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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)])}
(append([_xd, _yd, _ae]) /\ append([_xd, _yd, _zd])) -> eq_eltlist([_zd, _ae])
)
(reverse, F:
{() -> reverse([nil, nil])
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce])}
(reverse([_de, _ee]) /\ reverse([_de, _fe])) -> eq_eltlist([_ee, _fe])
)
(length, F:
{() -> length([nil, z])
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)])}
(length([_he, _ie]) /\ length([_he, _je])) -> eq_nat([_ie, _je])
)
}

properties:
{(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me])}


over-approximation: {append, length, reverse}
under-approximation: {}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> reverse([nil, nil]) -> 0
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 0
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 0
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 0
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 0
}


Solving took 66.819906 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1018, q_gen_1019, q_gen_1020, q_gen_1021, q_gen_1026, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1031, q_gen_1040, q_gen_1041, q_gen_1042, q_gen_1049, q_gen_1050, q_gen_1051, q_gen_1058, q_gen_1059, q_gen_1065, q_gen_1066, q_gen_1074, q_gen_1075, q_gen_1076, q_gen_1081, q_gen_1082, q_gen_1083, q_gen_1084, q_gen_1087, q_gen_1089, q_gen_1092, q_gen_1093, q_gen_1097, q_gen_1098, q_gen_1099, q_gen_1100, q_gen_1101, q_gen_1102, q_gen_1108, q_gen_1109, q_gen_1110, q_gen_1111, q_gen_1112, q_gen_1113, q_gen_1114, q_gen_1125, q_gen_1126, q_gen_1127, q_gen_1128, q_gen_1129, q_gen_1130, q_gen_1134, q_gen_1135, q_gen_1136, q_gen_1137, q_gen_1139, q_gen_1140, q_gen_1141, q_gen_1144, q_gen_1145, q_gen_1147, q_gen_1148, q_gen_1149, q_gen_1155, q_gen_1156, q_gen_1157, q_gen_1158, q_gen_1160, q_gen_1161, q_gen_1162, q_gen_1163, q_gen_1173, q_gen_1174, q_gen_1175, q_gen_1176, q_gen_1177, q_gen_1179, q_gen_1181, q_gen_1182, q_gen_1183, q_gen_1184, q_gen_1185, q_gen_1186, q_gen_1187, q_gen_1188, q_gen_1189, q_gen_1192},
Q_f={},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<a>() -> q_gen_1083
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1083, q_gen_1028) -> q_gen_1114
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1163
<nil, nil>() -> q_gen_1016
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1019
<a, a>() -> q_gen_1020
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1076
<nil, cons>(q_gen_1083, q_gen_1114) -> q_gen_1113
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1126
<b, a>() -> q_gen_1129
<nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1136
<a, b>() -> q_gen_1137
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1141
<cons, cons>(q_gen_1020, q_gen_1076) -> q_gen_1185
<cons, cons>(q_gen_1129, q_gen_1141) -> q_gen_1189
<nil, nil, nil>() -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1020, q_gen_1019) -> q_gen_1018
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1021
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1026
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<b, b, b>() -> q_gen_1030
<nil, cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1031
<cons, nil, cons>(q_gen_1020, q_gen_1016) -> q_gen_1040
<cons, nil, cons>(q_gen_1017, q_gen_1019) -> q_gen_1041
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1049
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1051
<cons, cons, cons>(q_gen_1030, q_gen_1049) -> q_gen_1058
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1059
<cons, cons, cons>(q_gen_1066, q_gen_1027) -> q_gen_1065
<a, b, a>() -> q_gen_1066
<cons, cons, cons>(q_gen_1066, q_gen_1075) -> q_gen_1074
<cons, nil, cons>(q_gen_1017, q_gen_1076) -> q_gen_1075
<cons, cons, cons>(q_gen_1084, q_gen_1082) -> q_gen_1081
<nil, nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1082
<b, a, b>() -> q_gen_1084
<nil, cons, cons>(q_gen_1020, q_gen_1050) -> q_gen_1087
<nil, cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1089
<cons, cons, cons>(q_gen_1093, q_gen_1082) -> q_gen_1092
<a, a, a>() -> q_gen_1093
<cons, cons, cons>(q_gen_1093, q_gen_1051) -> q_gen_1097
<cons, cons, cons>(q_gen_1093, q_gen_1099) -> q_gen_1098
<cons, cons, cons>(q_gen_1066, q_gen_1100) -> q_gen_1099
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1100
<cons, cons, cons>(q_gen_1093, q_gen_1027) -> q_gen_1102
<cons, cons, cons>(q_gen_1093, q_gen_1109) -> q_gen_1108
<cons, cons, cons>(q_gen_1066, q_gen_1011) -> q_gen_1109
<cons, cons, cons>(q_gen_1093, q_gen_1111) -> q_gen_1110
<cons, cons, cons>(q_gen_1066, q_gen_1040) -> q_gen_1111
<nil, cons, cons>(q_gen_1017, q_gen_1113) -> q_gen_1112
<nil, cons, cons>(q_gen_1020, q_gen_1126) -> q_gen_1125
<cons, cons, cons>(q_gen_1093, q_gen_1128) -> q_gen_1127
<nil, cons, cons>(q_gen_1129, q_gen_1050) -> q_gen_1128
<cons, cons, cons>(q_gen_1030, q_gen_1100) -> q_gen_1130
<cons, cons, cons>(q_gen_1066, q_gen_1135) -> q_gen_1134
<nil, cons, cons>(q_gen_1137, q_gen_1136) -> q_gen_1135
<cons, cons, cons>(q_gen_1066, q_gen_1140) -> q_gen_1139
<cons, nil, cons>(q_gen_1017, q_gen_1141) -> q_gen_1140
<cons, cons, cons>(q_gen_1066, q_gen_1145) -> q_gen_1144
<nil, nil, cons>(q_gen_1083, q_gen_1101) -> q_gen_1145
<nil, nil, cons>(q_gen_1083, q_gen_1114) -> q_gen_1147
<cons, nil, cons>(q_gen_1017, q_gen_1113) -> q_gen_1148
<nil, cons, cons>(q_gen_1017, q_gen_1141) -> q_gen_1149
<cons, cons, cons>(q_gen_1030, q_gen_1156) -> q_gen_1155
<nil, cons, cons>(q_gen_1017, q_gen_1076) -> q_gen_1156
<cons, cons, cons>(q_gen_1066, q_gen_1158) -> q_gen_1157
<cons, cons, cons>(q_gen_1030, q_gen_1149) -> q_gen_1158
<cons, cons, cons>(q_gen_1066, q_gen_1161) -> q_gen_1160
<cons, cons, cons>(q_gen_1030, q_gen_1162) -> q_gen_1161
<nil, nil, cons>(q_gen_1029, q_gen_1163) -> q_gen_1162
<cons, cons, cons>(q_gen_1084, q_gen_1099) -> q_gen_1173
<cons, cons, cons>(q_gen_1093, q_gen_1175) -> q_gen_1174
<cons, cons, cons>(q_gen_1030, q_gen_1176) -> q_gen_1175
<cons, nil, cons>(q_gen_1020, q_gen_1141) -> q_gen_1176
<cons, cons, cons>(q_gen_1093, q_gen_1100) -> q_gen_1177
<cons, cons, cons>(q_gen_1066, q_gen_1082) -> q_gen_1179
<cons, cons, cons>(q_gen_1093, q_gen_1011) -> q_gen_1181
<cons, cons, cons>(q_gen_1084, q_gen_1040) -> q_gen_1182
<cons, cons, cons>(q_gen_1030, q_gen_1184) -> q_gen_1183
<nil, cons, cons>(q_gen_1020, q_gen_1185) -> q_gen_1184
<cons, cons, cons>(q_gen_1066, q_gen_1187) -> q_gen_1186
<cons, cons, cons>(q_gen_1084, q_gen_1188) -> q_gen_1187
<nil, cons, cons>(q_gen_1020, q_gen_1189) -> q_gen_1188
<nil, cons, cons>(q_gen_1017, q_gen_1126) -> q_gen_1192
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1012, q_gen_1013, q_gen_1014, q_gen_1024, q_gen_1025, q_gen_1034, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1047, q_gen_1048, q_gen_1054, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1062, q_gen_1063, q_gen_1064, q_gen_1071, q_gen_1072, q_gen_1077, q_gen_1078, q_gen_1079, q_gen_1080, q_gen_1085, q_gen_1086, q_gen_1090, q_gen_1095, q_gen_1096, q_gen_1104, q_gen_1105, q_gen_1106, q_gen_1119, q_gen_1121, q_gen_1122, q_gen_1123, q_gen_1124, q_gen_1132, q_gen_1153, q_gen_1154, q_gen_1164, q_gen_1165, q_gen_1166, q_gen_1169, q_gen_1170, q_gen_1171, q_gen_1172, q_gen_1178},
Q_f={},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons>(q_gen_1064, q_gen_1013) -> q_gen_1063
<a>() -> q_gen_1064
<s>(q_gen_1057) -> q_gen_1080
<cons>(q_gen_1064, q_gen_1035) -> q_gen_1086
<cons>(q_gen_1036, q_gen_1086) -> q_gen_1123
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1165
<cons>(q_gen_1036, q_gen_1123) -> q_gen_1170
<s>(q_gen_1080) -> q_gen_1172
<nil, z>() -> q_gen_1010
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1012
<b, z>() -> q_gen_1014
<cons, s>(q_gen_1025, q_gen_1013) -> q_gen_1024
<a, z>() -> q_gen_1025
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1034
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1048, q_gen_1035) -> q_gen_1047
<a, s>(q_gen_1038) -> q_gen_1048
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1054
<b, s>(q_gen_1057) -> q_gen_1056
<cons, s>(q_gen_1037, q_gen_1063) -> q_gen_1062
<cons, s>(q_gen_1072, q_gen_1035) -> q_gen_1071
<a, s>(q_gen_1057) -> q_gen_1072
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1077
<cons, s>(q_gen_1079, q_gen_1035) -> q_gen_1078
<b, s>(q_gen_1080) -> q_gen_1079
<cons, s>(q_gen_1072, q_gen_1086) -> q_gen_1085
<cons, s>(q_gen_1048, q_gen_1063) -> q_gen_1090
<cons, s>(q_gen_1072, q_gen_1055) -> q_gen_1095
<cons, s>(q_gen_1072, q_gen_1013) -> q_gen_1096
<cons, s>(q_gen_1048, q_gen_1013) -> q_gen_1104
<cons, s>(q_gen_1072, q_gen_1063) -> q_gen_1105
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1106
<cons, s>(q_gen_1056, q_gen_1063) -> q_gen_1119
<cons, s>(q_gen_1056, q_gen_1086) -> q_gen_1121
<cons, s>(q_gen_1124, q_gen_1123) -> q_gen_1122
<a, s>(q_gen_1080) -> q_gen_1124
<cons, s>(q_gen_1124, q_gen_1055) -> q_gen_1132
<cons, s>(q_gen_1124, q_gen_1035) -> q_gen_1153
<cons, s>(q_gen_1079, q_gen_1123) -> q_gen_1154
<cons, s>(q_gen_1124, q_gen_1165) -> q_gen_1164
<cons, s>(q_gen_1056, q_gen_1165) -> q_gen_1166
<cons, s>(q_gen_1171, q_gen_1170) -> q_gen_1169
<b, s>(q_gen_1172) -> q_gen_1171
<cons, s>(q_gen_1124, q_gen_1013) -> q_gen_1178
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046, q_gen_1052, q_gen_1053, q_gen_1060, q_gen_1061, q_gen_1067, q_gen_1068, q_gen_1069, q_gen_1070, q_gen_1073, q_gen_1088, q_gen_1091, q_gen_1094, q_gen_1103, q_gen_1107, q_gen_1115, q_gen_1116, q_gen_1117, q_gen_1118, q_gen_1120, q_gen_1131, q_gen_1133, q_gen_1138, q_gen_1142, q_gen_1143, q_gen_1146, q_gen_1150, q_gen_1151, q_gen_1152, q_gen_1159, q_gen_1167, q_gen_1168, q_gen_1180, q_gen_1190, q_gen_1191},
Q_f={},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons>(q_gen_1118, q_gen_1045) -> q_gen_1117
<a>() -> q_gen_1118
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1152
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<cons, cons>(q_gen_1023, q_gen_1053) -> q_gen_1052
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1053
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1060
