053):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879},
Q_f={q_gen_3879},
Delta=
{
<b, b>() -> q_gen_3879
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877},
Q_f={q_gen_3877},
Delta=
{
<nil, nil>() -> q_gen_3877
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 1
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 1
}
Sat witness: Found: (() -> leq([a, y]), {
y -> b
})

-------------------------------------------
Step 4, which took 0.009473 s (model generation: 0.009275,  model checking: 0.000198):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879},
Q_f={q_gen_3879},
Delta=
{
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877},
Q_f={q_gen_3877},
Delta=
{
<nil, nil>() -> q_gen_3877
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 1
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 1
}
Sat witness: Found: (() -> insert([x, nil, cons(x, nil)]), {
x -> b
})

-------------------------------------------
Step 5, which took 0.010033 s (model generation: 0.009862,  model checking: 0.000171):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879},
Q_f={q_gen_3879},
Delta=
{
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877},
Q_f={q_gen_3877},
Delta=
{
<nil, nil>() -> q_gen_3877
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 1
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 6, which took 0.015319 s (model generation: 0.012114,  model checking: 0.003205):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884},
Q_f={q_gen_3884},
Delta=
{
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879},
Q_f={q_gen_3879},
Delta=
{
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877},
Q_f={q_gen_3877},
Delta=
{
<nil, nil>() -> q_gen_3877
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 1
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 2
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 7, which took 0.010092 s (model generation: 0.009912,  model checking: 0.000180):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884},
Q_f={q_gen_3884},
Delta=
{
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<b, b>() -> q_gen_3887
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879},
Q_f={q_gen_3879},
Delta=
{
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877},
Q_f={q_gen_3877},
Delta=
{
<nil, nil>() -> q_gen_3877
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 1
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 2
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> nil  ;  _zo -> cons(b, nil)  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 8, which took 0.014692 s (model generation: 0.013626,  model checking: 0.001066):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884},
Q_f={q_gen_3884},
Delta=
{
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<b, b>() -> q_gen_3887
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879},
Q_f={q_gen_3879},
Delta=
{
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 1
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 4
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 2
}
Sat witness: Found: ((insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]), {
_to -> cons(b, nil)  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 9, which took 0.009496 s (model generation: 0.009294,  model checking: 0.000202):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884},
Q_f={q_gen_3884},
Delta=
{
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879},
Q_f={q_gen_3879},
Delta=
{
<a, b>() -> q_gen_3879
<b, a>() -> q_gen_3879
<b, b>() -> q_gen_3879
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 1
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 4
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 4
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 2
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 10, which took 0.009185 s (model generation: 0.009048,  model checking: 0.000137):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895},
Q_f={q_gen_3884},
Delta=
{
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879},
Q_f={q_gen_3879},
Delta=
{
<a, b>() -> q_gen_3879
<b, a>() -> q_gen_3879
<b, b>() -> q_gen_3879
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> reverse([nil, nil]) -> 3
() -> sort([nil, nil]) -> 3
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 2
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 4
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 4
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 3
}
Sat witness: Found: ((leq([b, a])) -> BOT, {

})

-------------------------------------------
Step 11, which took 0.012269 s (model generation: 0.012009,  model checking: 0.000260):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895},
Q_f={q_gen_3884},
Delta=
{
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> reverse([nil, nil]) -> 4
() -> sort([nil, nil]) -> 4
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 3
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 4
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 4
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 4
}
Sat witness: Found: (() -> leq([a, y]), {
y -> a
})

-------------------------------------------
Step 12, which took 0.038564 s (model generation: 0.037910,  model checking: 0.000654):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895},
Q_f={q_gen_3884},
Delta=
{
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> reverse([nil, nil]) -> 4
() -> sort([nil, nil]) -> 4
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 4
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 4
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 4
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 4
}
Sat witness: Found: (() -> insert([x, nil, cons(x, nil)]), {
x -> a
})

-------------------------------------------
Step 13, which took 0.014768 s (model generation: 0.014462,  model checking: 0.000306):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895},
Q_f={q_gen_3884},
Delta=
{
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> reverse([nil, nil]) -> 4
() -> sort([nil, nil]) -> 4
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 4
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 4
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 4
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 14, which took 0.017525 s (model generation: 0.016325,  model checking: 0.001200):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895},
Q_f={q_gen_3884},
Delta=
{
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> reverse([nil, nil]) -> 4
() -> sort([nil, nil]) -> 4
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 4
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 4
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 4
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 5
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 15, which took 0.014398 s (model generation: 0.014059,  model checking: 0.000339):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895},
Q_f={q_gen_3884},
Delta=
{
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> reverse([nil, nil]) -> 4
() -> sort([nil, nil]) -> 4
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 4
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 4
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 4
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 5
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> nil  ;  _zo -> cons(b, nil)  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 16, which took 0.013124 s (model generation: 0.012640,  model checking: 0.000484):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895},
Q_f={q_gen_3884},
Delta=
{
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> reverse([nil, nil]) -> 4
() -> sort([nil, nil]) -> 4
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 4
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 4
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 7
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 5
}
Sat witness: Found: ((insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]), {
_to -> cons(a, cons(a, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 17, which took 0.014455 s (model generation: 0.013398,  model checking: 0.001057):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895},
Q_f={q_gen_3884},
Delta=
{
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> reverse([nil, nil]) -> 4
() -> sort([nil, nil]) -> 4
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 4
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 7
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 7
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 5
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 18, which took 0.012796 s (model generation: 0.012663,  model checking: 0.000133):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> reverse([nil, nil]) -> 4
() -> sort([nil, nil]) -> 4
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 7
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 7
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 7
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 5
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> nil  ;  _jp -> cons(b, nil)  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 19, which took 0.015065 s (model generation: 0.013616,  model checking: 0.001449):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 5
() -> reverse([nil, nil]) -> 5
() -> sort([nil, nil]) -> 5
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 7
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 7
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 7
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 6
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 6
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 20, which took 0.016906 s (model generation: 0.016006,  model checking: 0.000900):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 6
() -> reverse([nil, nil]) -> 6
() -> sort([nil, nil]) -> 6
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 7
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 7
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 7
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 7
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> nil  ;  _zo -> cons(a, nil)  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 21, which took 0.018445 s (model generation: 0.017829,  model checking: 0.000616):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 7
() -> reverse([nil, nil]) -> 7
() -> sort([nil, nil]) -> 7
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 7
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 7
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 7
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 10
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> cons(b, nil)  ;  _pp -> cons(a, nil)  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 22, which took 0.016994 s (model generation: 0.015686,  model checking: 0.001308):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3900, q_gen_3911, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3900
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3911
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3911
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 7
() -> reverse([nil, nil]) -> 7
() -> sort([nil, nil]) -> 7
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 7
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 10
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 8
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 10
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(a, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 23, which took 0.016396 s (model generation: 0.015960,  model checking: 0.000436):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3901, q_gen_3911, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<a, a>() -> q_gen_3901
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, nil, cons>(q_gen_3901, q_gen_3894) -> q_gen_3911
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3911
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 7
() -> reverse([nil, nil]) -> 7
() -> sort([nil, nil]) -> 7
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 10
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 10
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 8
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 10
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> nil  ;  _jp -> cons(a, nil)  ;  h1 -> a  ;  t1 -> nil
})

