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


Learning problem is:

env: {
elt -> {a, b}  ;  elt_bin_tree -> {leaf, node}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, n2])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)])}
(plus([_xz, _yz, _aaa]) /\ plus([_xz, _yz, _zz])) -> eq_nat([_zz, _aaa])
)
(numnodes, F:
{() -> numnodes([leaf, z])
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)])}
(numnodes([_eaa, _faa]) /\ numnodes([_eaa, _gaa])) -> eq_nat([_faa, _gaa])
)
}

properties:
{(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa])}


over-approximation: {numnodes, plus}
under-approximation: {leq}

Clause system for inference is:

{
() -> leq([z, n2]) -> 0
() -> numnodes([leaf, z]) -> 0
() -> plus([n, z, n]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 0
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 0
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 0
}


Solving took 60.000590 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6836, q_gen_6837, q_gen_6838, q_gen_6841, q_gen_6842, q_gen_6867, q_gen_6868, q_gen_6874, q_gen_6887, q_gen_6899, q_gen_6900, q_gen_6901, q_gen_6988},
Q_f={},
Delta=
{
<z>() -> q_gen_6838
<s>(q_gen_6838) -> q_gen_6842
<z, z>() -> q_gen_6830
<s, s>(q_gen_6830) -> q_gen_6836
<z, s>(q_gen_6838) -> q_gen_6837
<z, s>(q_gen_6842) -> q_gen_6841
<s, s>(q_gen_6868) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6868
<s, s>(q_gen_6867) -> q_gen_6874
<s, s>(q_gen_6874) -> q_gen_6887
<s, s>(q_gen_6900) -> q_gen_6899
<s, s>(q_gen_6901) -> q_gen_6900
<s, z>(q_gen_6842) -> q_gen_6901
<s, s>(q_gen_6899) -> q_gen_6988
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6833, q_gen_6834, q_gen_6835, q_gen_6847, q_gen_6848, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6860, q_gen_6861, q_gen_6862, q_gen_6863, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6869, q_gen_6871, q_gen_6872, q_gen_6873, q_gen_6875, q_gen_6876, q_gen_6878, q_gen_6879, q_gen_6880, q_gen_6881, q_gen_6882, q_gen_6883, q_gen_6884, q_gen_6885, q_gen_6886, q_gen_6888, q_gen_6889, q_gen_6890, q_gen_6891, q_gen_6892, q_gen_6893, q_gen_6894, q_gen_6895, q_gen_6896, q_gen_6897, q_gen_6898, q_gen_6902, q_gen_6903, q_gen_6904, q_gen_6905, q_gen_6906, q_gen_6907, q_gen_6908, q_gen_6909, q_gen_6910, q_gen_6911, q_gen_6912, q_gen_6913, q_gen_6914, q_gen_6915, q_gen_6916, q_gen_6917, q_gen_6920, q_gen_6921, q_gen_6922, q_gen_6923, q_gen_6924, q_gen_6925, q_gen_6926, q_gen_6927, q_gen_6928, q_gen_6929, q_gen_6930, q_gen_6931, q_gen_6932, q_gen_6933, q_gen_6934, q_gen_6935, q_gen_6936, q_gen_6937, q_gen_6938, q_gen_6939, q_gen_6940, q_gen_6941, q_gen_6942, q_gen_6943, q_gen_6944, q_gen_6945, q_gen_6946, q_gen_6947, q_gen_6948, q_gen_6949, q_gen_6950, q_gen_6951, q_gen_6952, q_gen_6953, q_gen_6954, q_gen_6955, q_gen_6956, q_gen_6957, q_gen_6958, q_gen_6959, q_gen_6960, q_gen_6961, q_gen_6962, q_gen_6963, q_gen_6964, q_gen_6965, q_gen_6966, q_gen_6967, q_gen_6968, q_gen_6969, q_gen_6970, q_gen_6971, q_gen_6972, q_gen_6973, q_gen_6974, q_gen_6975, q_gen_6976, q_gen_6977, q_gen_6978, q_gen_6979, q_gen_6981, q_gen_6982, q_gen_6983, q_gen_6984, q_gen_6985, q_gen_6986, q_gen_6987, q_gen_6989, q_gen_6990, q_gen_6991, q_gen_6992, q_gen_6993, q_gen_6994, q_gen_6995, q_gen_6996, q_gen_6997, q_gen_6998, q_gen_6999, q_gen_7000, q_gen_7001, q_gen_7002, q_gen_7003, q_gen_7004, q_gen_7005, q_gen_7006, q_gen_7007, q_gen_7008, q_gen_7009, q_gen_7010, q_gen_7011, q_gen_7012, q_gen_7013, q_gen_7014, q_gen_7015, q_gen_7016, q_gen_7017, q_gen_7018, q_gen_7019, q_gen_7020, q_gen_7021, q_gen_7022, q_gen_7023, q_gen_7024, q_gen_7025, q_gen_7026, q_gen_7027, q_gen_7028},
Q_f={},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6879
<b>() -> q_gen_6880
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6882
<s>(q_gen_6862) -> q_gen_6884
<node>(q_gen_6880, q_gen_6882, q_gen_6834) -> q_gen_6886
<node>(q_gen_6880, q_gen_6882, q_gen_6882) -> q_gen_6890
<node>(q_gen_6880, q_gen_6890, q_gen_6890) -> q_gen_6893
<node>(q_gen_6865, q_gen_6882, q_gen_6834) -> q_gen_6898
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6904
<node>(q_gen_6880, q_gen_6904, q_gen_6904) -> q_gen_6906
<node>(q_gen_6880, q_gen_6893, q_gen_6893) -> q_gen_6908
<node>(q_gen_6880, q_gen_6912, q_gen_6912) -> q_gen_6911
<node>(q_gen_6865, q_gen_6834, q_gen_6882) -> q_gen_6912
<node>(q_gen_6865, q_gen_6834, q_gen_6911) -> q_gen_6914
<node>(q_gen_6880, q_gen_6834, q_gen_6882) -> q_gen_6917
<node>(q_gen_6865, q_gen_6917, q_gen_6834) -> q_gen_6921
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6923
<node>(q_gen_6880, q_gen_6864, q_gen_6923) -> q_gen_6925
<node>(q_gen_6880, q_gen_6834, q_gen_6917) -> q_gen_6927
<node>(q_gen_6865, q_gen_6890, q_gen_6927) -> q_gen_6929
<node>(q_gen_6880, q_gen_6912, q_gen_6882) -> q_gen_6931
<node>(q_gen_6880, q_gen_6890, q_gen_6931) -> q_gen_6933
<node>(q_gen_6865, q_gen_6937, q_gen_6882) -> q_gen_6936
<node>(q_gen_6880, q_gen_6938, q_gen_6882) -> q_gen_6937
<node>(q_gen_6865, q_gen_6882, q_gen_6917) -> q_gen_6938
<node>(q_gen_6880, q_gen_6882, q_gen_6944) -> q_gen_6943
<node>(q_gen_6880, q_gen_6917, q_gen_6834) -> q_gen_6944
<node>(q_gen_6865, q_gen_6882, q_gen_6882) -> q_gen_6945
<node>(q_gen_6865, q_gen_6945, q_gen_6943) -> q_gen_6947
<node>(q_gen_6880, q_gen_6834, q_gen_6950) -> q_gen_6949
<node>(q_gen_6880, q_gen_6951, q_gen_6898) -> q_gen_6950
<node>(q_gen_6880, q_gen_6952, q_gen_6834) -> q_gen_6951
<node>(q_gen_6880, q_gen_6917, q_gen_6890) -> q_gen_6952
<node>(q_gen_6865, q_gen_6890, q_gen_6949) -> q_gen_6954
<node>(q_gen_6865, q_gen_6882, q_gen_6945) -> q_gen_6956
<node>(q_gen_6865, q_gen_6921, q_gen_6834) -> q_gen_6960
<node>(q_gen_6880, q_gen_6886, q_gen_6882) -> q_gen_6962
<node>(q_gen_6865, q_gen_6886, q_gen_6962) -> q_gen_6964
<node>(q_gen_6865, q_gen_6927, q_gen_6834) -> q_gen_6972
<node>(q_gen_6880, q_gen_6834, q_gen_6927) -> q_gen_6976
<node>(q_gen_6880, q_gen_6834, q_gen_6904) -> q_gen_6979
<node>(q_gen_6865, q_gen_6882, q_gen_6979) -> q_gen_6982
<s>(q_gen_6884) -> q_gen_6985
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6987
<node>(q_gen_6865, q_gen_6898, q_gen_6864) -> q_gen_6990
<node>(q_gen_6865, q_gen_6990, q_gen_6864) -> q_gen_6992
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6995
<node>(q_gen_6865, q_gen_6834, q_gen_6998) -> q_gen_6997
<node>(q_gen_6865, q_gen_6864, q_gen_6987) -> q_gen_6998
<node>(q_gen_6865, q_gen_6997, q_gen_6864) -> q_gen_7000
<node>(q_gen_6880, q_gen_6834, q_gen_6879) -> q_gen_7002
<node>(q_gen_6880, q_gen_7004, q_gen_6834) -> q_gen_7003
<node>(q_gen_6865, q_gen_6834, q_gen_6904) -> q_gen_7004
<node>(q_gen_6880, q_gen_7003, q_gen_7002) -> q_gen_7006
<node>(q_gen_6865, q_gen_7009, q_gen_6912) -> q_gen_7008
<node>(q_gen_6865, q_gen_6834, q_gen_7010) -> q_gen_7009
<node>(q_gen_6865, q_gen_6912, q_gen_6834) -> q_gen_7010