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1061
<cons, cons>(q_gen_1070, q_gen_1068) -> q_gen_1067
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1068
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1070
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1073
<cons, cons>(q_gen_1033, q_gen_1053) -> q_gen_1088
<cons, cons>(q_gen_1033, q_gen_1068) -> q_gen_1091
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1094
<cons, cons>(q_gen_1070, q_gen_1009) -> q_gen_1103
<cons, cons>(q_gen_1069, q_gen_1022) -> q_gen_1107
<cons, cons>(q_gen_1023, q_gen_1116) -> q_gen_1115
<nil, cons>(q_gen_1118, q_gen_1117) -> q_gen_1116
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1120
<cons, cons>(q_gen_1023, q_gen_1052) -> q_gen_1131
<cons, cons>(q_gen_1070, q_gen_1060) -> q_gen_1133
<cons, cons>(q_gen_1033, q_gen_1052) -> q_gen_1138
<cons, cons>(q_gen_1070, q_gen_1022) -> q_gen_1142
<cons, cons>(q_gen_1070, q_gen_1131) -> q_gen_1143
<cons, cons>(q_gen_1070, q_gen_1088) -> q_gen_1146
<cons, cons>(q_gen_1023, q_gen_1151) -> q_gen_1150
<nil, cons>(q_gen_1046, q_gen_1152) -> q_gen_1151
<nil, cons>(q_gen_1118, q_gen_1152) -> q_gen_1159
<cons, cons>(q_gen_1070, q_gen_1168) -> q_gen_1167
<cons, cons>(q_gen_1023, q_gen_1060) -> q_gen_1168
<cons, cons>(q_gen_1070, q_gen_1032) -> q_gen_1180
<cons, cons>(q_gen_1033, q_gen_1191) -> q_gen_1190
<cons, cons>(q_gen_1069, q_gen_1053) -> q_gen_1191
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.008370 s (model generation: 0.006918,  model checking: 0.001452):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> reverse([nil, nil]) -> 3
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 1
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 1
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 1
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 1
}
Sat witness: Found: (() -> reverse([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.008790 s (model generation: 0.008618,  model checking: 0.000172):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009},
Q_f={q_gen_1009},
Delta=
{
<nil, nil>() -> q_gen_1009
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 1
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 1
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 1
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 2, which took 0.012016 s (model generation: 0.011688,  model checking: 0.000328):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010},
Q_f={q_gen_1010},
Delta=
{
<nil, z>() -> q_gen_1010
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009},
Q_f={q_gen_1009},
Delta=
{
<nil, nil>() -> q_gen_1009
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 1
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 1
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 1
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 3, which took 0.010858 s (model generation: 0.010743,  model checking: 0.000115):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011},
Q_f={q_gen_1011},
Delta=
{
<nil, nil, nil>() -> q_gen_1011
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010},
Q_f={q_gen_1010},
Delta=
{
<nil, z>() -> q_gen_1010
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009},
Q_f={q_gen_1009},
Delta=
{
<nil, nil>() -> q_gen_1009
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 1
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 1
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 1
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 4
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 4, which took 0.009881 s (model generation: 0.009070,  model checking: 0.000811):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011},
Q_f={q_gen_1011},
Delta=
{
<nil, nil, nil>() -> q_gen_1011
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009},
Q_f={q_gen_1009},
Delta=
{
<nil, nil>() -> q_gen_1009
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 1
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 4
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 2
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 4
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 5, which took 0.008213 s (model generation: 0.007748,  model checking: 0.000465):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017},
Q_f={q_gen_1011},
Delta=
{
<nil, nil>() -> q_gen_1016
<b, b>() -> q_gen_1017
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009},
Q_f={q_gen_1009},
Delta=
{
<nil, nil>() -> q_gen_1009
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 2
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 4
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 3
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 6, which took 0.008326 s (model generation: 0.008060,  model checking: 0.000266):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017},
Q_f={q_gen_1011},
Delta=
{
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009},
Q_f={q_gen_1009},
Delta=
{
<nil, nil>() -> q_gen_1009
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 5
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 4
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 3
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 4
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> nil  ;  _ce -> cons(b, nil)  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 7, which took 0.008910 s (model generation: 0.008666,  model checking: 0.000244):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017},
Q_f={q_gen_1011},
Delta=
{
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023},
Q_f={q_gen_1009},
Delta=
{
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 5
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 4
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 4
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 7
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 8, which took 0.011145 s (model generation: 0.009970,  model checking: 0.001175):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017},
Q_f={q_gen_1011},
Delta=
{
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023},
Q_f={q_gen_1009},
Delta=
{
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 5
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 7
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 5
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 7
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 9, which took 0.010113 s (model generation: 0.009582,  model checking: 0.000531):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023},
Q_f={q_gen_1009},
Delta=
{
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 5
() -> reverse([nil, nil]) -> 5
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 8
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 7
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 6
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 7
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> nil  ;  _ce -> cons(a, nil)  ;  h1 -> a  ;  t1 -> nil
})

-------------------------------------------
Step 10, which took 0.011380 s (model generation: 0.010502,  model checking: 0.000878):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023},
Q_f={q_gen_1009},
Delta=
{
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 6
() -> reverse([nil, nil]) -> 6
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 8
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 7
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 7
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 10
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 11, which took 0.018070 s (model generation: 0.017660,  model checking: 0.000410):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1036, q_gen_1038},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1013
<nil>() -> q_gen_1013
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1014
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023},
Q_f={q_gen_1009},
Delta=
{
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> reverse([nil, nil]) -> 7
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 8
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 7
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 10
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 10
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(z)  ;  _le -> cons(b, nil)  ;  _me -> s(s(z))  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 12, which took 0.013715 s (model generation: 0.013032,  model checking: 0.000683):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1019, q_gen_1021, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1019
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1021) -> q_gen_1021
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1021
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1021
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1036, q_gen_1038},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1013
<nil>() -> q_gen_1013
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1014
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023},
Q_f={q_gen_1009},
Delta=
{
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> reverse([nil, nil]) -> 7
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 8
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 10
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 10
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 10
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(a, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 13, which took 0.014246 s (model generation: 0.013681,  model checking: 0.000565):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1019, q_gen_1021, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1019
<cons, cons, cons>(q_gen_1030, q_gen_1021) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1019) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1021
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1021
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1036, q_gen_1038},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1013