-------------------------------------------
Step 24, which took 0.019146 s (model generation: 0.018343,  model checking: 0.000803):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3900, q_gen_3911, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3900
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3911
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<a>() -> q_gen_3883
<b>() -> q_gen_3883
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> insert([x, nil, cons(x, nil)]) -> 8
() -> leq([a, y]) -> 8
() -> leq([b, b]) -> 8
() -> reverse([nil, nil]) -> 8
() -> sort([nil, nil]) -> 8
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 10
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 10
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 8
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 10
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, nil)
})

-------------------------------------------
Step 25, which took 0.019155 s (model generation: 0.017270,  model checking: 0.001885):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> insert([x, nil, cons(x, nil)]) -> 9
() -> leq([a, y]) -> 9
() -> leq([b, b]) -> 9
() -> reverse([nil, nil]) -> 9
() -> sort([nil, nil]) -> 9
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 10
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 10
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 9
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 9
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 11
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, nil)  ;  _zo -> cons(a, cons(b, nil))  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 26, which took 0.020083 s (model generation: 0.018653,  model checking: 0.001430):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> insert([x, nil, cons(x, nil)]) -> 10
() -> leq([a, y]) -> 10
() -> leq([b, b]) -> 10
() -> reverse([nil, nil]) -> 10
() -> sort([nil, nil]) -> 10
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 10
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 13
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 10
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 10
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 11
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 27, which took 0.019777 s (model generation: 0.018776,  model checking: 0.001001):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918},
Q_f={q_gen_3878},
Delta=
{
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> insert([x, nil, cons(x, nil)]) -> 10
() -> leq([a, y]) -> 10
() -> leq([b, b]) -> 10
() -> reverse([nil, nil]) -> 10
() -> sort([nil, nil]) -> 10
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 13
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 13
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 11
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 11
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 11
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> nil  ;  _jp -> cons(b, cons(b, nil))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 28, which took 0.021258 s (model generation: 0.020077,  model checking: 0.001181):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> insert([x, nil, cons(x, nil)]) -> 11
() -> leq([a, y]) -> 11
() -> leq([b, b]) -> 11
() -> reverse([nil, nil]) -> 11
() -> sort([nil, nil]) -> 11
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 13
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 13
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 11
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 11
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 14
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> nil  ;  _op -> cons(b, nil)  ;  _pp -> cons(b, nil)  ;  l -> nil
})