<node>(q_gen_6880, q_gen_6834, q_gen_7012) -> q_gen_7011
<node>(q_gen_6880, q_gen_7010, q_gen_6834) -> q_gen_7012
<node>(q_gen_6865, q_gen_7011, q_gen_7008) -> q_gen_7014
<node>(q_gen_6865, q_gen_7018, q_gen_7017) -> q_gen_7016
<node>(q_gen_6880, q_gen_6834, q_gen_7018) -> q_gen_7017
<node>(q_gen_6880, q_gen_6864, q_gen_6904) -> q_gen_7018
<node>(q_gen_6880, q_gen_7017, q_gen_6879) -> q_gen_7019
<node>(q_gen_6865, q_gen_7019, q_gen_7016) -> q_gen_7021
<node>(q_gen_6865, q_gen_6834, q_gen_6917) -> q_gen_7023
<node>(q_gen_6865, q_gen_7025, q_gen_6834) -> q_gen_7024
<node>(q_gen_6865, q_gen_7026, q_gen_6882) -> q_gen_7025
<node>(q_gen_6880, q_gen_7023, q_gen_6834) -> q_gen_7026
<node>(q_gen_6880, q_gen_7024, q_gen_7023) -> q_gen_7028
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6833
<b, z>() -> q_gen_6835
<node, s>(q_gen_6848, q_gen_6834, q_gen_6834) -> q_gen_6847
<a, z>() -> q_gen_6848
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
<node, s>(q_gen_6861, q_gen_6834, q_gen_6834) -> q_gen_6860
<b, s>(q_gen_6862) -> q_gen_6861
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6863
<node, s>(q_gen_6848, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6869
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6871
<a, s>(q_gen_6862) -> q_gen_6872
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6873
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6875
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6876
<node, s>(q_gen_6872, q_gen_6834, q_gen_6879) -> q_gen_6878
<node, s>(q_gen_6883, q_gen_6882, q_gen_6834) -> q_gen_6881
<b, s>(q_gen_6884) -> q_gen_6883
<node, s>(q_gen_6861, q_gen_6886, q_gen_6834) -> q_gen_6885
<node, s>(q_gen_6835, q_gen_6882, q_gen_6882) -> q_gen_6888
<node, s>(q_gen_6859, q_gen_6834, q_gen_6890) -> q_gen_6889
<node, s>(q_gen_6861, q_gen_6890, q_gen_6890) -> q_gen_6891
<node, s>(q_gen_6852, q_gen_6893, q_gen_6834) -> q_gen_6892
<node, s>(q_gen_6859, q_gen_6882, q_gen_6834) -> q_gen_6894
<node, s>(q_gen_6896, q_gen_6882, q_gen_6834) -> q_gen_6895
<a, s>(q_gen_6884) -> q_gen_6896
<node, s>(q_gen_6852, q_gen_6898, q_gen_6834) -> q_gen_6897
<node, s>(q_gen_6861, q_gen_6898, q_gen_6834) -> q_gen_6902
<node, s>(q_gen_6861, q_gen_6904, q_gen_6904) -> q_gen_6903
<node, s>(q_gen_6852, q_gen_6906, q_gen_6834) -> q_gen_6905
<node, s>(q_gen_6872, q_gen_6908, q_gen_6834) -> q_gen_6907
<node, s>(q_gen_6883, q_gen_6893, q_gen_6893) -> q_gen_6909
<node, s>(q_gen_6848, q_gen_6834, q_gen_6911) -> q_gen_6910
<node, s>(q_gen_6859, q_gen_6914, q_gen_6834) -> q_gen_6913
<node, s>(q_gen_6872, q_gen_6882, q_gen_6834) -> q_gen_6915
<node, s>(q_gen_6872, q_gen_6917, q_gen_6834) -> q_gen_6916
<node, s>(q_gen_6896, q_gen_6921, q_gen_6834) -> q_gen_6920
<node, s>(q_gen_6883, q_gen_6864, q_gen_6923) -> q_gen_6922
<node, s>(q_gen_6861, q_gen_6925, q_gen_6834) -> q_gen_6924
<node, s>(q_gen_6859, q_gen_6890, q_gen_6927) -> q_gen_6926
<node, s>(q_gen_6872, q_gen_6929, q_gen_6834) -> q_gen_6928
<node, s>(q_gen_6861, q_gen_6890, q_gen_6931) -> q_gen_6930
<node, s>(q_gen_6852, q_gen_6933, q_gen_6834) -> q_gen_6932
<node, s>(q_gen_6872, q_gen_6898, q_gen_6834) -> q_gen_6934
<node, s>(q_gen_6848, q_gen_6936, q_gen_6834) -> q_gen_6935
<node, s>(q_gen_6872, q_gen_6937, q_gen_6882) -> q_gen_6939
<node, s>(q_gen_6859, q_gen_6834, q_gen_6882) -> q_gen_6940
<node, s>(q_gen_6861, q_gen_6834, q_gen_6912) -> q_gen_6941
<node, s>(q_gen_6872, q_gen_6945, q_gen_6943) -> q_gen_6942
<node, s>(q_gen_6852, q_gen_6947, q_gen_6834) -> q_gen_6946
<node, s>(q_gen_6848, q_gen_6890, q_gen_6949) -> q_gen_6948
<node, s>(q_gen_6852, q_gen_6834, q_gen_6954) -> q_gen_6953
<node, s>(q_gen_6872, q_gen_6956, q_gen_6834) -> q_gen_6955
<node, s>(q_gen_6896, q_gen_6882, q_gen_6945) -> q_gen_6957
<node, s>(q_gen_6872, q_gen_6921, q_gen_6834) -> q_gen_6958
<node, s>(q_gen_6883, q_gen_6960, q_gen_6834) -> q_gen_6959
<node, s>(q_gen_6896, q_gen_6886, q_gen_6962) -> q_gen_6961
<node, s>(q_gen_6861, q_gen_6964, q_gen_6834) -> q_gen_6963
<node, s>(q_gen_6872, q_gen_6834, q_gen_6882) -> q_gen_6965
<node, s>(q_gen_6883, q_gen_6912, q_gen_6834) -> q_gen_6966
<node, s>(q_gen_6896, q_gen_6834, q_gen_6882) -> q_gen_6967
<node, s>(q_gen_6872, q_gen_6912, q_gen_6834) -> q_gen_6968
<node, s>(q_gen_6835, q_gen_6917, q_gen_6834) -> q_gen_6969
<node, s>(q_gen_6861, q_gen_6834, q_gen_6944) -> q_gen_6970
<node, s>(q_gen_6872, q_gen_6972, q_gen_6834) -> q_gen_6971
<node, s>(q_gen_6896, q_gen_6927, q_gen_6834) -> q_gen_6973
<node, s>(q_gen_6852, q_gen_6834, q_gen_6927) -> q_gen_6974
<node, s>(q_gen_6872, q_gen_6834, q_gen_6976) -> q_gen_6975
<node, s>(q_gen_6896, q_gen_6917, q_gen_6834) -> q_gen_6977
<node, s>(q_gen_6872, q_gen_6882, q_gen_6979) -> q_gen_6978
<node, s>(q_gen_6883, q_gen_6834, q_gen_6982) -> q_gen_6981
<node, s>(q_gen_6984, q_gen_6864, q_gen_6864) -> q_gen_6983
<b, s>(q_gen_6985) -> q_gen_6984
<node, s>(q_gen_6861, q_gen_6987, q_gen_6834) -> q_gen_6986
<node, s>(q_gen_6872, q_gen_6990, q_gen_6864) -> q_gen_6989
<node, s>(q_gen_6883, q_gen_6992, q_gen_6834) -> q_gen_6991
<node, s>(q_gen_6883, q_gen_6834, q_gen_6864) -> q_gen_6993
<node, s>(q_gen_6861, q_gen_6995, q_gen_6834) -> q_gen_6994
<node, s>(q_gen_6848, q_gen_6997, q_gen_6864) -> q_gen_6996
<node, s>(q_gen_6852, q_gen_7000, q_gen_6834) -> q_gen_6999
<node, s>(q_gen_6852, q_gen_7003, q_gen_7002) -> q_gen_7001
<node, s>(q_gen_6835, q_gen_7006, q_gen_6834) -> q_gen_7005
<node, s>(q_gen_6848, q_gen_7011, q_gen_7008) -> q_gen_7007
<node, s>(q_gen_6852, q_gen_6834, q_gen_7014) -> q_gen_7013
<node, s>(q_gen_6872, q_gen_7019, q_gen_7016) -> q_gen_7015
<node, s>(q_gen_6852, q_gen_7021, q_gen_6834) -> q_gen_7020
<node, s>(q_gen_6835, q_gen_7024, q_gen_7023) -> q_gen_7022
<node, s>(q_gen_6852, q_gen_6834, q_gen_7028) -> q_gen_7027
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6831, q_gen_6832, q_gen_6839, q_gen_6840, q_gen_6843, q_gen_6844, q_gen_6845, q_gen_6846, q_gen_6849, q_gen_6850, q_gen_6854, q_gen_6855, q_gen_6856, q_gen_6857, q_gen_6870, q_gen_6877, q_gen_6918, q_gen_6919, q_gen_6980},
Q_f={},
Delta=
{
<z>() -> q_gen_6846
<s>(q_gen_6846) -> q_gen_6857
<z, z>() -> q_gen_6832
<s, s>(q_gen_6832) -> q_gen_6840
<z, s>(q_gen_6846) -> q_gen_6850
<s, s>(q_gen_6840) -> q_gen_6919
<z, z, z>() -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6831
<s, z, s>(q_gen_6840) -> q_gen_6839
<s, z, s>(q_gen_6832) -> q_gen_6843
<s, s, s>(q_gen_6845) -> q_gen_6844
<z, z, s>(q_gen_6846) -> q_gen_6845
<z, s, s>(q_gen_6850) -> q_gen_6849
<s, z, s>(q_gen_6850) -> q_gen_6854
<s, s, s>(q_gen_6856) -> q_gen_6855
<z, z, s>(q_gen_6857) -> q_gen_6856
<s, s, s>(q_gen_6854) -> q_gen_6870
<z, s, s>(q_gen_6840) -> q_gen_6877
<s, z, s>(q_gen_6919) -> q_gen_6918
<z, s, s>(q_gen_6919) -> q_gen_6980
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.008798 s (model generation: 0.008533,  model checking: 0.000265):