<nil>() -> q_gen_1013
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1014
<b, z>() -> q_gen_1014
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023},
Q_f={q_gen_1009},
Delta=
{
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 8
() -> reverse([nil, nil]) -> 8
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 8
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 10
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 10
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 10
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, nil)
})

-------------------------------------------
Step 14, which took 0.013537 s (model generation: 0.013063,  model checking: 0.000474):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023},
Q_f={q_gen_1009},
Delta=
{
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 8
() -> reverse([nil, nil]) -> 8
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 11
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 10
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 10
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 10
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(b, nil)  ;  _ce -> cons(b, nil)  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 15, which took 0.015030 s (model generation: 0.013818,  model checking: 0.001212):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 9
() -> reverse([nil, nil]) -> 9
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 11
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 10
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 10
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 13
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 16, which took 0.015914 s (model generation: 0.015157,  model checking: 0.000757):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1038) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> reverse([nil, nil]) -> 10
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 11
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 10
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 13
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 13
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(z)  ;  _le -> nil  ;  _me -> z  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 17, which took 0.016777 s (model generation: 0.015818,  model checking: 0.000959):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1038) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> reverse([nil, nil]) -> 10
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 11
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 13
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 13
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 13
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 18, which took 0.018718 s (model generation: 0.017586,  model checking: 0.001132):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1038) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 11
() -> reverse([nil, nil]) -> 11
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 14
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 13
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 13
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 13
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> nil  ;  _ce -> cons(b, cons(b, nil))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 19, which took 0.018358 s (model generation: 0.016590,  model checking: 0.001768):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1038) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> length([nil, z]) -> 12
() -> reverse([nil, nil]) -> 12
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 14
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 13
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 13
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 16
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 20, which took 0.019426 s (model generation: 0.018160,  model checking: 0.001266):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> reverse([nil, nil]) -> 13
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 14
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 13
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 16
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 16
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(z))  ;  _le -> cons(b, nil)  ;  _me -> s(z)  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 21, which took 0.018903 s (model generation: 0.018516,  model checking: 0.000387):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> reverse([nil, nil]) -> 13
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 14
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 16
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 16
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 16
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 22, which took 0.020082 s (model generation: 0.018914,  model checking: 0.001168):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 14
() -> reverse([nil, nil]) -> 14
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 17
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 16
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 16
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 16
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(b, cons(b, nil))  ;  _ce -> cons(b, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 23, which took 0.029835 s (model generation: 0.028075,  model checking: 0.001760):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> length([nil, z]) -> 15
() -> reverse([nil, nil]) -> 15
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 17
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 16
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 16
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 19
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 24, which took 0.024640 s (model generation: 0.023354,  model checking: 0.001286):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> reverse([nil, nil]) -> 16
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 17
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 16
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 19
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 19
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> z  ;  _le -> cons(b, nil)  ;  _me -> s(z)  ;  l1 -> nil
})

-------------------------------------------
Step 25, which took 0.026235 s (model generation: 0.024562,  model checking: 0.001673):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> reverse([nil, nil]) -> 16
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 17
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 19
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 19
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 19
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 26, which took 0.026573 s (model generation: 0.025152,  model checking: 0.001421):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> length([nil, z]) -> 17
() -> reverse([nil, nil]) -> 17
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 20
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 19
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 19
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 19
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 27, which took 0.028308 s (model generation: 0.027026,  model checking: 0.001282):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> length([nil, z]) -> 18
() -> reverse([nil, nil]) -> 18
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 20
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 19
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 22
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 20
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(z))  ;  _le -> cons(a, cons(b, nil))  ;  _me -> s(s(s(z)))  ;  l1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 28, which took 0.040834 s (model generation: 0.036126,  model checking: 0.004708):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1057) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1057) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> reverse([nil, nil]) -> 19
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 20
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 22
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 22
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 20
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 29, which took 0.036693 s (model generation: 0.033933,  model checking: 0.002760):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1057) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, s>(q_gen_1057) -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> length([nil, z]) -> 20
() -> reverse([nil, nil]) -> 20
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 20
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 22
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 22
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 23
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(s(s(z)))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 30, which took 0.043536 s (model generation: 0.041031,  model checking: 0.002505):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1057) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, s>(q_gen_1057) -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> length([nil, z]) -> 21
() -> reverse([nil, nil]) -> 21
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 21
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 22
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 25
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 23
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(z)  ;  _le -> cons(b, nil)  ;  _me -> s(s(s(z)))  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 31, which took 0.045356 s (model generation: 0.039625,  model checking: 0.005731):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1057) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1057) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> length([nil, z]) -> 22