-------------------------------------------
Step 29, which took 0.023519 s (model generation: 0.021551,  model checking: 0.001968):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> insert([x, nil, cons(x, nil)]) -> 12
() -> leq([a, y]) -> 12
() -> leq([b, b]) -> 12
() -> reverse([nil, nil]) -> 12
() -> sort([nil, nil]) -> 12
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 13
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 13
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 12
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 12
(leq([b, a])) -> BOT -> 12
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 14
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, nil)  ;  _zo -> cons(a, cons(a, nil))  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 30, which took 0.025136 s (model generation: 0.022655,  model checking: 0.002481):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> insert([x, nil, cons(x, nil)]) -> 13
() -> leq([a, y]) -> 13
() -> leq([b, b]) -> 13
() -> reverse([nil, nil]) -> 13
() -> sort([nil, nil]) -> 13
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 13
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 16
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 13
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 13
(leq([b, a])) -> BOT -> 13
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 14
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 31, which took 0.023861 s (model generation: 0.022049,  model checking: 0.001812):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> insert([x, nil, cons(x, nil)]) -> 13
() -> leq([a, y]) -> 13
() -> leq([b, b]) -> 13
() -> reverse([nil, nil]) -> 13
() -> sort([nil, nil]) -> 13
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 16
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 16
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 14
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 14
(leq([b, a])) -> BOT -> 14
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 14
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(a, cons(b, nil))  ;  _jp -> cons(a, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 32, which took 0.028447 s (model generation: 0.026320,  model checking: 0.002127):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> insert([x, nil, cons(x, nil)]) -> 14
() -> leq([a, y]) -> 14
() -> leq([b, b]) -> 14
() -> reverse([nil, nil]) -> 14
() -> sort([nil, nil]) -> 14
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 16
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 16
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 14
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 14
(leq([b, a])) -> BOT -> 14
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 17
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> cons(b, cons(b, nil))  ;  _pp -> cons(a, cons(a, nil))  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 33, which took 0.026861 s (model generation: 0.026447,  model checking: 0.000414):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> insert([x, nil, cons(x, nil)]) -> 14
() -> leq([a, y]) -> 14
() -> leq([b, b]) -> 14
() -> reverse([nil, nil]) -> 14
() -> sort([nil, nil]) -> 14
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 16
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 16
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 14
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 15
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 17
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 34, which took 0.028483 s (model generation: 0.026375,  model checking: 0.002108):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> insert([x, nil, cons(x, nil)]) -> 15
() -> leq([a, y]) -> 15
() -> leq([b, b]) -> 15
() -> reverse([nil, nil]) -> 15
() -> sort([nil, nil]) -> 15
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 16
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 16
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 15
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 16
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 17
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, nil)  ;  _zo -> cons(b, cons(a, nil))  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 35, which took 0.031535 s (model generation: 0.028784,  model checking: 0.002751):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> insert([x, nil, cons(x, nil)]) -> 16
() -> leq([a, y]) -> 16
() -> leq([b, b]) -> 16
() -> reverse([nil, nil]) -> 16
() -> sort([nil, nil]) -> 16
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 16
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 19
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 16
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 17
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 17
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 36, which took 0.031132 s (model generation: 0.029889,  model checking: 0.001243):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> insert([x, nil, cons(x, nil)]) -> 16
() -> leq([a, y]) -> 16
() -> leq([b, b]) -> 16
() -> reverse([nil, nil]) -> 16
() -> sort([nil, nil]) -> 16
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 19
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 19
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 17
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 17
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 17
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> nil  ;  _jp -> cons(b, cons(a, nil))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 37, which took 0.038277 s (model generation: 0.033688,  model checking: 0.004589):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> insert([x, nil, cons(x, nil)]) -> 17
() -> leq([a, y]) -> 17
() -> leq([b, b]) -> 17
() -> reverse([nil, nil]) -> 17
() -> sort([nil, nil]) -> 17
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 19
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 19
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 17
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 17
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 20
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> cons(b, cons(b, nil))  ;  _pp -> cons(b, cons(a, nil))  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 38, which took 0.038896 s (model generation: 0.036564,  model checking: 0.002332):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> insert([x, nil, cons(x, nil)]) -> 18
() -> leq([a, y]) -> 18
() -> leq([b, b]) -> 18
() -> reverse([nil, nil]) -> 18
() -> sort([nil, nil]) -> 18
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 19
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 19
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 18
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 18
(leq([b, a])) -> BOT -> 18
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 20
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, nil)  ;  _zo -> cons(b, cons(a, nil))  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 39, which took 0.038016 s (model generation: 0.037437,  model checking: 0.000579):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> insert([x, nil, cons(x, nil)]) -> 18
() -> leq([a, y]) -> 18
() -> leq([b, b]) -> 18
() -> reverse([nil, nil]) -> 18
() -> sort([nil, nil]) -> 18
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 19
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 19
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 18
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 21
(leq([b, a])) -> BOT -> 19
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 20
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 40, which took 0.043068 s (model generation: 0.039198,  model checking: 0.003870):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> insert([x, nil, cons(x, nil)]) -> 19
() -> leq([a, y]) -> 19
() -> leq([b, b]) -> 19
() -> reverse([nil, nil]) -> 19
() -> sort([nil, nil]) -> 19
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 19
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 22
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 19
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 21
(leq([b, a])) -> BOT -> 20
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 20
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(a, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 41, which took 0.041801 s (model generation: 0.041188,  model checking: 0.000613):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> insert([x, nil, cons(x, nil)]) -> 19
() -> leq([a, y]) -> 19
() -> leq([b, b]) -> 19
() -> reverse([nil, nil]) -> 19
() -> sort([nil, nil]) -> 19
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 19
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 22
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 22
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 21
(leq([b, a])) -> BOT -> 20
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 20
}
Sat witness: Found: ((insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]), {
_to -> cons(a, cons(b, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 42, which took 0.045963 s (model generation: 0.042174,  model checking: 0.003789):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> insert([x, nil, cons(x, nil)]) -> 20
() -> leq([a, y]) -> 20
() -> leq([b, b]) -> 20
() -> reverse([nil, nil]) -> 20
() -> sort([nil, nil]) -> 20
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 20
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 22
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 22
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 21
(leq([b, a])) -> BOT -> 20
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 23
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, cons(b, nil))  ;  _op -> cons(b, cons(b, nil))  ;  _pp -> cons(a, cons(a, nil))  ;  l -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 43, which took 0.045158 s (model generation: 0.043879,  model checking: 0.001279):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> insert([x, nil, cons(x, nil)]) -> 20
() -> leq([a, y]) -> 20
() -> leq([b, b]) -> 20
() -> reverse([nil, nil]) -> 20
() -> sort([nil, nil]) -> 20
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 23
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 22
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 22
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 21
(leq([b, a])) -> BOT -> 21
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 23
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(b, nil)  ;  _jp -> cons(b, nil)  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 44, which took 0.049914 s (model generation: 0.048413,  model checking: 0.001501):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3908
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> insert([x, nil, cons(x, nil)]) -> 21
() -> leq([a, y]) -> 21
() -> leq([b, b]) -> 21
() -> reverse([nil, nil]) -> 21
() -> sort([nil, nil]) -> 21
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 23
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 22
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 22
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 22
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 23
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 45, which took 0.055417 s (model generation: 0.053191,  model checking: 0.002226):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<b, a>() -> q_gen_3892
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> insert([x, nil, cons(x, nil)]) -> 22
() -> leq([a, y]) -> 22
() -> leq([b, b]) -> 22
() -> reverse([nil, nil]) -> 22
() -> sort([nil, nil]) -> 22
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 23
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 22
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 22
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 23
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 23
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, cons(b, nil))  ;  _zo -> cons(a, cons(a, cons(b, nil)))  ;  y -> b  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 46, which took 0.065672 s (model generation: 0.063719,  model checking: 0.001953):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3908
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> insert([x, nil, cons(x, nil)]) -> 22
() -> leq([a, y]) -> 22
() -> leq([b, b]) -> 22
() -> reverse([nil, nil]) -> 22
() -> sort([nil, nil]) -> 22
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 23
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 22
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 25
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 23
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 23
}
Sat witness: Found: ((insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]), {
_to -> cons(a, cons(b, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 47, which took 0.060152 s (model generation: 0.058902,  model checking: 0.001250):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3908
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> insert([x, nil, cons(x, nil)]) -> 22
() -> leq([a, y]) -> 22
() -> leq([b, b]) -> 22
() -> reverse([nil, nil]) -> 22
() -> sort([nil, nil]) -> 22
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 23
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 25
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 25
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 23
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 23
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 48, which took 0.059604 s (model generation: 0.058602,  model checking: 0.001002):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3908
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> insert([x, nil, cons(x, nil)]) -> 23
() -> leq([a, y]) -> 23
() -> leq([b, b]) -> 23
() -> reverse([nil, nil]) -> 23
() -> sort([nil, nil]) -> 23
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 23
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 25
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 25
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 23
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 26
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> nil  ;  _pp -> nil  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 49, which took 0.061176 s (model generation: 0.060933,  model checking: 0.000243):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3908
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> insert([x, nil, cons(x, nil)]) -> 23
() -> leq([a, y]) -> 23
() -> leq([b, b]) -> 23
() -> reverse([nil, nil]) -> 23
() -> sort([nil, nil]) -> 23
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 26
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 25
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 25
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 24
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 26
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> nil  ;  _jp -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 50, which took 0.063326 s (model generation: 0.062167,  model checking: 0.001159):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3908
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> insert([x, nil, cons(x, nil)]) -> 24
() -> leq([a, y]) -> 24
() -> leq([b, b]) -> 24
() -> reverse([nil, nil]) -> 24
() -> sort([nil, nil]) -> 24
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 26
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 25
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 25
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 25
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 26
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 51, which took 0.075225 s (model generation: 0.073292,  model checking: 0.001933):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> insert([x, nil, cons(x, nil)]) -> 25
() -> leq([a, y]) -> 25
() -> leq([b, b]) -> 25
() -> reverse([nil, nil]) -> 25
() -> sort([nil, nil]) -> 25
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 26
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 25
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 25
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 26
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 26
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, nil)  ;  _zo -> cons(b, cons(b, nil))  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 52, which took 0.081336 s (model generation: 0.076892,  model checking: 0.004444):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3905
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> insert([x, nil, cons(x, nil)]) -> 25
() -> leq([a, y]) -> 25
() -> leq([b, b]) -> 25
() -> reverse([nil, nil]) -> 25
() -> sort([nil, nil]) -> 25
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 26
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 28
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 26
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 26
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 26
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(a, cons(b, nil))  ;  h1 -> b  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 53, which took 0.115518 s (model generation: 0.114136,  model checking: 0.001382):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3903, q_gen_3908, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3922
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3922
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3922
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> insert([x, nil, cons(x, nil)]) -> 26
() -> leq([a, y]) -> 26
() -> leq([b, b]) -> 26
() -> reverse([nil, nil]) -> 26
() -> sort([nil, nil]) -> 26
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 26
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 28
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 26
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 26
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 29
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> cons(b, cons(b, nil))  ;  _pp -> cons(b, cons(b, nil))  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 54, which took 0.137378 s (model generation: 0.132925,  model checking: 0.004453):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3907, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<b, a>() -> q_gen_3892
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3907
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3907
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3907
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3923
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> insert([x, nil, cons(x, nil)]) -> 27
() -> leq([a, y]) -> 27
() -> leq([b, b]) -> 27
() -> reverse([nil, nil]) -> 27
() -> sort([nil, nil]) -> 27
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 27
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 28
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 27
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 28
(leq([b, a])) -> BOT -> 27
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 29
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, nil)  ;  _zo -> cons(b, cons(b, nil))  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 55, which took 0.116938 s (model generation: 0.110891,  model checking: 0.006047):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3905
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> insert([x, nil, cons(x, nil)]) -> 28
() -> leq([a, y]) -> 28
() -> leq([b, b]) -> 28
() -> reverse([nil, nil]) -> 28
() -> sort([nil, nil]) -> 28
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 28
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 31
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 28
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 29
(leq([b, a])) -> BOT -> 28
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 29
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 56, which took 0.138341 s (model generation: 0.137045,  model checking: 0.001296):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> insert([x, nil, cons(x, nil)]) -> 28
() -> leq([a, y]) -> 28
() -> leq([b, b]) -> 28
() -> reverse([nil, nil]) -> 28
() -> sort([nil, nil]) -> 28
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 31
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 31
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 29
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 29
(leq([b, a])) -> BOT -> 29
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 29
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(a, nil)  ;  _jp -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 57, which took 0.126954 s (model generation: 0.125469,  model checking: 0.001485):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3892, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, a>() -> q_gen_3892
<cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3908
<cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3886) -> q_gen_3881
<b, cons, cons>(q_gen_3892, q_gen_3908) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3905
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> insert([x, nil, cons(x, nil)]) -> 29
() -> leq([a, y]) -> 29
() -> leq([b, b]) -> 29
() -> reverse([nil, nil]) -> 29
() -> sort([nil, nil]) -> 29
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 31
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 31
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 29
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 29
(leq([b, a])) -> BOT -> 29
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 32
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> cons(b, cons(a, cons(b, nil)))  ;  _pp -> cons(b, cons(b, cons(b, nil)))  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 58, which took 0.154022 s (model generation: 0.149678,  model checking: 0.004344):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3905
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> insert([x, nil, cons(x, nil)]) -> 30
() -> leq([a, y]) -> 30
() -> leq([b, b]) -> 30
() -> reverse([nil, nil]) -> 30
() -> sort([nil, nil]) -> 30
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 31
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 31
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 30
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 30
(leq([b, a])) -> BOT -> 30
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 32
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, nil)  ;  _zo -> cons(b, cons(b, nil))  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 59, which took 0.194941 s (model generation: 0.191781,  model checking: 0.003160):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> insert([x, nil, cons(x, nil)]) -> 31
() -> leq([a, y]) -> 31
() -> leq([b, b]) -> 31
() -> reverse([nil, nil]) -> 31
() -> sort([nil, nil]) -> 31
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 31
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 34
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 31
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 31
(leq([b, a])) -> BOT -> 31
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 32
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(a, nil))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 60, which took 0.212700 s (model generation: 0.210842,  model checking: 0.001858):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> insert([x, nil, cons(x, nil)]) -> 31
() -> leq([a, y]) -> 31
() -> leq([b, b]) -> 31
() -> reverse([nil, nil]) -> 31
() -> sort([nil, nil]) -> 31
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 34
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 34
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 32
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 32
(leq([b, a])) -> BOT -> 32
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 32
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> nil  ;  _jp -> cons(b, nil)  ;  h1 -> a  ;  t1 -> nil
})