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

}

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

}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={},
Q_f={},
Delta=
{

}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 0
() -> numnodes([leaf, z]) -> 0
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 1
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 1
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.008575 s (model generation: 0.008504,  model checking: 0.000071):

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

}

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

}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828},
Q_f={q_gen_6828},
Delta=
{
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 0
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 1
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 1
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 1
}
Sat witness: Found: (() -> numnodes([leaf, z]), {

})

-------------------------------------------
Step 2, which took 0.008085 s (model generation: 0.008027,  model checking: 0.000058):

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829},
Q_f={q_gen_6829},
Delta=
{
<leaf, z>() -> q_gen_6829
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828},
Q_f={q_gen_6828},
Delta=
{
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 1
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 1
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 1
}
Sat witness: Found: (() -> leq([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 3, which took 0.008904 s (model generation: 0.008804,  model checking: 0.000100):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830},
Q_f={q_gen_6830},
Delta=
{
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829},
Q_f={q_gen_6829},
Delta=
{
<leaf, z>() -> q_gen_6829
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828},
Q_f={q_gen_6828},
Delta=
{
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 1
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 1
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]), {
_wz -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 4, which took 0.010922 s (model generation: 0.010194,  model checking: 0.000728):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830},
Q_f={q_gen_6830},
Delta=
{
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829},
Q_f={q_gen_6829},
Delta=
{
<leaf, z>() -> q_gen_6829
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832},
Q_f={q_gen_6828},
Delta=
{
<z, z>() -> q_gen_6832
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 4
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 2
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 4
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> z  ;  _daa -> z  ;  e -> b  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 5, which took 0.010117 s (model generation: 0.010028,  model checking: 0.000089):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830},
Q_f={q_gen_6830},
Delta=
{
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832},
Q_f={q_gen_6828},
Delta=
{
<z, z>() -> q_gen_6832
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 4
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 2
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 4
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 6, which took 0.008458 s (model generation: 0.008343,  model checking: 0.000115):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830},
Q_f={q_gen_6830},
Delta=
{
<s, s>(q_gen_6830) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832},
Q_f={q_gen_6828},
Delta=
{
<z, z>() -> q_gen_6832
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 4
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 5
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 4
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> z  ;  _iaa -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 7, which took 0.015996 s (model generation: 0.015801,  model checking: 0.000195):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832},
Q_f={q_gen_6828},
Delta=
{
<z, z>() -> q_gen_6832
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 4
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 5
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 8, which took 0.009361 s (model generation: 0.008704,  model checking: 0.000657):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832},
Q_f={q_gen_6828},
Delta=
{
<s, s>(q_gen_6832) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 4
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 4
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 5
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 4
}
Sat witness: Found: (() -> leq([z, n2]), {
n2 -> s(s(z))
})