() -> reverse([nil, nil]) -> 22
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 22
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 25
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 25
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 23
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 32, which took 0.040956 s (model generation: 0.038235,  model checking: 0.002721):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1057) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1057) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
() -> reverse([nil, nil]) -> 23
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 23
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 25
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 25
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 26
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 33, which took 0.041412 s (model generation: 0.041008,  model checking: 0.000404):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1019, q_gen_1020, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<nil, nil>() -> q_gen_1016
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1019
<cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1019
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1019
<a, a>() -> q_gen_1020
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1020, q_gen_1019) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1019) -> q_gen_1027
<cons, nil, cons>(q_gen_1020, q_gen_1016) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1027
<nil, cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1032
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1032
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1032
<a, a>() -> q_gen_1033
<a, b>() -> q_gen_1033
<b, a>() -> q_gen_1033
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
() -> reverse([nil, nil]) -> 23
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 26
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 25
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 25
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 26
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> nil  ;  _ce -> cons(a, cons(b, nil))  ;  h1 -> a  ;  t1 -> nil
})

-------------------------------------------
Step 34, which took 0.047140 s (model generation: 0.046552,  model checking: 0.000588):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1019, q_gen_1020, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<nil, nil>() -> q_gen_1016
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1019
<cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1019
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1019
<a, a>() -> q_gen_1020
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1020, q_gen_1019) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1019) -> q_gen_1027
<cons, nil, cons>(q_gen_1020, q_gen_1016) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1027
<nil, cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1032
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1032
<a, a>() -> q_gen_1033
<a, b>() -> q_gen_1033
<b, a>() -> q_gen_1033
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 24
() -> reverse([nil, nil]) -> 24
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 26
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 25
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 25
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 26
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 35, which took 0.052957 s (model generation: 0.052251,  model checking: 0.000706):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1069},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1069
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 25
() -> reverse([nil, nil]) -> 25
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 26
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 25
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 28
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 26
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(z))  ;  _le -> cons(a, cons(b, nil))  ;  _me -> s(s(s(z)))  ;  l1 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 36, which took 0.061256 s (model generation: 0.056847,  model checking: 0.004409):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1057, q_gen_1064},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1064, q_gen_1035) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<cons>(q_gen_1064, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<s>(q_gen_1038) -> q_gen_1057
<a>() -> q_gen_1064
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1057) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1057) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 25
() -> reverse([nil, nil]) -> 25
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 26
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 28
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 28
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 26
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(a, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 37, which took 0.064870 s (model generation: 0.063891,  model checking: 0.000979):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1069},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1069, q_gen_1043) -> q_gen_1022
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1069
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 26
() -> reverse([nil, nil]) -> 26
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 29
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 28
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 28
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 27
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(a, nil))  ;  h1 -> a  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 38, which took 0.063988 s (model generation: 0.061355,  model checking: 0.002633):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1057, q_gen_1064},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1064, q_gen_1035) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<cons>(q_gen_1064, q_gen_1013) -> q_gen_1035
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<s>(q_gen_1038) -> q_gen_1057
<a>() -> q_gen_1064
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1057) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1057) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> length([nil, z]) -> 27
() -> reverse([nil, nil]) -> 27
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 29
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 28
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 28
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 30
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 39, which took 0.064985 s (model generation: 0.063379,  model checking: 0.001606):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1057) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1057) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> reverse([nil, nil]) -> 28
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 29
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 28
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 31
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 30
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(z)  ;  _le -> cons(a, nil)  ;  _me -> s(s(s(z)))  ;  l1 -> cons(a, nil)
})

-------------------------------------------
Step 40, which took 0.072356 s (model generation: 0.060344,  model checking: 0.012012):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> reverse([nil, nil]) -> 28
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 29
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 31
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 31
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 30
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 41, which took 0.093512 s (model generation: 0.092206,  model checking: 0.001306):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1022
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> length([nil, z]) -> 29
() -> reverse([nil, nil]) -> 29
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 32
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 31
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 31
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 30
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(b, nil))  ;  h1 -> a  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 42, which took 0.092808 s (model generation: 0.092108,  model checking: 0.000700):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1019, q_gen_1020, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<nil, nil>() -> q_gen_1016
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1019
<cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1019
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1019
<a, a>() -> q_gen_1020
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1019) -> q_gen_1011
<nil, cons, cons>(q_gen_1020, q_gen_1019) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1019) -> q_gen_1027
<cons, nil, cons>(q_gen_1020, q_gen_1016) -> q_gen_1027
<nil, cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, b>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1032
<a, a>() -> q_gen_1033
<b, a>() -> q_gen_1033
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 30
() -> reverse([nil, nil]) -> 30
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 32
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 31
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 31
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 30
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, nil)
})

-------------------------------------------
Step 43, which took 0.114903 s (model generation: 0.114096,  model checking: 0.000807):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1057, q_gen_1072},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1010