-------------------------------------------
Step 61, which took 0.214331 s (model generation: 0.207380,  model checking: 0.006951):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> insert([x, nil, cons(x, nil)]) -> 32
() -> leq([a, y]) -> 32
() -> leq([b, b]) -> 32
() -> reverse([nil, nil]) -> 32
() -> sort([nil, nil]) -> 32
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 34
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 34
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 32
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 32
(leq([b, a])) -> BOT -> 32
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 35
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, cons(b, nil))  ;  _op -> cons(b, nil)  ;  _pp -> cons(b, nil)  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 62, which took 0.210877 s (model generation: 0.207416,  model checking: 0.003461):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> insert([x, nil, cons(x, nil)]) -> 33
() -> leq([a, y]) -> 33
() -> leq([b, b]) -> 33
() -> reverse([nil, nil]) -> 33
() -> sort([nil, nil]) -> 33
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 34
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 34
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 33
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 37
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 33
(leq([b, a])) -> BOT -> 33
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 35
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> nil  ;  _zo -> cons(a, nil)  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 63, which took 0.235309 s (model generation: 0.232519,  model checking: 0.002790):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3983},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> insert([x, nil, cons(x, nil)]) -> 34
() -> leq([a, y]) -> 34
() -> leq([b, b]) -> 34
() -> reverse([nil, nil]) -> 34
() -> sort([nil, nil]) -> 34
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 34
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 37
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 34
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 37
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 34
(leq([b, a])) -> BOT -> 34
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 35
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 64, which took 0.249047 s (model generation: 0.247223,  model checking: 0.001824):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> insert([x, nil, cons(x, nil)]) -> 34
() -> leq([a, y]) -> 34
() -> leq([b, b]) -> 34
() -> reverse([nil, nil]) -> 34
() -> sort([nil, nil]) -> 34
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 37
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 37
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 35
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 37
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 35
(leq([b, a])) -> BOT -> 35
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 35
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(b, cons(b, nil))  ;  _jp -> cons(b, cons(a, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 65, which took 0.301069 s (model generation: 0.298934,  model checking: 0.002135):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3983},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 35
() -> insert([x, nil, cons(x, nil)]) -> 35
() -> leq([a, y]) -> 35
() -> leq([b, b]) -> 35
() -> reverse([nil, nil]) -> 35
() -> sort([nil, nil]) -> 35
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 37
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 37
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 35
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 37
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 35
(leq([b, a])) -> BOT -> 35
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 38
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> cons(a, nil)  ;  _pp -> cons(a, nil)  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 66, which took 0.187410 s (model generation: 0.184381,  model checking: 0.003029):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3922
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> insert([x, nil, cons(x, nil)]) -> 36
() -> leq([a, y]) -> 36
() -> leq([b, b]) -> 36
() -> reverse([nil, nil]) -> 36
() -> sort([nil, nil]) -> 36
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 37
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 37
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 36
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 36
(leq([b, a])) -> BOT -> 36
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 38
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(a, nil)  ;  _zo -> cons(a, cons(b, nil))  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 67, which took 0.224194 s (model generation: 0.219704,  model checking: 0.004490):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3907, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3907
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> insert([x, nil, cons(x, nil)]) -> 37
() -> leq([a, y]) -> 37
() -> leq([b, b]) -> 37
() -> reverse([nil, nil]) -> 37
() -> sort([nil, nil]) -> 37
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 37
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 40
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 37
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 37
(leq([b, a])) -> BOT -> 37
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 38
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 68, which took 0.254085 s (model generation: 0.252887,  model checking: 0.001198):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3900, q_gen_3901, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3925},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<b, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3900
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3900
<a, a>() -> q_gen_3901
<a, b>() -> q_gen_3901
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3901, q_gen_3900) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3925) -> q_gen_3925
<cons, nil, cons>(q_gen_3901, q_gen_3894) -> q_gen_3925
<nil, cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_3925
<nil, cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3925
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3928, q_gen_3929, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3928) -> q_gen_3928
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3928
<cons, cons>(q_gen_3929, q_gen_3928) -> q_gen_3928
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3928
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3928
<a, a>() -> q_gen_3929
<a, b>() -> q_gen_3929
<b, a>() -> q_gen_3929
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> insert([x, nil, cons(x, nil)]) -> 37
() -> leq([a, y]) -> 37
() -> leq([b, b]) -> 37
() -> reverse([nil, nil]) -> 37
() -> sort([nil, nil]) -> 37
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 40
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 40
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 38
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 38
(leq([b, a])) -> BOT -> 38
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 38
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> nil  ;  _jp -> cons(a, nil)  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 69, which took 0.317932 s (model generation: 0.317069,  model checking: 0.000863):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3900, q_gen_3901, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3925},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3900
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3900
<a, a>() -> q_gen_3901
<a, b>() -> q_gen_3901
<b, a>() -> q_gen_3901
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3901, q_gen_3900) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3925) -> q_gen_3925
<cons, nil, cons>(q_gen_3901, q_gen_3894) -> q_gen_3925
<cons, nil, cons>(q_gen_3901, q_gen_3900) -> q_gen_3925
<nil, cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_3925
<nil, cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3925
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3928, q_gen_3929, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3928) -> q_gen_3928
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3928
<cons, cons>(q_gen_3929, q_gen_3928) -> q_gen_3928
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3928
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3928
<a, a>() -> q_gen_3929
<a, b>() -> q_gen_3929
<b, a>() -> q_gen_3929
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> insert([x, nil, cons(x, nil)]) -> 38
() -> leq([a, y]) -> 38
() -> leq([b, b]) -> 38
() -> reverse([nil, nil]) -> 38
() -> sort([nil, nil]) -> 38
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 40
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 40
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 38
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 38
(leq([b, a])) -> BOT -> 38
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 38
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 70, which took 0.279767 s (model generation: 0.273085,  model checking: 0.006682):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3900, q_gen_3901, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3927, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3900
<cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3900
<a, a>() -> q_gen_3901
<a, b>() -> q_gen_3901
<b, a>() -> q_gen_3901
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3927) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<cons, nil, cons>(q_gen_3901, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<nil, cons, cons>(q_gen_3901, q_gen_3900) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3901, q_gen_3933) -> q_gen_3927
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3927
<nil, cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3927
<nil, cons, cons>(q_gen_3901, q_gen_3933) -> q_gen_3927
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3928, q_gen_3929, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3928) -> q_gen_3928
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3928
<cons, cons>(q_gen_3929, q_gen_3928) -> q_gen_3928
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3928
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3928
<a, a>() -> q_gen_3929
<a, b>() -> q_gen_3929
<b, a>() -> q_gen_3929
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> insert([x, nil, cons(x, nil)]) -> 38
() -> leq([a, y]) -> 38
() -> leq([b, b]) -> 38
() -> reverse([nil, nil]) -> 38
() -> sort([nil, nil]) -> 38
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 40
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 40
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 38
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 38
(leq([b, a])) -> BOT -> 38
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 41
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, cons(b, nil))  ;  _op -> cons(b, cons(b, nil))  ;  _pp -> cons(a, cons(a, nil))  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 71, which took 0.524487 s (model generation: 0.520028,  model checking: 0.004459):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3934
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3907, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3907
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3945, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3945) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3945
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> insert([x, nil, cons(x, nil)]) -> 39
() -> leq([a, y]) -> 39
() -> leq([b, b]) -> 39
() -> reverse([nil, nil]) -> 39
() -> sort([nil, nil]) -> 39
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 40
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 40
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 39
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 43
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 39
(leq([b, a])) -> BOT -> 39
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 41
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, cons(a, nil))  ;  _zo -> cons(a, cons(b, cons(b, nil)))  ;  y -> b  ;  z -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 72, which took 0.408482 s (model generation: 0.402746,  model checking: 0.005736):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3934
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3907, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3907
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> insert([x, nil, cons(x, nil)]) -> 40
() -> leq([a, y]) -> 40
() -> leq([b, b]) -> 40
() -> reverse([nil, nil]) -> 40
() -> sort([nil, nil]) -> 40
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 40
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 43
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 40
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 43
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 40
(leq([b, a])) -> BOT -> 40
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 41
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(a, cons(a, nil)))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, cons(a, nil)))  ;  t1 -> nil
})