-------------------------------------------
Step 9, which took 0.009137 s (model generation: 0.008933,  model checking: 0.000204):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832},
Q_f={q_gen_6828},
Delta=
{
<s, s>(q_gen_6832) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 4
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 4
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 5
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]), {
_wz -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 10, which took 0.011009 s (model generation: 0.009863,  model checking: 0.001146):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 4
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 7
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 5
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 7
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> z  ;  _daa -> z  ;  e -> a  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 11, which took 0.011323 s (model generation: 0.010795,  model checking: 0.000528):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 7
() -> numnodes([leaf, z]) -> 5
() -> plus([n, z, n]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 7
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 6
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 10
}
Sat witness: Found: ((plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]), {
_wz -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 12, which took 0.015185 s (model generation: 0.014107,  model checking: 0.001078):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 7
() -> numnodes([leaf, z]) -> 6
() -> plus([n, z, n]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 6
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 10
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 7
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 10
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> z  ;  _daa -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 13, which took 0.012097 s (model generation: 0.011158,  model checking: 0.000939):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 8
() -> numnodes([leaf, z]) -> 7
() -> plus([n, z, n]) -> 8
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 7
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 10
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 8
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 13
}
Sat witness: Found: ((plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]), {
_wz -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 14, which took 0.015222 s (model generation: 0.013629,  model checking: 0.001593):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 9
() -> numnodes([leaf, z]) -> 8
() -> plus([n, z, n]) -> 9
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 8
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 13
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 9
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 13
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> z  ;  _daa -> s(z)  ;  e -> a  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 15, which took 0.016252 s (model generation: 0.014448,  model checking: 0.001804):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 10
() -> numnodes([leaf, z]) -> 9
() -> plus([n, z, n]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9
(leq([s(nn1), z])) -> BOT -> 9
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 16
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 10
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 14
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> z  ;  _daa -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 16, which took 0.024060 s (model generation: 0.021942,  model checking: 0.002118):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 11
() -> numnodes([leaf, z]) -> 10
() -> plus([n, z, n]) -> 11
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 19
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 11
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 15
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(z)  ;  _daa -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, leaf, leaf)
})

-------------------------------------------
Step 17, which took 0.018090 s (model generation: 0.016709,  model checking: 0.001381):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6865},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 11
() -> numnodes([leaf, z]) -> 11
() -> plus([n, z, n]) -> 11
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 19
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 14
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 15
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(z))  ;  _iaa -> s(z)  ;  e -> a  ;  t1 -> node(a, leaf, leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 18, which took 0.019252 s (model generation: 0.019218,  model checking: 0.000034):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<s, z>(q_gen_6838) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6865},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 11
() -> numnodes([leaf, z]) -> 11
() -> plus([n, z, n]) -> 11
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 14
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 19
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 14
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 15
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 19, which took 0.018889 s (model generation: 0.018798,  model checking: 0.000091):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6868},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<s, s>(q_gen_6868) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, z>(q_gen_6838) -> q_gen_6868
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6865},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 11
() -> numnodes([leaf, z]) -> 11
() -> plus([n, z, n]) -> 11
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 19
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 14
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 15
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 20, which took 0.021030 s (model generation: 0.018507,  model checking: 0.002523):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6864, q_gen_6865, q_gen_6866},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 12
() -> numnodes([leaf, z]) -> 12
() -> plus([n, z, n]) -> 12
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 15
(leq([s(nn1), z])) -> BOT -> 15
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 22
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 15
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 16
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(z)  ;  _caa -> z  ;  _daa -> s(z)  ;  e -> b  ;  t1 -> node(a, leaf, leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 21, which took 0.021108 s (model generation: 0.019874,  model checking: 0.001234):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6865},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 13
() -> numnodes([leaf, z]) -> 13
() -> plus([n, z, n]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 16
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 22
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 16
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 19
}
Sat witness: Found: ((plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]), {
_wz -> s(s(z))  ;  mm -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 22, which took 0.021945 s (model generation: 0.020365,  model checking: 0.001580):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6864, q_gen_6865, q_gen_6866},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 14
() -> numnodes([leaf, z]) -> 14
() -> plus([n, z, n]) -> 14
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 16
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 22
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 19
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 19
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(s(z))  ;  e -> a  ;  t1 -> node(a, leaf, leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 23, which took 0.024681 s (model generation: 0.023135,  model checking: 0.001546):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6848, q_gen_6853, q_gen_6864, q_gen_6865, q_gen_6866},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6834, q_gen_6834) -> q_gen_6829
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6848
<a, z>() -> q_gen_6848
<node, s>(q_gen_6848, q_gen_6864, q_gen_6834) -> q_gen_6866
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 15
() -> numnodes([leaf, z]) -> 15
() -> plus([n, z, n]) -> 15
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 22
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 22
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 20
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(z))  ;  _iaa -> s(z)  ;  e -> b  ;  t1 -> node(a, leaf, leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 24, which took 0.025540 s (model generation: 0.023910,  model checking: 0.001630):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6864, q_gen_6865, q_gen_6866},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 16
() -> numnodes([leaf, z]) -> 16
() -> plus([n, z, n]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 18
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 22
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 25
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 21
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(s(z))  ;  e -> b  ;  t1 -> node(a, leaf, leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 25, which took 0.025891 s (model generation: 0.024179,  model checking: 0.001712):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6865},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 17
() -> numnodes([leaf, z]) -> 17
() -> plus([n, z, n]) -> 17
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 19
(leq([s(nn1), z])) -> BOT -> 19
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 25
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 25
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 22
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(z)  ;  _daa -> s(z)  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(a, leaf, leaf)
})

-------------------------------------------
Step 26, which took 0.058152 s (model generation: 0.032389,  model checking: 0.025763):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6864, q_gen_6865},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 18
() -> numnodes([leaf, z]) -> 18
() -> plus([n, z, n]) -> 18
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 18
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 28
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 26
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 23
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(s(z))  ;  _daa -> s(s(z))  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(b, node(a, leaf, leaf), leaf)
})

-------------------------------------------
Step 27, which took 0.033353 s (model generation: 0.033170,  model checking: 0.000183):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6864, q_gen_6865, q_gen_6866},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6840, q_gen_6843, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s>(q_gen_6832) -> q_gen_6840
<s, s, s>(q_gen_6843) -> q_gen_6828
<s, z, s>(q_gen_6840) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<s, s, s>(q_gen_6828) -> q_gen_6843
<s, z, s>(q_gen_6832) -> q_gen_6843
<z, s, s>(q_gen_6840) -> q_gen_6843
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 18
() -> numnodes([leaf, z]) -> 18
() -> plus([n, z, n]) -> 21
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 19
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 28
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 26
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 23
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(z)
})

-------------------------------------------
Step 28, which took 0.033881 s (model generation: 0.033307,  model checking: 0.000574):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867, q_gen_6868},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6868) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6868
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6864, q_gen_6865, q_gen_6866},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 19
() -> numnodes([leaf, z]) -> 19
() -> plus([n, z, n]) -> 21
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 21
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 28
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 26
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 23
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 29, which took 0.032656 s (model generation: 0.030772,  model checking: 0.001884):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6864, q_gen_6865},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 20
() -> numnodes([leaf, z]) -> 20
() -> plus([n, z, n]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 24
(leq([s(nn1), z])) -> BOT -> 22
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 28
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 29
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 24
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> b  ;  t1 -> node(b, node(b, leaf, leaf), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 30, which took 0.040516 s (model generation: 0.034801,  model checking: 0.005715):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6864, q_gen_6865, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 21
() -> numnodes([leaf, z]) -> 21
() -> plus([n, z, n]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 25
(leq([s(nn1), z])) -> BOT -> 23
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 31
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 29
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 25
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(z)  ;  _daa -> s(z)  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(b, node(b, leaf, leaf), node(b, leaf, leaf))
})