<cons, s>(q_gen_1072, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1038) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1057) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1072, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1072, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1072
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 30
() -> reverse([nil, nil]) -> 30
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 32
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 31
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 31
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 33
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(s(z))  ;  ll -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 44, which took 0.093347 s (model generation: 0.092129,  model checking: 0.001218):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1018, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050},
Q_f={q_gen_1011, q_gen_1018},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1018) -> q_gen_1018
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1018
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1018
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1070},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1022) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1022
<a, b>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1070, q_gen_1009) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<b, a>() -> q_gen_1070
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 31
() -> reverse([nil, nil]) -> 31
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 32
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 31
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 34
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 33
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(z))  ;  _le -> cons(b, cons(b, nil))  ;  _me -> s(s(s(z)))  ;  l1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 45, which took 0.095631 s (model generation: 0.094851,  model checking: 0.000780):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 31
() -> reverse([nil, nil]) -> 31
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 32
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 34
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 34
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 33
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(a, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 46, which took 0.129960 s (model generation: 0.129237,  model checking: 0.000723):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 32
() -> reverse([nil, nil]) -> 32
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 35
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 34
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 34
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 33
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> nil  ;  _ce -> cons(b, cons(a, cons(a, nil)))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 47, which took 0.136476 s (model generation: 0.134961,  model checking: 0.001515):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050},
Q_f={q_gen_1011},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1069},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1069, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1022) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1069
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 33
() -> reverse([nil, nil]) -> 33
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 35
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 34
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 37
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 34
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(z))  ;  _le -> cons(b, cons(a, nil))  ;  _me -> s(s(s(z)))  ;  l1 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 48, which took 0.216272 s (model generation: 0.213419,  model checking: 0.002853):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> length([nil, z]) -> 34
() -> reverse([nil, nil]) -> 34
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 35
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 34
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 37
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 37
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 49, which took 0.262007 s (model generation: 0.249348,  model checking: 0.012659):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> length([nil, z]) -> 34
() -> reverse([nil, nil]) -> 34
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 35
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 37
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 37
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 37
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 50, which took 0.371851 s (model generation: 0.370374,  model checking: 0.001477):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1026, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050},
Q_f={q_gen_1011, q_gen_1026},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1026) -> q_gen_1026
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1026
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1026
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1026
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 35
() -> length([nil, z]) -> 35
() -> reverse([nil, nil]) -> 35
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 38
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 37
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 37
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 37
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(b, nil)  ;  _ce -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 51, which took 0.380056 s (model generation: 0.375743,  model checking: 0.004313):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> length([nil, z]) -> 36
() -> reverse([nil, nil]) -> 36
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 38
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 37
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 40
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 38
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(s(z)))  ;  _le -> cons(a, cons(b, cons(b, nil)))  ;  _me -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 52, which took 0.340755 s (model generation: 0.324883,  model checking: 0.015872):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> length([nil, z]) -> 37
() -> reverse([nil, nil]) -> 37
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 38
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 40
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 40
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 38
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 53, which took 0.393087 s (model generation: 0.387510,  model checking: 0.005577):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 38
() -> length([nil, z]) -> 38
() -> reverse([nil, nil]) -> 38
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 39
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 40
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 43
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 39
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(z))  ;  _le -> cons(a, cons(b, cons(b, nil)))  ;  _me -> s(s(s(z)))  ;  l1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 54, which took 0.453239 s (model generation: 0.448888,  model checking: 0.004351):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 39
() -> length([nil, z]) -> 39
() -> reverse([nil, nil]) -> 39
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 42
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 40
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 43
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 40
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, cons(b, nil))  ;  _ce -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  h1 -> b  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 55, which took 0.617647 s (model generation: 0.615525,  model checking: 0.002122):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1069},
Q_f={q_gen_1009, q_gen_1022, q_gen_1032},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1069, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1032
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1032) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1069
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> length([nil, z]) -> 40
() -> reverse([nil, nil]) -> 40
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 42
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 43
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 43
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 41
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 56, which took 0.597899 s (model generation: 0.596257,  model checking: 0.001642):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046, q_gen_1069},
Q_f={q_gen_1009, q_gen_1022, q_gen_1032},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1009
<cons, cons>(q_gen_1069, q_gen_1044) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1022
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1032
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1032) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1044
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1069
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 41
() -> length([nil, z]) -> 41
() -> reverse([nil, nil]) -> 41
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 45
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 43
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 43
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 42
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(a, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 57, which took 0.467878 s (model generation: 0.464996,  model checking: 0.002882):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046, q_gen_1069},