-------------------------------------------
Step 73, which took 0.446015 s (model generation: 0.444691,  model checking: 0.001324):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3934
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3907, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3907
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> insert([x, nil, cons(x, nil)]) -> 40
() -> leq([a, y]) -> 40
() -> leq([b, b]) -> 40
() -> reverse([nil, nil]) -> 40
() -> sort([nil, nil]) -> 40
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 43
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 43
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 41
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 43
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 41
(leq([b, a])) -> BOT -> 41
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 41
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> nil  ;  _jp -> cons(b, cons(b, nil))  ;  h1 -> a  ;  t1 -> nil
})

-------------------------------------------
Step 74, which took 0.472070 s (model generation: 0.466346,  model checking: 0.005724):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3907, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3907
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 41
() -> insert([x, nil, cons(x, nil)]) -> 41
() -> leq([a, y]) -> 41
() -> leq([b, b]) -> 41
() -> reverse([nil, nil]) -> 41
() -> sort([nil, nil]) -> 41
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 43
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 43
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 41
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 43
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 41
(leq([b, a])) -> BOT -> 41
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 44
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> cons(a, cons(b, nil))  ;  _pp -> cons(a, cons(b, nil))  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 75, which took 0.465614 s (model generation: 0.463874,  model checking: 0.001740):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3900, q_gen_3901, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3925, q_gen_3933},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3900
<cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3900
<cons, cons>(q_gen_3901, q_gen_3933) -> q_gen_3900
<a, a>() -> q_gen_3901
<a, b>() -> q_gen_3901
<b, a>() -> q_gen_3901
<cons, cons>(q_gen_3901, q_gen_3900) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3925) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3900) -> q_gen_3884
<nil, cons, cons>(q_gen_3901, q_gen_3900) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3901, q_gen_3894) -> q_gen_3925
<cons, nil, cons>(q_gen_3901, q_gen_3933) -> q_gen_3925
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3925
<nil, cons, cons>(q_gen_3901, q_gen_3894) -> q_gen_3925
<nil, cons, cons>(q_gen_3901, q_gen_3933) -> q_gen_3925
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3928, q_gen_3929, q_gen_3937, q_gen_3938},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3928
<cons, cons>(q_gen_3918, q_gen_3928) -> q_gen_3928
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3928
<cons, cons>(q_gen_3929, q_gen_3928) -> q_gen_3928
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3928
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3928
<a, a>() -> q_gen_3929
<a, b>() -> q_gen_3929
<b, a>() -> q_gen_3929
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> insert([x, nil, cons(x, nil)]) -> 42
() -> leq([a, y]) -> 42
() -> leq([b, b]) -> 42
() -> reverse([nil, nil]) -> 42
() -> sort([nil, nil]) -> 42
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 43
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 43
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 42
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 43
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 42
(leq([b, a])) -> BOT -> 42
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 44
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, nil)
})