-------------------------------------------
Step 31, which took 0.050667 s (model generation: 0.042158,  model checking: 0.008509):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6872},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6834, q_gen_6864) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6866
<a, s>(q_gen_6862) -> q_gen_6872
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 22
() -> numnodes([leaf, z]) -> 22
() -> plus([n, z, n]) -> 24
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 24
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 31
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 32
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 26
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(s(z))  ;  e -> b  ;  t1 -> node(b, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, node(b, leaf, leaf), node(b, leaf, leaf)))  ;  t2 -> leaf
})

-------------------------------------------
Step 32, which took 0.070868 s (model generation: 0.046420,  model checking: 0.024448):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 23
() -> numnodes([leaf, z]) -> 23
() -> plus([n, z, n]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 24
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 27
(leq([s(nn1), z])) -> BOT -> 25
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 34
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 32
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 27
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(z)  ;  _caa -> z  ;  _daa -> s(z)  ;  e -> a  ;  t1 -> node(b, leaf, leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 33, which took 0.054356 s (model generation: 0.049561,  model checking: 0.004795):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6872},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6862) -> q_gen_6853
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6834, q_gen_6864) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6866
<a, s>(q_gen_6862) -> q_gen_6872
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 24
() -> numnodes([leaf, z]) -> 24
() -> plus([n, z, n]) -> 26
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 26
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 34
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 35
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 28
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(z))  ;  e -> b  ;  t1 -> node(a, node(b, leaf, leaf), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 34, which took 0.087418 s (model generation: 0.059200,  model checking: 0.028218):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<s>(q_gen_6853) -> q_gen_6853
<z>() -> q_gen_6853
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 25
() -> numnodes([leaf, z]) -> 25
() -> plus([n, z, n]) -> 27
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 27
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 37
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 35
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 29
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(s(z))  ;  _caa -> z  ;  _daa -> s(s(z))  ;  e -> b  ;  t1 -> node(a, node(b, leaf, leaf), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 35, which took 0.083551 s (model generation: 0.066322,  model checking: 0.017229):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6872, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6834, q_gen_6864) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6834) -> q_gen_6866
<a, s>(q_gen_6862) -> q_gen_6872
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 26
() -> numnodes([leaf, z]) -> 26
() -> plus([n, z, n]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 30
(leq([s(nn1), z])) -> BOT -> 28
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 37
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 38
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 30
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(s(z))  ;  e -> b  ;  t1 -> node(b, node(a, node(a, leaf, leaf), leaf), node(a, node(a, leaf, leaf), leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 36, which took 0.089992 s (model generation: 0.079574,  model checking: 0.010418):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6872, q_gen_6884},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<s>(q_gen_6862) -> q_gen_6884
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6834, q_gen_6864) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6884) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6834) -> q_gen_6866
<a, s>(q_gen_6862) -> q_gen_6872
<a, s>(q_gen_6884) -> q_gen_6872
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6828
<z, z, z>() -> q_gen_6828
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 27
() -> numnodes([leaf, z]) -> 27
() -> plus([n, z, n]) -> 29
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 29
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 40
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 38
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 31
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> z  ;  _daa -> s(s(z))  ;  e -> a  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 37, which took 0.098122 s (model generation: 0.081368,  model checking: 0.016754):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 28
() -> numnodes([leaf, z]) -> 28
() -> plus([n, z, n]) -> 30
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 30
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 40
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 41
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 32
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> a  ;  t1 -> node(b, node(b, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, node(b, leaf, leaf), node(b, leaf, leaf))), node(b, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, node(b, leaf, leaf), node(b, leaf, leaf))))  ;  t2 -> leaf
})

-------------------------------------------
Step 38, which took 0.155441 s (model generation: 0.096284,  model checking: 0.059157):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6834
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 29
() -> numnodes([leaf, z]) -> 29
() -> plus([n, z, n]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 33
(leq([s(nn1), z])) -> BOT -> 31
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 43
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 41
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 33
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(z)  ;  _caa -> z  ;  _daa -> s(z)  ;  e -> a  ;  t1 -> node(a, leaf, node(b, node(a, leaf, node(b, leaf, leaf)), node(a, leaf, node(b, leaf, leaf))))  ;  t2 -> leaf
})

-------------------------------------------
Step 39, which took 0.122195 s (model generation: 0.102353,  model checking: 0.019842):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6884},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<s>(q_gen_6862) -> q_gen_6884
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6884) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, s>(q_gen_6884) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 30
() -> numnodes([leaf, z]) -> 30
() -> plus([n, z, n]) -> 32
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 31
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 34
(leq([s(nn1), z])) -> BOT -> 32
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 43
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 44
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 34
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(s(z))  ;  e -> b  ;  t1 -> node(a, node(b, leaf, leaf), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 40, which took 0.151837 s (model generation: 0.115459,  model checking: 0.036378):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 31
() -> numnodes([leaf, z]) -> 31
() -> plus([n, z, n]) -> 33
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 33
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 46
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 44
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 35
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(s(s(z)))  ;  _caa -> z  ;  _daa -> s(s(s(z)))  ;  e -> a  ;  t1 -> node(a, node(b, leaf, node(b, leaf, leaf)), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 41, which took 0.170851 s (model generation: 0.141223,  model checking: 0.029628):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 32
() -> numnodes([leaf, z]) -> 32
() -> plus([n, z, n]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 34
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 46
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 47
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 36
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> b  ;  t1 -> node(b, node(a, leaf, leaf), node(a, leaf, node(a, leaf, leaf)))  ;  t2 -> leaf
})

-------------------------------------------
Step 42, which took 0.229561 s (model generation: 0.147401,  model checking: 0.082160):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 33
() -> numnodes([leaf, z]) -> 33
() -> plus([n, z, n]) -> 35
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 37
(leq([s(nn1), z])) -> BOT -> 35
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 49
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 47
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 37
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(s(z))  ;  _caa -> z  ;  _daa -> s(s(z))  ;  e -> a  ;  t1 -> node(a, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, leaf, node(b, leaf, node(b, leaf, leaf))))  ;  t2 -> leaf
})

-------------------------------------------
Step 43, which took 0.240595 s (model generation: 0.171808,  model checking: 0.068787):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6864) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 34
() -> numnodes([leaf, z]) -> 34
() -> plus([n, z, n]) -> 36
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 36
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 49
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 50
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 38
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(s(z))  ;  e -> b  ;  t1 -> node(b, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, node(a, leaf, node(b, leaf, leaf)), node(b, leaf, leaf)))  ;  t2 -> leaf
})