Q_f={q_gen_1009, q_gen_1022, q_gen_1032},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1069, q_gen_1032) -> q_gen_1009
<cons, cons>(q_gen_1069, q_gen_1044) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1022
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1022
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1022
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1032
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1022) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1044
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1069
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 42
() -> length([nil, z]) -> 42
() -> reverse([nil, nil]) -> 42
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 45
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 43
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 46
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 43
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(z)  ;  _le -> cons(a, cons(b, nil))  ;  _me -> s(s(z))  ;  l1 -> cons(a, nil)
})

-------------------------------------------
Step 58, which took 0.585262 s (model generation: 0.580832,  model checking: 0.004430):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1083, q_gen_1101},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<a>() -> q_gen_1083
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1083, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1083, q_gen_1101) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, cons>(q_gen_1083, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<nil, nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 43
() -> length([nil, z]) -> 43
() -> reverse([nil, nil]) -> 43
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 45
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 46
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 46
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 44
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(a, cons(a, nil))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 59, which took 0.627167 s (model generation: 0.623577,  model checking: 0.003590):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1083, q_gen_1101},
Q_f={q_gen_1011},
Delta=
{
<cons>(q_gen_1083, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<a>() -> q_gen_1083
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, cons>(q_gen_1083, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<nil, nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> length([nil, z]) -> 44
() -> reverse([nil, nil]) -> 44
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 48
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 46
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 46
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 45
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> nil  ;  _ce -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 60, which took 2.773405 s (model generation: 2.769148,  model checking: 0.004257):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1101, q_gen_1113},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1113
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1113) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1113) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1057) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 45
() -> length([nil, z]) -> 45
() -> reverse([nil, nil]) -> 45
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 48
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 46
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 49
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 46
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(z))  ;  _le -> cons(a, cons(b, nil))  ;  _me -> s(s(s(s(z))))  ;  l1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 61, which took 0.722387 s (model generation: 0.694051,  model checking: 0.028336):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046, q_gen_1070},
Q_f={q_gen_1009, q_gen_1022, q_gen_1032},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1022) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1032) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<a, b>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1070, q_gen_1009) -> q_gen_1043
<cons, cons>(q_gen_1070, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1044
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1044
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1044
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1044
<b, a>() -> q_gen_1070
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 46
() -> length([nil, z]) -> 46
() -> reverse([nil, nil]) -> 46
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 51
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 47
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 49
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 47
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(b, nil))  ;  h1 -> a  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 62, which took 1.124234 s (model generation: 1.121884,  model checking: 0.002350):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1101, q_gen_1113},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1113
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1113) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1113) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1080},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1080
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1080) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1080) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 47
() -> length([nil, z]) -> 47
() -> reverse([nil, nil]) -> 47
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 51
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 47
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 49
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 50
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 63, which took 1.329263 s (model generation: 1.323544,  model checking: 0.005719):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1101, q_gen_1113},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1113
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1113) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1113) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1080},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1080
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1080) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, s>(q_gen_1080) -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 47
() -> length([nil, z]) -> 47
() -> reverse([nil, nil]) -> 47
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 51
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 50
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 49
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 50
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, cons(b, nil)))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 64, which took 1.051316 s (model generation: 1.049541,  model checking: 0.001775):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1080},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1080
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1080) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, s>(q_gen_1080) -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1117},
Q_f={q_gen_1009},
Delta=
{
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1117
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, cons>(q_gen_1046, q_gen_1117) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 48
() -> length([nil, z]) -> 48
() -> reverse([nil, nil]) -> 48
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 51
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 50
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 52
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 50
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> z  ;  _le -> cons(a, cons(b, nil))  ;  _me -> s(s(z))  ;  l1 -> nil
})

-------------------------------------------
Step 65, which took 1.084708 s (model generation: 1.048063,  model checking: 0.036645):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<a, b>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> length([nil, z]) -> 49
() -> reverse([nil, nil]) -> 49
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 51
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 53
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 52
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 51
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 66, which took 1.129293 s (model generation: 1.125582,  model checking: 0.003711):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1022
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<a, b>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> length([nil, z]) -> 50
() -> reverse([nil, nil]) -> 50
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 54
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 53
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 52
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 52
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 67, which took 1.520590 s (model generation: 1.515450,  model checking: 0.005140):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011, q_gen_1027},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1070},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1070, q_gen_1022) -> q_gen_1022
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1070, q_gen_1009) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<b, a>() -> q_gen_1070
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 51
() -> length([nil, z]) -> 51
() -> reverse([nil, nil]) -> 51
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 54
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 53
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 55
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 53