-------------------------------------------
Step 76, which took 0.405263 s (model generation: 0.402217,  model checking: 0.003046):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3922},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3922
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3936) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3877
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> insert([x, nil, cons(x, nil)]) -> 43
() -> leq([a, y]) -> 43
() -> leq([b, b]) -> 43
() -> reverse([nil, nil]) -> 43
() -> sort([nil, nil]) -> 43
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 43
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 43
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 43
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 43
(leq([b, a])) -> BOT -> 43
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 44
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(b, cons(b, nil))  ;  _zo -> cons(a, cons(b, cons(a, nil)))  ;  y -> b  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 77, which took 0.412405 s (model generation: 0.398930,  model checking: 0.013475):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3907, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3907
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3945, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3945) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3945
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> insert([x, nil, cons(x, nil)]) -> 43
() -> leq([a, y]) -> 43
() -> leq([b, b]) -> 43
() -> reverse([nil, nil]) -> 43
() -> sort([nil, nil]) -> 43
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 43
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 46
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 44
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 44
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 44
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(b, cons(a, nil)))  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 78, which took 0.848464 s (model generation: 0.845717,  model checking: 0.002747):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3907, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3907
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3907
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3936) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> insert([x, nil, cons(x, nil)]) -> 43
() -> leq([a, y]) -> 43
() -> leq([b, b]) -> 43
() -> reverse([nil, nil]) -> 43
() -> sort([nil, nil]) -> 43
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 46
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 46
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 44
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 44
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 44
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(a, nil)  ;  _jp -> cons(a, nil)  ;  h1 -> a  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 79, which took 1.127532 s (model generation: 1.123667,  model checking: 0.003865):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3913
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3888
<a, a>() -> q_gen_3889
<a, b>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> insert([x, nil, cons(x, nil)]) -> 44
() -> leq([a, y]) -> 44
() -> leq([b, b]) -> 44
() -> reverse([nil, nil]) -> 44
() -> sort([nil, nil]) -> 44
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 46
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 46
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 44
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 44
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 47
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, nil)  ;  _op -> cons(a, nil)  ;  _pp -> cons(a, nil)  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 80, which took 0.431350 s (model generation: 0.427982,  model checking: 0.003368):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3913
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 45
() -> insert([x, nil, cons(x, nil)]) -> 45
() -> leq([a, y]) -> 45
() -> leq([b, b]) -> 45
() -> reverse([nil, nil]) -> 45
() -> sort([nil, nil]) -> 45
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 46
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 46
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 45
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 45
(leq([b, a])) -> BOT -> 45
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 47
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(a, cons(a, nil))  ;  _zo -> cons(a, cons(a, cons(b, nil)))  ;  y -> b  ;  z -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 81, which took 0.417591 s (model generation: 0.415323,  model checking: 0.002268):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3913
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 46
() -> insert([x, nil, cons(x, nil)]) -> 46
() -> leq([a, y]) -> 46
() -> leq([b, b]) -> 46
() -> reverse([nil, nil]) -> 46
() -> sort([nil, nil]) -> 46
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 46
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 49
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 46
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 46
(leq([b, a])) -> BOT -> 46
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 47
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 82, which took 0.526132 s (model generation: 0.524831,  model checking: 0.001301):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3913, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3932, q_gen_3933, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884, q_gen_3932},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3913) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3932) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3913
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3913
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3913
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3913
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3913
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3932
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3932
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 46
() -> insert([x, nil, cons(x, nil)]) -> 46
() -> leq([a, y]) -> 46
() -> leq([b, b]) -> 46
() -> reverse([nil, nil]) -> 46
() -> sort([nil, nil]) -> 46
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 49
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 49
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 47
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 47
(leq([b, a])) -> BOT -> 47
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 47
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(a, nil)  ;  _jp -> cons(a, cons(a, nil))  ;  h1 -> a  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 83, which took 0.451593 s (model generation: 0.408601,  model checking: 0.042992):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3929, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3929, q_gen_3917) -> q_gen_3878
<cons, cons>(q_gen_3929, q_gen_3935) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3936) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 47
() -> insert([x, nil, cons(x, nil)]) -> 47
() -> leq([a, y]) -> 47
() -> leq([b, b]) -> 47
() -> reverse([nil, nil]) -> 47
() -> sort([nil, nil]) -> 47
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 49
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 49
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 47
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 47
(leq([b, a])) -> BOT -> 47
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 50
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(a, cons(b, cons(b, nil)))  ;  _op -> cons(a, cons(a, cons(b, nil)))  ;  _pp -> cons(b, cons(b, cons(b, nil)))  ;  l -> cons(a, cons(a, cons(b, nil)))
})

-------------------------------------------
Step 84, which took 22.543956 s (model generation: 0.510154,  model checking: 22.033802):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3929, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3929, q_gen_3935) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3936) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3917) -> q_gen_3936
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 48
() -> insert([x, nil, cons(x, nil)]) -> 48
() -> leq([a, y]) -> 48
() -> leq([b, b]) -> 48
() -> reverse([nil, nil]) -> 48
() -> sort([nil, nil]) -> 48
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 49
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 52
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 48
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 50
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 48
(leq([b, a])) -> BOT -> 48
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 50
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(b, cons(a, cons(a, cons(b, nil)))))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, cons(a, cons(a, cons(b, nil)))))  ;  t1 -> nil
})

-------------------------------------------
Step 85, which took 0.548276 s (model generation: 0.544728,  model checking: 0.003548):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3929, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<cons, cons>(q_gen_3929, q_gen_3935) -> q_gen_3917
<b, b>() -> q_gen_3918
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3936) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3917) -> q_gen_3936
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> insert([x, nil, cons(x, nil)]) -> 49
() -> leq([a, y]) -> 49
() -> leq([b, b]) -> 49
() -> reverse([nil, nil]) -> 49
() -> sort([nil, nil]) -> 49
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 52
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 52
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 49
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 50
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 49
(leq([b, a])) -> BOT -> 49
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 50
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(a, nil)  ;  _jp -> cons(a, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 86, which took 0.531211 s (model generation: 0.485187,  model checking: 0.046024):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3929, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3929, q_gen_3935) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3917) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3917
<b, b>() -> q_gen_3918
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3936) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3917) -> q_gen_3936
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> insert([x, nil, cons(x, nil)]) -> 50
() -> leq([a, y]) -> 50
() -> leq([b, b]) -> 50
() -> reverse([nil, nil]) -> 50
() -> sort([nil, nil]) -> 50
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 52
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 52
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 50
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 50
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 50
(leq([b, a])) -> BOT -> 50
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 53
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, cons(b, cons(b, nil)))  ;  _op -> cons(a, nil)  ;  _pp -> cons(a, nil)  ;  l -> cons(b, cons(b, cons(a, nil)))
})