-------------------------------------------
Step 44, which took 0.351734 s (model generation: 0.208349,  model checking: 0.143385):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<a, s>(q_gen_6853) -> q_gen_6852
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 35
() -> numnodes([leaf, z]) -> 35
() -> plus([n, z, n]) -> 37
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 39
(leq([s(nn1), z])) -> BOT -> 37
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 52
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 50
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 39
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(s(z))  ;  _caa -> z  ;  _daa -> s(s(z))  ;  e -> a  ;  t1 -> node(a, node(b, leaf, leaf), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 45, which took 0.306239 s (model generation: 0.214602,  model checking: 0.091637):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6859, q_gen_6879, q_gen_6864) -> q_gen_6851
<b, s>(q_gen_6853) -> q_gen_6852
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 36
() -> numnodes([leaf, z]) -> 36
() -> plus([n, z, n]) -> 38
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 37
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 40
(leq([s(nn1), z])) -> BOT -> 38
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 52
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 53
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 40
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(z)  ;  e -> a  ;  t1 -> node(a, node(b, node(a, node(b, leaf, leaf), node(b, leaf, node(b, leaf, leaf))), node(b, leaf, leaf)), node(b, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 46, which took 0.576053 s (model generation: 0.248795,  model checking: 0.327258):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6848, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, z>() -> q_gen_6848
<b, s>(q_gen_6862) -> q_gen_6848
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6834, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6864, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6864) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 37
() -> numnodes([leaf, z]) -> 37
() -> plus([n, z, n]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 41
(leq([s(nn1), z])) -> BOT -> 39
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 55
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 53
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 41
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(s(z))  ;  _daa -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, leaf, node(b, leaf, leaf))
})

-------------------------------------------
Step 47, which took 0.616507 s (model generation: 0.354668,  model checking: 0.261839):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6834, q_gen_6879) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6864) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6879) -> q_gen_6879
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6879) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 38
() -> numnodes([leaf, z]) -> 38
() -> plus([n, z, n]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 39
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 42
(leq([s(nn1), z])) -> BOT -> 40
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 55
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 56
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 42
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(s(z))  ;  e -> b  ;  t1 -> node(a, node(a, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, node(b, leaf, leaf), node(b, node(b, leaf, node(b, leaf, leaf)), leaf)))  ;  t2 -> leaf
})

-------------------------------------------
Step 48, which took 0.344846 s (model generation: 0.344180,  model checking: 0.000666):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6834
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6840, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s>(q_gen_6832) -> q_gen_6840
<s, s>(q_gen_6840) -> q_gen_6840
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<s, z, s>(q_gen_6840) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, s, s>(q_gen_6840) -> q_gen_6845
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 39
() -> numnodes([leaf, z]) -> 39
() -> plus([n, z, n]) -> 41
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 40
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 42
(leq([s(nn1), z])) -> BOT -> 41
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 55
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 56
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 45
}
Sat witness: Found: ((plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]), {
_wz -> s(z)  ;  mm -> s(z)  ;  n -> z
})

-------------------------------------------
Step 49, which took 0.502426 s (model generation: 0.310797,  model checking: 0.191629):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6848, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6864) -> q_gen_6829
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, z>() -> q_gen_6848
<b, s>(q_gen_6853) -> q_gen_6848
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6834, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 40
() -> numnodes([leaf, z]) -> 40
() -> plus([n, z, n]) -> 42
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 41
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 43
(leq([s(nn1), z])) -> BOT -> 42
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 58
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 56
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 46
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(z)  ;  _daa -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, leaf, node(b, node(b, node(b, node(b, leaf, node(b, leaf, leaf)), node(b, node(b, leaf, leaf), node(b, leaf, leaf))), leaf), node(a, node(b, leaf, leaf), leaf))))
})

-------------------------------------------
Step 50, which took 0.588438 s (model generation: 0.519556,  model checking: 0.068882):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880, q_gen_6904},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6904, q_gen_6904) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<node>(q_gen_6865, q_gen_6834, q_gen_6904) -> q_gen_6904
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6904
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6904
<node>(q_gen_6880, q_gen_6834, q_gen_6904) -> q_gen_6904
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6904
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6904) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6904) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6904, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6904, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6904, q_gen_6904) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 41
() -> numnodes([leaf, z]) -> 41
() -> plus([n, z, n]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 42
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 44
(leq([s(nn1), z])) -> BOT -> 43
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 58
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 59
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 47
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> a  ;  t1 -> node(a, node(b, leaf, leaf), node(a, node(b, leaf, leaf), node(b, leaf, leaf)))  ;  t2 -> leaf
})

-------------------------------------------
Step 51, which took 0.828813 s (model generation: 0.648877,  model checking: 0.179936):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6872, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6852, q_gen_6879, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6879, q_gen_6879) -> q_gen_6866
<a, s>(q_gen_6862) -> q_gen_6872
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 42
() -> numnodes([leaf, z]) -> 42
() -> plus([n, z, n]) -> 44
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 43
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 45
(leq([s(nn1), z])) -> BOT -> 44
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 61
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 59
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 48
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(s(s(z)))  ;  _caa -> z  ;  _daa -> s(s(s(z)))  ;  e -> b  ;  t1 -> node(a, node(a, node(b, leaf, node(b, leaf, leaf)), leaf), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 52, which took 0.687846 s (model generation: 0.626102,  model checking: 0.061744):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6860, q_gen_6861, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6861, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6861, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6861, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6860
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6860
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6860
<node, s>(q_gen_6835, q_gen_6879, q_gen_6864) -> q_gen_6860
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6860
<node, s>(q_gen_6852, q_gen_6879, q_gen_6864) -> q_gen_6860
<node, s>(q_gen_6861, q_gen_6834, q_gen_6834) -> q_gen_6860
<node, s>(q_gen_6861, q_gen_6864, q_gen_6834) -> q_gen_6860
<node, s>(q_gen_6861, q_gen_6864, q_gen_6864) -> q_gen_6860
<node, s>(q_gen_6861, q_gen_6864, q_gen_6879) -> q_gen_6860
<node, s>(q_gen_6861, q_gen_6879, q_gen_6879) -> q_gen_6860
<a, s>(q_gen_6862) -> q_gen_6861
<b, s>(q_gen_6862) -> q_gen_6861
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 43
() -> numnodes([leaf, z]) -> 43
() -> plus([n, z, n]) -> 45
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 44
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 46
(leq([s(nn1), z])) -> BOT -> 45
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 61
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 62
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 49
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> b  ;  t1 -> node(a, node(b, node(b, leaf, leaf), leaf), node(b, node(b, node(b, leaf, leaf), leaf), node(b, leaf, leaf)))  ;  t2 -> leaf
})

-------------------------------------------
Step 53, which took 0.912347 s (model generation: 0.732603,  model checking: 0.179744):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6879) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6879
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6864) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6879) -> q_gen_6879
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6879) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 44
() -> numnodes([leaf, z]) -> 44
() -> plus([n, z, n]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 45
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 47
(leq([s(nn1), z])) -> BOT -> 46
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 64
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 62
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 50
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(s(s(z)))  ;  _caa -> z  ;  _daa -> s(s(s(z)))  ;  e -> b  ;  t1 -> node(a, leaf, node(b, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 54, which took 0.950863 s (model generation: 0.792088,  model checking: 0.158775):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6848, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6848, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6879) -> q_gen_6829
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, z>() -> q_gen_6848
<b, s>(q_gen_6862) -> q_gen_6848
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6864, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6848, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6879, q_gen_6864) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 45
() -> numnodes([leaf, z]) -> 45
() -> plus([n, z, n]) -> 47
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 46
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 48
(leq([s(nn1), z])) -> BOT -> 47
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 64
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 65
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 51
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> a  ;  t1 -> node(a, leaf, node(b, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 55, which took 1.390833 s (model generation: 1.129323,  model checking: 0.261510):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6859, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6859, q_gen_6879, q_gen_6864) -> q_gen_6851
<b, s>(q_gen_6853) -> q_gen_6852
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 46
() -> numnodes([leaf, z]) -> 46
() -> plus([n, z, n]) -> 48
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 47
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 49
(leq([s(nn1), z])) -> BOT -> 48
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 67
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 65
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 52
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(z)  ;  _daa -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(b, leaf, node(b, leaf, leaf)), leaf)
})