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(s(z)))  ;  _le -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _me -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 68, which took 6.457395 s (model generation: 6.451858,  model checking: 0.005537):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1080},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1080
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1080) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, s>(q_gen_1080) -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<a, b>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1044) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 52
() -> length([nil, z]) -> 52
() -> reverse([nil, nil]) -> 52
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 54
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 53
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 55
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 56
}
Sat witness: Found: ((length([ll, _ge])) -> length([cons(x, ll), s(_ge)]), {
_ge -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 69, which took 4.591031 s (model generation: 4.585977,  model checking: 0.005054):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1018, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011, q_gen_1018},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1018) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1018
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1018
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1018
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1018
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1080},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1080) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1080
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1080) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, s>(q_gen_1080) -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1070},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<b, a>() -> q_gen_1070
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> length([nil, z]) -> 53
() -> reverse([nil, nil]) -> 53
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 54
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 56
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 55
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 56
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 70, which took 2.667156 s (model generation: 2.665190,  model checking: 0.001966):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1080},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1080) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1080
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1080) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, s>(q_gen_1080) -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1044) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1044
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 54
() -> length([nil, z]) -> 54
() -> reverse([nil, nil]) -> 54
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 57
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 56
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 55
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 56
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> a  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 71, which took 2.724067 s (model generation: 2.722009,  model checking: 0.002058):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050, q_gen_1101, q_gen_1113},
Q_f={q_gen_1011, q_gen_1027},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1113
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1113) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1027
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1113) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1080},
Q_f={q_gen_1010},
Delta=
{
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1013
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1080) -> q_gen_1038
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1080
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, s>(q_gen_1080) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, s>(q_gen_1080) -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1039
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<a, b>() -> q_gen_1023
<b, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 55
() -> length([nil, z]) -> 55
() -> reverse([nil, nil]) -> 55
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 57
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 56
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 58
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 56
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(z)  ;  _le -> cons(a, nil)  ;  _me -> s(s(s(s(z))))  ;  l1 -> cons(a, nil)
})

-------------------------------------------
Step 72, which took 5.876481 s (model generation: 5.840707,  model checking: 0.035774):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1026, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050, q_gen_1101},
Q_f={q_gen_1011, q_gen_1026},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1026) -> q_gen_1026
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1026
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1026
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1026
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1068, q_gen_1069},
Q_f={q_gen_1009},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1068) -> q_gen_1009
<cons, cons>(q_gen_1069, q_gen_1068) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<a, a>() -> q_gen_1023
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1068
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1069
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 56
() -> length([nil, z]) -> 56
() -> reverse([nil, nil]) -> 56
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 60
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 57
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 58
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 57
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(a, nil))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 73, which took 3.069301 s (model generation: 3.067720,  model checking: 0.001581):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1018, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050, q_gen_1083, q_gen_1093, q_gen_1101},
Q_f={q_gen_1011, q_gen_1018},
Delta=
{
<cons>(q_gen_1083, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<a>() -> q_gen_1083
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1050
<cons, cons, cons>(q_gen_1030, q_gen_1018) -> q_gen_1011
<cons, cons, cons>(q_gen_1093, q_gen_1042) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, cons>(q_gen_1083, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1018
<cons, cons, cons>(q_gen_1093, q_gen_1011) -> q_gen_1018
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1018
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1018
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1018
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<cons, cons, cons>(q_gen_1093, q_gen_1018) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
<nil, nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1042
<a, a, a>() -> q_gen_1093
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<s>(q_gen_1038) -> q_gen_1038
<z>() -> q_gen_1038
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046, q_gen_1069},
Q_f={q_gen_1009, q_gen_1022, q_gen_1032},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1009
<cons, cons>(q_gen_1069, q_gen_1032) -> q_gen_1009
<cons, cons>(q_gen_1069, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1022
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<a, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1009) -> q_gen_1043
<cons, cons>(q_gen_1069, q_gen_1022) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<a, b>() -> q_gen_1069
<b, a>() -> q_gen_1069
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 57
() -> length([nil, z]) -> 57
() -> reverse([nil, nil]) -> 57
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 60
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 60
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 58
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 58
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 74, which took 3.969268 s (model generation: 3.963250,  model checking: 0.006018):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1027, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1050, q_gen_1101, q_gen_1113},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1113
<cons, nil, cons>(q_gen_1017, q_gen_1113) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, cons, cons>(q_gen_1030, q_gen_1027) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1027
<nil, cons, cons>(q_gen_1017, q_gen_1113) -> q_gen_1027
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1027
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1057, q_gen_1072},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1010
<cons, s>(q_gen_1072, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1057) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1072, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1072, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1072
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1022
<a, b>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<b, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 58
() -> length([nil, z]) -> 58
() -> reverse([nil, nil]) -> 58
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 60
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 60
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 61
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 59
}
Sat witness: Found: ((length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]), {