-------------------------------------------
Step 87, which took 0.764763 s (model generation: 0.762734,  model checking: 0.002029):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3929, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> insert([x, nil, cons(x, nil)]) -> 50
() -> leq([a, y]) -> 50
() -> leq([b, b]) -> 50
() -> reverse([nil, nil]) -> 50
() -> sort([nil, nil]) -> 50
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 52
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 52
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 50
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 53
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 51
(leq([b, a])) -> BOT -> 51
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 53
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(a, cons(a, nil))  ;  _zo -> cons(b, cons(b, cons(a, nil)))  ;  y -> a  ;  z -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 88, which took 0.812626 s (model generation: 0.807133,  model checking: 0.005493):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3929, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 51
() -> insert([x, nil, cons(x, nil)]) -> 51
() -> leq([a, y]) -> 51
() -> leq([b, b]) -> 51
() -> reverse([nil, nil]) -> 51
() -> sort([nil, nil]) -> 51
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 52
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 55
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 51
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 53
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 52
(leq([b, a])) -> BOT -> 52
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 53
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(a, cons(a, nil)))  ;  h1 -> b  ;  l2 -> cons(a, cons(a, cons(a, nil)))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 89, which took 0.997476 s (model generation: 0.995125,  model checking: 0.002351):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3917, q_gen_3918, q_gen_3929, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878, q_gen_3917},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3917
<b, b>() -> q_gen_3918
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3917) -> q_gen_3935
<cons, cons>(q_gen_3929, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<a, b>() -> q_gen_3906
<b, a>() -> q_gen_3906
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 52
() -> insert([x, nil, cons(x, nil)]) -> 52
() -> leq([a, y]) -> 52
() -> leq([b, b]) -> 52
() -> reverse([nil, nil]) -> 52
() -> sort([nil, nil]) -> 52
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 55
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 55
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 52
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 53
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 53
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 53
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(b, nil)  ;  _jp -> cons(b, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 90, which took 1.729951 s (model generation: 1.682693,  model checking: 0.047258):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3923, q_gen_3924, q_gen_4015},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3923) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3888
<cons, cons>(q_gen_4015, q_gen_3877) -> q_gen_3888
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_4015, q_gen_3888) -> q_gen_3905
<cons, cons>(q_gen_4015, q_gen_3923) -> q_gen_3905
<a, b>() -> q_gen_3906
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
<a, a>() -> q_gen_4015
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> insert([x, nil, cons(x, nil)]) -> 53
() -> leq([a, y]) -> 53
() -> leq([b, b]) -> 53
() -> reverse([nil, nil]) -> 53
() -> sort([nil, nil]) -> 53
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 55
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 55
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 53
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 53
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 53
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 56
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(b, cons(a, nil))  ;  _op -> cons(a, nil)  ;  _pp -> cons(a, nil)  ;  l -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 91, which took 1.530189 s (model generation: 1.526561,  model checking: 0.003628):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3893
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<a, b>() -> q_gen_3887
<b, b>() -> q_gen_3887
<b, a>() -> q_gen_3903
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3888, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877, q_gen_3888},
Delta=
{
<cons, cons>(q_gen_3906, q_gen_3888) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3906, q_gen_3923) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3888) -> q_gen_3888
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3888
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3905
<a, b>() -> q_gen_3906
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> insert([x, nil, cons(x, nil)]) -> 53
() -> leq([a, y]) -> 53
() -> leq([b, b]) -> 53
() -> reverse([nil, nil]) -> 53
() -> sort([nil, nil]) -> 53
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 55
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 55
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 53
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 56
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 54
(leq([b, a])) -> BOT -> 54
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 56
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(a, cons(a, nil))  ;  _zo -> cons(a, cons(b, cons(b, nil)))  ;  y -> b  ;  z -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 92, which took 1.581622 s (model generation: 1.573530,  model checking: 0.008092):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<a, b>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<b, a>() -> q_gen_3998
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3908
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3923) -> q_gen_3877
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3905
<a, b>() -> q_gen_3906
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 54
() -> insert([x, nil, cons(x, nil)]) -> 54
() -> leq([a, y]) -> 54
() -> leq([b, b]) -> 54
() -> reverse([nil, nil]) -> 54
() -> sort([nil, nil]) -> 54
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 55
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 58
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 54
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 56
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 55
(leq([b, a])) -> BOT -> 55
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 56
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(a, cons(b, nil))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 93, which took 5.014555 s (model generation: 5.006394,  model checking: 0.008161):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3983, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3983
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3983) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3908
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3923) -> q_gen_3877
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3905
<a, b>() -> q_gen_3906
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3923
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 55
() -> insert([x, nil, cons(x, nil)]) -> 55
() -> leq([a, y]) -> 55
() -> leq([b, b]) -> 55
() -> reverse([nil, nil]) -> 55
() -> sort([nil, nil]) -> 55
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 58
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 58
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 55
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 56
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 56
(leq([b, a])) -> BOT -> 56
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 56
}
Sat witness: Found: ((append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]), {
_ip -> cons(b, nil)  ;  _jp -> cons(b, cons(a, nil))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 94, which took 4.288262 s (model generation: 4.259923,  model checking: 0.028339):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3894
<cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3908
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3929, q_gen_3935, q_gen_3937, q_gen_3938, q_gen_3946, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3946) -> q_gen_3878
<cons, cons>(q_gen_3929, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3929, q_gen_3935) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3946) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<b, b>() -> q_gen_3918
<a, a>() -> q_gen_3929
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3935
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3946
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3946
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3923) -> q_gen_3877
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3905
<a, b>() -> q_gen_3906
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3923
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 56
() -> insert([x, nil, cons(x, nil)]) -> 56
() -> leq([a, y]) -> 56
() -> leq([b, b]) -> 56
() -> reverse([nil, nil]) -> 56
() -> sort([nil, nil]) -> 56
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 58
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 58
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 56
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 56
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 56
(leq([b, a])) -> BOT -> 56
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 59
}
Sat witness: Found: ((reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]), {
_np -> cons(a, cons(a, nil))  ;  _op -> cons(a, cons(a, cons(a, nil)))  ;  _pp -> cons(b, cons(b, cons(b, nil)))  ;  l -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 95, which took 3.608600 s (model generation: 3.589816,  model checking: 0.018784):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3933
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3933
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3908
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3947},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3878
<cons, cons>(q_gen_3947, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3947, q_gen_3936) -> q_gen_3935
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<a, b>() -> q_gen_3947
<b, a>() -> q_gen_3947
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3923, q_gen_3924},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3923) -> q_gen_3877
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3905
<a, b>() -> q_gen_3906
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<b, a>() -> q_gen_3924
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 56
() -> insert([x, nil, cons(x, nil)]) -> 56
() -> leq([a, y]) -> 56
() -> leq([b, b]) -> 56
() -> reverse([nil, nil]) -> 56
() -> sort([nil, nil]) -> 56
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 58
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 58
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 56
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 59
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 57
(leq([b, a])) -> BOT -> 57
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 59
}
Sat witness: Found: ((insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]), {
_yo -> cons(a, cons(a, nil))  ;  _zo -> cons(a, cons(b, cons(b, nil)))  ;  y -> a  ;  z -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 96, which took 3.034005 s (model generation: 3.025621,  model checking: 0.008384):