-------------------------------------------
Step 56, which took 1.105117 s (model generation: 1.035849,  model checking: 0.069268):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6872, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6852, q_gen_6879, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6879, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6879, q_gen_6879) -> q_gen_6866
<a, s>(q_gen_6862) -> q_gen_6872
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 47
() -> numnodes([leaf, z]) -> 47
() -> plus([n, z, n]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 48
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 50
(leq([s(nn1), z])) -> BOT -> 49
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 67
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 68
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 53
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> a  ;  t1 -> node(a, node(b, leaf, node(b, leaf, node(b, leaf, leaf))), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 57, which took 1.904742 s (model generation: 1.594002,  model checking: 0.310740):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6872, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6879, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6879, q_gen_6864) -> q_gen_6866
<a, s>(q_gen_6862) -> q_gen_6872
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 48
() -> numnodes([leaf, z]) -> 48
() -> plus([n, z, n]) -> 50
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 49
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 51
(leq([s(nn1), z])) -> BOT -> 50
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 70
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 68
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 54
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(s(z))  ;  _daa -> s(s(z))  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(b, leaf, node(b, leaf, node(b, leaf, node(b, leaf, leaf))))
})

-------------------------------------------
Step 58, which took 1.399288 s (model generation: 1.287843,  model checking: 0.111445):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6866, q_gen_6872, q_gen_6879},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6879, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6872, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6862) -> q_gen_6835
<b, z>() -> q_gen_6835
<a, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6879, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6852, q_gen_6834, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6852, q_gen_6879, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6834, q_gen_6864) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6834) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6864, q_gen_6879) -> q_gen_6866
<node, s>(q_gen_6872, q_gen_6879, q_gen_6864) -> q_gen_6866
<a, s>(q_gen_6862) -> q_gen_6872
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 49
() -> numnodes([leaf, z]) -> 49
() -> plus([n, z, n]) -> 51
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 50
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 52
(leq([s(nn1), z])) -> BOT -> 51
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 70
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 71
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 55
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> a  ;  t1 -> node(a, node(b, leaf, node(b, leaf, leaf)), leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 59, which took 2.650844 s (model generation: 2.201044,  model checking: 0.449800):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880, q_gen_6882},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6882) -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6882) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6882) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<node>(q_gen_6865, q_gen_6864, q_gen_6882) -> q_gen_6882
<node>(q_gen_6865, q_gen_6882, q_gen_6864) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6882) -> q_gen_6882
<node>(q_gen_6880, q_gen_6864, q_gen_6882) -> q_gen_6882
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6882, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6882, q_gen_6864) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6882, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6882) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 50
() -> numnodes([leaf, z]) -> 50
() -> plus([n, z, n]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 51
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 53
(leq([s(nn1), z])) -> BOT -> 52
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 73
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 71
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 56
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(s(s(z)))  ;  _daa -> s(s(s(z)))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, node(b, leaf, leaf), node(b, leaf, node(a, node(a, leaf, leaf), leaf)))
})

-------------------------------------------
Step 60, which took 2.886658 s (model generation: 2.690150,  model checking: 0.196508):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6834
<node>(q_gen_6880, q_gen_6864, q_gen_6879) -> q_gen_6834
<node>(q_gen_6880, q_gen_6879, q_gen_6879) -> q_gen_6834
<s>(q_gen_6862) -> q_gen_6853
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6879, q_gen_6834) -> q_gen_6864
<a>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6879
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6864, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6879, q_gen_6864) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
<b, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 51
() -> numnodes([leaf, z]) -> 51
() -> plus([n, z, n]) -> 53
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 52
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 53
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 73
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 74
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 57
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(s(z)))))  ;  _iaa -> s(s(s(z)))  ;  e -> b  ;  t1 -> node(b, node(a, leaf, leaf), node(a, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 61, which took 3.114756 s (model generation: 2.185020,  model checking: 0.929736):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6834
<s>(q_gen_6862) -> q_gen_6853
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6879, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6834) -> q_gen_6879
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6879, q_gen_6864) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
<b, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 52
() -> numnodes([leaf, z]) -> 52
() -> plus([n, z, n]) -> 54
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 53
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 55
(leq([s(nn1), z])) -> BOT -> 54
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 76
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 74
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 58
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(s(s(z)))  ;  _caa -> z  ;  _daa -> s(s(s(z)))  ;  e -> b  ;  t1 -> node(a, node(a, node(a, node(b, leaf, leaf), leaf), node(a, leaf, leaf)), node(a, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 62, which took 4.219434 s (model generation: 3.774956,  model checking: 0.444478):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880, q_gen_6882},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6882, q_gen_6882) -> q_gen_6834
<node>(q_gen_6880, q_gen_6882, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6882) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6882) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6882) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6882) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6882) -> q_gen_6882
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6882
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6882, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6882, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6882) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 53
() -> numnodes([leaf, z]) -> 53
() -> plus([n, z, n]) -> 55
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 54
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 56
(leq([s(nn1), z])) -> BOT -> 55
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 76
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 77
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 59
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(s(z))))  ;  _iaa -> s(s(s(z)))  ;  e -> b  ;  t1 -> node(b, leaf, node(a, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 63, which took 3.741721 s (model generation: 2.818190,  model checking: 0.923531):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6834
<s>(q_gen_6862) -> q_gen_6853
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6879, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6834) -> q_gen_6879
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6879, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6879, q_gen_6879) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
<b, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 54
() -> numnodes([leaf, z]) -> 54
() -> plus([n, z, n]) -> 56
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 55
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 57
(leq([s(nn1), z])) -> BOT -> 56
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 79
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 77
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 60
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> s(z)  ;  _caa -> z  ;  _daa -> s(z)  ;  e -> b  ;  t1 -> node(a, node(a, leaf, node(a, node(a, leaf, leaf), node(b, node(a, leaf, leaf), node(a, leaf, leaf)))), node(a, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 64, which took 4.615017 s (model generation: 3.095741,  model checking: 1.519276):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880, q_gen_6882},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6882, q_gen_6882) -> q_gen_6834
<node>(q_gen_6880, q_gen_6882, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6882) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6882) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6882
<node>(q_gen_6865, q_gen_6864, q_gen_6882) -> q_gen_6882
<node>(q_gen_6865, q_gen_6882, q_gen_6864) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6882) -> q_gen_6882
<node>(q_gen_6880, q_gen_6864, q_gen_6882) -> q_gen_6882
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6882) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6882, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6882) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6882, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6882, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6882) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 55
() -> numnodes([leaf, z]) -> 55
() -> plus([n, z, n]) -> 57
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 56
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 58
(leq([s(nn1), z])) -> BOT -> 57
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 79
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 80
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 61
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(z))  ;  _iaa -> s(z)  ;  e -> b  ;  t1 -> node(b, node(b, node(a, leaf, node(a, node(a, leaf, leaf), leaf)), leaf), node(b, leaf, node(b, node(a, leaf, leaf), leaf)))  ;  t2 -> leaf
})