_ke -> s(s(s(z)))  ;  _le -> cons(a, cons(b, nil))  ;  _me -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 75, which took 4.078166 s (model generation: 4.052998,  model checking: 0.025168):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1016, q_gen_1017, q_gen_1018, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050, q_gen_1101, q_gen_1113},
Q_f={q_gen_1011, q_gen_1018},
Delta=
{
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1101
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1113
<cons, cons, cons>(q_gen_1030, q_gen_1018) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1011
<cons, nil, cons>(q_gen_1017, q_gen_1113) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1018
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1018
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1018
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1018
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1113) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1045, q_gen_1046},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1022
<a, b>() -> q_gen_1023
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<b, a>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 59
() -> length([nil, z]) -> 59
() -> reverse([nil, nil]) -> 59
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 60
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 63
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 61
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 60
}
Sat witness: Found: ((append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]), {
_wd -> cons(b, cons(a, cons(a, cons(b, cons(b, nil)))))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, cons(a, cons(b, nil))))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 76, which took 4.099815 s (model generation: 4.094148,  model checking: 0.005667):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1042, q_gen_1050},
Q_f={q_gen_1011, q_gen_1015},
Delta=
{
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1028
<nil>() -> q_gen_1028
<a>() -> q_gen_1029
<b>() -> q_gen_1029
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<a, a>() -> q_gen_1017
<a, b>() -> q_gen_1017
<b, a>() -> q_gen_1017
<b, b>() -> q_gen_1017
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1015
<cons, cons, cons>(q_gen_1030, q_gen_1042) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<a, a, a>() -> q_gen_1030
<a, b, a>() -> q_gen_1030
<b, a, b>() -> q_gen_1030
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1042
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1042
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057},
Q_f={q_gen_1010},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<a>() -> q_gen_1036
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1010
<nil, z>() -> q_gen_1010
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<a, s>(q_gen_1038) -> q_gen_1037
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1023, q_gen_1032, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046, q_gen_1070},
Q_f={q_gen_1009, q_gen_1032},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<a>() -> q_gen_1046
<b>() -> q_gen_1046
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1032) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1044) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<b, b>() -> q_gen_1023
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1032
<cons, cons>(q_gen_1033, q_gen_1032) -> q_gen_1032
<a, a>() -> q_gen_1033
<a, b>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1032) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1044
<cons, cons>(q_gen_1033, q_gen_1044) -> q_gen_1044
<cons, cons>(q_gen_1070, q_gen_1009) -> q_gen_1044
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1044
<b, a>() -> q_gen_1070
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 60
() -> length([nil, z]) -> 60
() -> reverse([nil, nil]) -> 60
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 63
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 63
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 61
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 61
}
Sat witness: Found: ((append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]), {
_be -> cons(a, nil)  ;  _ce -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> a  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 77, which took 4.018848 s (model generation: 4.017733,  model checking: 0.001115):

Model:
|_
{
append -> 
{{{
Q={q_gen_1011, q_gen_1015, q_gen_1016, q_gen_1017, q_gen_1020, q_gen_1028, q_gen_1029, q_gen_1030, q_gen_1040, q_gen_1050, q_gen_1066, q_gen_1083, q_gen_1101, q_gen_1114, q_gen_1147, q_gen_1157, q_gen_1160, q_gen_1189},
Q_f={q_gen_1011, q_gen_1015, q_gen_1157, q_gen_1160},
Delta=
{
<nil>() -> q_gen_1028
<b>() -> q_gen_1029
<a>() -> q_gen_1083
<cons>(q_gen_1029, q_gen_1028) -> q_gen_1101
<cons>(q_gen_1029, q_gen_1101) -> q_gen_1114
<cons>(q_gen_1083, q_gen_1028) -> q_gen_1114
<cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1016
<cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1016
<nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1016
<nil, cons>(q_gen_1083, q_gen_1114) -> q_gen_1016
<nil, nil>() -> q_gen_1016
<b, b>() -> q_gen_1017
<a, a>() -> q_gen_1020
<a, b>() -> q_gen_1020
<b, a>() -> q_gen_1020
<cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1050
<nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1050
<cons, cons>(q_gen_1020, q_gen_1050) -> q_gen_1189
<cons, cons, cons>(q_gen_1030, q_gen_1015) -> q_gen_1011
<cons, cons, cons>(q_gen_1066, q_gen_1015) -> q_gen_1011
<nil, nil, cons>(q_gen_1029, q_gen_1101) -> q_gen_1011
<nil, nil, cons>(q_gen_1083, q_gen_1101) -> q_gen_1011
<nil, nil, nil>() -> q_gen_1011
<cons, cons, cons>(q_gen_1066, q_gen_1040) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<cons, nil, cons>(q_gen_1017, q_gen_1050) -> q_gen_1015
<nil, cons, cons>(q_gen_1017, q_gen_1016) -> q_gen_1015
<nil, cons, cons>(q_gen_1020, q_gen_1016) -> q_gen_1015
<nil, nil, cons>(q_gen_1029, q_gen_1028) -> q_gen_1015
<b, b, b>() -> q_gen_1030
<cons, cons, cons>(q_gen_1030, q_gen_1011) -> q_gen_1040
<cons, cons, cons>(q_gen_1066, q_gen_1011) -> q_gen_1040
<cons, nil, cons>(q_gen_1020, q_gen_1016) -> q_gen_1040
<nil, cons, cons>(q_gen_1017, q_gen_1050) -> q_gen_1040
<nil, cons, cons>(q_gen_1020, q_gen_1050) -> q_gen_1040
<nil, nil, cons>(q_gen_1083, q_gen_1028) -> q_gen_1040
<a, a, a>() -> q_gen_1066
<a, b, a>() -> q_gen_1066
<b, a, b>() -> q_gen_1066
<cons, cons, cons>(q_gen_1030, q_gen_1040) -> q_gen_1147
<nil, nil, cons>(q_gen_1083, q_gen_1114) -> q_gen_1147
<cons, cons, cons>(q_gen_1066, q_gen_1147) -> q_gen_1157
<cons, cons, cons>(q_gen_1030, q_gen_1160) -> q_gen_1160
<cons, cons, cons>(q_gen_1066, q_gen_1160) -> q_gen_1160
<cons, nil, cons>(q_gen_1020, q_gen_1050) -> q_gen_1160
<nil, cons, cons>(q_gen_1020, q_gen_1189) -> q_gen_1160
<nil, nil, cons>(q_gen_1029, q_gen_1114) -> q_gen_1160
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1010, q_gen_1012, q_gen_1013, q_gen_1014, q_gen_1035, q_gen_1036, q_gen_1037, q_gen_1038, q_gen_1039, q_gen_1055, q_gen_1056, q_gen_1057, q_gen_1064, q_gen_1086},
Q_f={q_gen_1010, q_gen_1012},
Delta=
{
<nil>() -> q_gen_1013
<cons>(q_gen_1036, q_gen_1013) -> q_gen_1035
<cons>(q_gen_1036, q_gen_1055) -> q_gen_1035
<b>() -> q_gen_1036
<z>() -> q_gen_1038
<cons>(q_gen_1036, q_gen_1035) -> q_gen_1055
<cons>(q_gen_1064, q_gen_1013) -> q_gen_1055
<s>(q_gen_1038) -> q_gen_1057
<s>(q_gen_1057) -> q_gen_1057
<a>() -> q_gen_1064
<cons>(q_gen_1036, q_gen_1086) -> q_gen_1086
<cons>(q_gen_1064, q_gen_1035) -> q_gen_1086
<cons, s>(q_gen_1037, q_gen_1035) -> q_gen_1010
<cons, s>(q_gen_1037, q_gen_1055) -> q_gen_1010
<cons, s>(q_gen_1056, q_gen_1086) -> q_gen_1010
<nil, z>() -> q_gen_1010
<cons, s>(q_gen_1014, q_gen_1013) -> q_gen_1012
<cons, s>(q_gen_1014, q_gen_1035) -> q_gen_1012
<cons, s>(q_gen_1056, q_gen_1055) -> q_gen_1012
<a, s>(q_gen_1038) -> q_gen_1014
<a, z>() -> q_gen_1014
<b, z>() -> q_gen_1014
<b, s>(q_gen_1038) -> q_gen_1037
<cons, s>(q_gen_1014, q_gen_1055) -> q_gen_1039
<cons, s>(q_gen_1037, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1013) -> q_gen_1039
<cons, s>(q_gen_1056, q_gen_1035) -> q_gen_1039
<a, s>(q_gen_1057) -> q_gen_1056
<b, s>(q_gen_1057) -> q_gen_1056
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_1009, q_gen_1022, q_gen_1023, q_gen_1033, q_gen_1043, q_gen_1044, q_gen_1045, q_gen_1046, q_gen_1070, q_gen_1116, q_gen_1118},
Q_f={q_gen_1009, q_gen_1022},
Delta=
{
<cons>(q_gen_1046, q_gen_1045) -> q_gen_1045
<cons>(q_gen_1118, q_gen_1045) -> q_gen_1045
<nil>() -> q_gen_1045
<b>() -> q_gen_1046
<a>() -> q_gen_1118
<cons, cons>(q_gen_1023, q_gen_1116) -> q_gen_1009
<cons, cons>(q_gen_1070, q_gen_1043) -> q_gen_1009
<nil, nil>() -> q_gen_1009
<cons, cons>(q_gen_1023, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1033, q_gen_1009) -> q_gen_1022
<cons, cons>(q_gen_1033, q_gen_1022) -> q_gen_1022
<cons, cons>(q_gen_1070, q_gen_1022) -> q_gen_1022
<b, b>() -> q_gen_1023
<a, a>() -> q_gen_1033
<a, b>() -> q_gen_1033
<cons, cons>(q_gen_1023, q_gen_1044) -> q_gen_1043
<cons, cons>(q_gen_1033, q_gen_1043) -> q_gen_1043
<cons, cons>(q_gen_1070, q_gen_1009) -> q_gen_1043
<nil, cons>(q_gen_1046, q_gen_1045) -> q_gen_1043
<cons, cons>(q_gen_1023, q_gen_1022) -> q_gen_1044
<cons, cons>(q_gen_1023, q_gen_1043) -> q_gen_1044
<cons, nil>(q_gen_1046, q_gen_1045) -> q_gen_1044
<b, a>() -> q_gen_1070
<cons, cons>(q_gen_1033, q_gen_1044) -> q_gen_1116
<cons, cons>(q_gen_1070, q_gen_1044) -> q_gen_1116
<nil, cons>(q_gen_1118, q_gen_1045) -> q_gen_1116
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 63
() -> length([nil, z]) -> 61
() -> reverse([nil, nil]) -> 61
(append([_be, cons(h1, nil), _ce]) /\ reverse([t1, _be])) -> reverse([cons(h1, t1), _ce]) -> 63
(append([t1, l2, _wd])) -> append([cons(h1, t1), l2, cons(h1, _wd)]) -> 63
(length([_le, _me]) /\ length([l1, _ke]) /\ reverse([l1, _le])) -> eq_nat([_ke, _me]) -> 61
(length([ll, _ge])) -> length([cons(x, ll), s(_ge)]) -> 61
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(b, nil))
})

Total time: 66.819906
Reason for stopping: DontKnow. Stopped because: timeout