Model:
|_
{
append -> 
{{{
Q={q_gen_3884, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3914, q_gen_3915, q_gen_3916, q_gen_3933, q_gen_3934, q_gen_3998, q_gen_4011, q_gen_4044},
Q_f={q_gen_3884, q_gen_3893},
Delta=
{
<cons>(q_gen_3915, q_gen_3914) -> q_gen_3914
<nil>() -> q_gen_3914
<a>() -> q_gen_3915
<b>() -> q_gen_3915
<cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3894
<nil, nil>() -> q_gen_3894
<a, a>() -> q_gen_3895
<b, b>() -> q_gen_3895
<nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3933
<a, b>() -> q_gen_3998
<b, a>() -> q_gen_3998
<cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_4011
<cons, cons>(q_gen_3895, q_gen_4044) -> q_gen_4011
<cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_4044
<cons, cons>(q_gen_3998, q_gen_4011) -> q_gen_4044
<cons, nil, cons>(q_gen_3895, q_gen_4011) -> q_gen_3884
<cons, nil, cons>(q_gen_3895, q_gen_4044) -> q_gen_3884
<cons, nil, cons>(q_gen_3998, q_gen_3933) -> q_gen_3884
<nil, cons, cons>(q_gen_3895, q_gen_3894) -> q_gen_3884
<nil, nil, nil>() -> q_gen_3884
<cons, cons, cons>(q_gen_3916, q_gen_3893) -> q_gen_3893
<cons, cons, cons>(q_gen_3916, q_gen_3934) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3894) -> q_gen_3893
<cons, nil, cons>(q_gen_3895, q_gen_3933) -> q_gen_3893
<nil, nil, cons>(q_gen_3915, q_gen_3914) -> q_gen_3893
<a, a, a>() -> q_gen_3916
<a, b, a>() -> q_gen_3916
<b, a, b>() -> q_gen_3916
<b, b, b>() -> q_gen_3916
<cons, cons, cons>(q_gen_3916, q_gen_3884) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3895, q_gen_4044) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3894) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_3933) -> q_gen_3934
<nil, cons, cons>(q_gen_3998, q_gen_4011) -> q_gen_3934
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  insert -> 
{{{
Q={q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3886, q_gen_3887, q_gen_3898, q_gen_3903, q_gen_3904, q_gen_3908},
Q_f={q_gen_3881},
Delta=
{
<nil>() -> q_gen_3882
<b>() -> q_gen_3883
<a>() -> q_gen_3898
<cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3886
<cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3886
<nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3886
<a, a>() -> q_gen_3887
<b, b>() -> q_gen_3887
<a, b>() -> q_gen_3903
<b, a>() -> q_gen_3903
<cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3908
<cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3908
<nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3908
<a, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3881
<a, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3881
<a, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3881
<b, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3881
<b, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3881
<a, cons, cons>(q_gen_3887, q_gen_3886) -> q_gen_3904
<a, nil, cons>(q_gen_3883, q_gen_3882) -> q_gen_3904
<b, cons, cons>(q_gen_3887, q_gen_3908) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3886) -> q_gen_3904
<b, cons, cons>(q_gen_3903, q_gen_3908) -> q_gen_3904
<b, nil, cons>(q_gen_3898, q_gen_3882) -> q_gen_3904
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3879, q_gen_3890},
Q_f={q_gen_3879},
Delta=
{
<a, a>() -> q_gen_3879
<a, b>() -> q_gen_3879
<b, b>() -> q_gen_3879
<b, a>() -> q_gen_3890
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3878, q_gen_3918, q_gen_3935, q_gen_3936, q_gen_3937, q_gen_3938, q_gen_3948},
Q_f={q_gen_3878},
Delta=
{
<cons>(q_gen_3938, q_gen_3937) -> q_gen_3937
<nil>() -> q_gen_3937
<a>() -> q_gen_3938
<b>() -> q_gen_3938
<cons, cons>(q_gen_3918, q_gen_3878) -> q_gen_3878
<cons, cons>(q_gen_3918, q_gen_3935) -> q_gen_3878
<cons, cons>(q_gen_3948, q_gen_3935) -> q_gen_3878
<nil, nil>() -> q_gen_3878
<a, a>() -> q_gen_3918
<a, b>() -> q_gen_3918
<b, b>() -> q_gen_3918
<cons, cons>(q_gen_3918, q_gen_3936) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3878) -> q_gen_3935
<cons, cons>(q_gen_3948, q_gen_3936) -> q_gen_3936
<cons, nil>(q_gen_3938, q_gen_3937) -> q_gen_3936
<nil, cons>(q_gen_3938, q_gen_3937) -> q_gen_3936
<b, a>() -> q_gen_3948
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_3877, q_gen_3889, q_gen_3905, q_gen_3906, q_gen_3923, q_gen_3924, q_gen_3961},
Q_f={q_gen_3877},
Delta=
{
<cons, cons>(q_gen_3889, q_gen_3877) -> q_gen_3877
<cons, cons>(q_gen_3889, q_gen_3961) -> q_gen_3877
<cons, cons>(q_gen_3906, q_gen_3923) -> q_gen_3877
<cons, cons>(q_gen_3924, q_gen_3905) -> q_gen_3877
<nil, nil>() -> q_gen_3877
<a, a>() -> q_gen_3889
<b, b>() -> q_gen_3889
<cons, cons>(q_gen_3906, q_gen_3877) -> q_gen_3905
<cons, cons>(q_gen_3906, q_gen_3961) -> q_gen_3905
<cons, cons>(q_gen_3924, q_gen_3961) -> q_gen_3905
<a, b>() -> q_gen_3906
<cons, cons>(q_gen_3889, q_gen_3905) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3877) -> q_gen_3923
<cons, cons>(q_gen_3924, q_gen_3923) -> q_gen_3923
<b, a>() -> q_gen_3924
<cons, cons>(q_gen_3889, q_gen_3923) -> q_gen_3961
<cons, cons>(q_gen_3906, q_gen_3905) -> q_gen_3961
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 57
() -> insert([x, nil, cons(x, nil)]) -> 57
() -> leq([a, y]) -> 57
() -> leq([b, b]) -> 57
() -> reverse([nil, nil]) -> 57
() -> sort([nil, nil]) -> 57
(append([_ip, cons(h1, nil), _jp]) /\ reverse([t1, _ip])) -> reverse([cons(h1, t1), _jp]) -> 58
(append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]) -> 61
(insert([x, z, _to]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _to)]) -> 57
(insert([y, _yo, _zo]) /\ sort([z, _yo])) -> sort([cons(y, z), _zo]) -> 59
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 58
(leq([b, a])) -> BOT -> 58
(reverse([l, _op]) /\ sort([_op, _pp]) /\ sort([l, _np])) -> eq_eltlist([_np, _pp]) -> 59
}
Sat witness: Found: ((append([t1, l2, _dp])) -> append([cons(h1, t1), l2, cons(h1, _dp)]), {
_dp -> cons(b, cons(b, cons(a, nil)))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, cons(b, nil))
})

Total time: 63.826920
Reason for stopping: DontKnow. Stopped because: timeout