-------------------------------------------
Step 65, which took 4.921493 s (model generation: 2.783728,  model checking: 2.137765):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880, q_gen_6882},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6882) -> q_gen_6834
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6882) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6882) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6882
<node>(q_gen_6865, q_gen_6834, q_gen_6882) -> q_gen_6882
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6882) -> q_gen_6882
<node>(q_gen_6880, q_gen_6864, q_gen_6882) -> q_gen_6882
<node>(q_gen_6880, q_gen_6882, q_gen_6864) -> q_gen_6882
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6882, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6882) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6882, q_gen_6882) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6882, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6882, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6864) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 56
() -> numnodes([leaf, z]) -> 56
() -> plus([n, z, n]) -> 58
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 57
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 59
(leq([s(nn1), z])) -> BOT -> 58
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 82
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 80
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 62
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(z)  ;  _daa -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, node(b, leaf, node(b, node(a, node(a, leaf, node(b, leaf, leaf)), leaf), leaf)), node(a, node(a, leaf, node(a, node(a, leaf, node(b, leaf, leaf)), leaf)), node(a, leaf, node(b, leaf, leaf))))
})

-------------------------------------------
Step 66, which took 7.075747 s (model generation: 6.016182,  model checking: 1.059565):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6851, q_gen_6852, q_gen_6853, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6880, q_gen_6882},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6834, q_gen_6882) -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6882) -> q_gen_6834
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6834
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<s>(q_gen_6862) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6882, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6834) -> q_gen_6864
<node>(q_gen_6880, q_gen_6882, q_gen_6864) -> q_gen_6864
<a>() -> q_gen_6865
<b>() -> q_gen_6880
<node>(q_gen_6865, q_gen_6882, q_gen_6882) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6882
<node>(q_gen_6880, q_gen_6834, q_gen_6882) -> q_gen_6882
<node>(q_gen_6880, q_gen_6864, q_gen_6882) -> q_gen_6882
<node>(q_gen_6880, q_gen_6882, q_gen_6882) -> q_gen_6882
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6882, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6852, q_gen_6864, q_gen_6834) -> q_gen_6829
<a, s>(q_gen_6853) -> q_gen_6835
<a, z>() -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6882, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6835, q_gen_6882, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6834, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6864, q_gen_6882) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6834) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6864) -> q_gen_6851
<node, s>(q_gen_6852, q_gen_6882, q_gen_6882) -> q_gen_6851
<a, s>(q_gen_6862) -> q_gen_6852
<b, s>(q_gen_6853) -> q_gen_6852
<b, s>(q_gen_6862) -> q_gen_6852
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 57
() -> numnodes([leaf, z]) -> 57
() -> plus([n, z, n]) -> 59
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 58
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 60
(leq([s(nn1), z])) -> BOT -> 59
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 82
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 83
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 63
}
Sat witness: Found: ((numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]), {
_haa -> s(s(s(z)))  ;  _iaa -> s(s(z))  ;  e -> b  ;  t1 -> node(a, node(b, node(b, leaf, node(b, node(a, leaf, leaf), node(a, node(a, leaf, leaf), leaf))), node(b, node(a, leaf, leaf), leaf)), node(a, node(b, node(a, leaf, leaf), node(a, node(a, leaf, leaf), leaf)), node(b, leaf, node(b, node(a, leaf, leaf), node(a, node(a, leaf, leaf), leaf)))))  ;  t2 -> leaf
})

-------------------------------------------
Step 67, which took 6.375475 s (model generation: 5.116142,  model checking: 1.259333):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6830, q_gen_6838, q_gen_6867},
Q_f={q_gen_6830},
Delta=
{
<s>(q_gen_6838) -> q_gen_6838
<z>() -> q_gen_6838
<s, s>(q_gen_6830) -> q_gen_6830
<z, s>(q_gen_6838) -> q_gen_6830
<z, z>() -> q_gen_6830
<s, s>(q_gen_6867) -> q_gen_6867
<s, z>(q_gen_6838) -> q_gen_6867
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_6829, q_gen_6834, q_gen_6835, q_gen_6853, q_gen_6858, q_gen_6859, q_gen_6862, q_gen_6864, q_gen_6865, q_gen_6879, q_gen_6880},
Q_f={q_gen_6829},
Delta=
{
<leaf>() -> q_gen_6834
<node>(q_gen_6865, q_gen_6864, q_gen_6834) -> q_gen_6834
<node>(q_gen_6865, q_gen_6879, q_gen_6864) -> q_gen_6834
<node>(q_gen_6880, q_gen_6864, q_gen_6879) -> q_gen_6834
<s>(q_gen_6862) -> q_gen_6853
<z>() -> q_gen_6853
<s>(q_gen_6853) -> q_gen_6862
<node>(q_gen_6865, q_gen_6834, q_gen_6834) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6865, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6865, q_gen_6864, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6864) -> q_gen_6864
<node>(q_gen_6880, q_gen_6834, q_gen_6879) -> q_gen_6864
<node>(q_gen_6880, q_gen_6879, q_gen_6879) -> q_gen_6864
<a>() -> q_gen_6865
<node>(q_gen_6865, q_gen_6864, q_gen_6879) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6865, q_gen_6879, q_gen_6879) -> q_gen_6879
<node>(q_gen_6880, q_gen_6834, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6864, q_gen_6864) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6834) -> q_gen_6879
<node>(q_gen_6880, q_gen_6879, q_gen_6864) -> q_gen_6879
<b>() -> q_gen_6880
<leaf, z>() -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6864, q_gen_6834) -> q_gen_6829
<node, s>(q_gen_6835, q_gen_6879, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6864) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6834, q_gen_6879) -> q_gen_6829
<node, s>(q_gen_6859, q_gen_6879, q_gen_6834) -> q_gen_6829
<a, z>() -> q_gen_6835
<b, s>(q_gen_6853) -> q_gen_6835
<b, z>() -> q_gen_6835
<node, s>(q_gen_6835, q_gen_6834, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6835, q_gen_6879, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6834, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6834) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6864, q_gen_6879) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6879, q_gen_6864) -> q_gen_6858
<node, s>(q_gen_6859, q_gen_6879, q_gen_6879) -> q_gen_6858
<a, s>(q_gen_6853) -> q_gen_6859
<a, s>(q_gen_6862) -> q_gen_6859
<b, s>(q_gen_6862) -> q_gen_6859
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_6828, q_gen_6832, q_gen_6845, q_gen_6846},
Q_f={q_gen_6828},
Delta=
{
<s>(q_gen_6846) -> q_gen_6846
<z>() -> q_gen_6846
<s, s>(q_gen_6832) -> q_gen_6832
<z, s>(q_gen_6846) -> q_gen_6832
<z, z>() -> q_gen_6832
<s, s, s>(q_gen_6828) -> q_gen_6828
<s, s, s>(q_gen_6845) -> q_gen_6828
<s, z, s>(q_gen_6832) -> q_gen_6828
<z, s, s>(q_gen_6832) -> q_gen_6828
<z, z, z>() -> q_gen_6828
<z, z, s>(q_gen_6846) -> q_gen_6845
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 58
() -> numnodes([leaf, z]) -> 58
() -> plus([n, z, n]) -> 60
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 59
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 61
(leq([s(nn1), z])) -> BOT -> 60
(numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]) -> 85
(numnodes([t1, _haa]) /\ numnodes([node(e, t1, t2), _iaa])) -> leq([_haa, _iaa]) -> 83
(plus([n, mm, _wz])) -> plus([n, s(mm), s(_wz)]) -> 64
}
Sat witness: Found: ((numnodes([t1, _baa]) /\ numnodes([t2, _caa]) /\ plus([_baa, _caa, _daa])) -> numnodes([node(e, t1, t2), s(_daa)]), {
_baa -> z  ;  _caa -> s(z)  ;  _daa -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(a, node(a, node(b, node(a, leaf, node(b, leaf, node(b, leaf, leaf))), leaf), node(b, leaf, leaf)), leaf), node(a, leaf, node(b, leaf, node(b, leaf, leaf))))
})

Total time: 60.000590
Reason for stopping: DontKnow. Stopped because: timeout