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:
{
(leq, P:
{() -> leq([a, y])
() -> leq([b, b])
(leq([b, a])) -> BOT}
)
(insert, F:
{() -> insert([x, nil, cons(x, nil)])
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)])
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))])}
(insert([_fm, _gm, _hm]) /\ insert([_fm, _gm, _im])) -> eq_eltlist([_hm, _im])
)
(length, F:
{() -> length([nil, z])
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)])}
(length([_km, _lm]) /\ length([_km, _mm])) -> eq_nat([_lm, _mm])
)
}

properties:
{(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm])}


over-approximation: {insert, length}
under-approximation: {leq}

Clause system for inference is:

{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 0
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 0
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 0
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 0
(leq([b, a])) -> BOT -> 0
}


Solving took 64.992189 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3140, q_gen_3141, q_gen_3142, q_gen_3147, q_gen_3148, q_gen_3150, q_gen_3151, q_gen_3152, q_gen_3153, q_gen_3156, q_gen_3157, q_gen_3158, q_gen_3159, q_gen_3160, q_gen_3161, q_gen_3162, q_gen_3168, q_gen_3185, q_gen_3186, q_gen_3187, q_gen_3196, q_gen_3201, q_gen_3204, q_gen_3206, q_gen_3208, q_gen_3209, q_gen_3210, q_gen_3213, q_gen_3214, q_gen_3215, q_gen_3216, q_gen_3217, q_gen_3218, q_gen_3219, q_gen_3225, q_gen_3226, q_gen_3227, q_gen_3228, q_gen_3229, q_gen_3230, q_gen_3234, q_gen_3236, q_gen_3241, q_gen_3242, q_gen_3243, q_gen_3244, q_gen_3245, q_gen_3252, q_gen_3253, q_gen_3254, q_gen_3255, q_gen_3261, q_gen_3262, q_gen_3263, q_gen_3266, q_gen_3267, q_gen_3279, q_gen_3280, q_gen_3281, q_gen_3287, q_gen_3288, q_gen_3289, q_gen_3299, q_gen_3302, q_gen_3303, q_gen_3304, q_gen_3313, q_gen_3314, q_gen_3315, q_gen_3316, q_gen_3321, q_gen_3322, q_gen_3323, q_gen_3324, q_gen_3325, q_gen_3326, q_gen_3327, q_gen_3340, q_gen_3343},
Q_f={},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<a>() -> q_gen_3151
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<b, a>() -> q_gen_3153
<nil, cons>(q_gen_3151, q_gen_3138) -> q_gen_3157
<cons, cons>(q_gen_3148, q_gen_3157) -> q_gen_3159
<cons, cons>(q_gen_3162, q_gen_3157) -> q_gen_3161
<a, b>() -> q_gen_3162
<cons, cons>(q_gen_3142, q_gen_3187) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3187
<cons, cons>(q_gen_3153, q_gen_3187) -> q_gen_3210
<cons, cons>(q_gen_3153, q_gen_3141) -> q_gen_3215
<cons, cons>(q_gen_3148, q_gen_3215) -> q_gen_3217
<cons, cons>(q_gen_3162, q_gen_3159) -> q_gen_3219
<cons, cons>(q_gen_3142, q_gen_3157) -> q_gen_3228
<cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3230
<cons, cons>(q_gen_3153, q_gen_3228) -> q_gen_3243
<cons, cons>(q_gen_3142, q_gen_3161) -> q_gen_3245
<cons, cons>(q_gen_3153, q_gen_3255) -> q_gen_3254
<cons, cons>(q_gen_3153, q_gen_3210) -> q_gen_3255
<cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3263
<cons, cons>(q_gen_3142, q_gen_3281) -> q_gen_3280
<cons, cons>(q_gen_3142, q_gen_3210) -> q_gen_3281
<cons, cons>(q_gen_3142, q_gen_3289) -> q_gen_3288
<cons, cons>(q_gen_3142, q_gen_3255) -> q_gen_3289
<cons, cons>(q_gen_3153, q_gen_3304) -> q_gen_3303
<cons, cons>(q_gen_3153, q_gen_3186) -> q_gen_3304
<cons, cons>(q_gen_3153, q_gen_3315) -> q_gen_3314
<cons, cons>(q_gen_3142, q_gen_3316) -> q_gen_3315
<cons, cons>(q_gen_3142, q_gen_3228) -> q_gen_3316
<cons, cons>(q_gen_3148, q_gen_3323) -> q_gen_3322
<cons, cons>(q_gen_3148, q_gen_3324) -> q_gen_3323
<cons, cons>(q_gen_3142, q_gen_3325) -> q_gen_3324
<cons, cons>(q_gen_3148, q_gen_3326) -> q_gen_3325
<cons, cons>(q_gen_3148, q_gen_3327) -> q_gen_3326
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3327
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3140
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3147
<a, nil, cons>(q_gen_3151, q_gen_3138) -> q_gen_3150
<a, cons, cons>(q_gen_3153, q_gen_3141) -> q_gen_3152
<b, cons, cons>(q_gen_3148, q_gen_3157) -> q_gen_3156
<b, cons, cons>(q_gen_3148, q_gen_3159) -> q_gen_3158
<b, cons, cons>(q_gen_3142, q_gen_3161) -> q_gen_3160
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3168
<a, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3196
<a, cons, cons>(q_gen_3148, q_gen_3159) -> q_gen_3201
<a, cons, cons>(q_gen_3162, q_gen_3186) -> q_gen_3204
<b, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3206
<b, cons, cons>(q_gen_3153, q_gen_3187) -> q_gen_3208
<b, cons, cons>(q_gen_3148, q_gen_3210) -> q_gen_3209
<a, cons, cons>(q_gen_3153, q_gen_3187) -> q_gen_3213
<b, cons, cons>(q_gen_3148, q_gen_3215) -> q_gen_3214
<b, cons, cons>(q_gen_3148, q_gen_3217) -> q_gen_3216
<a, cons, cons>(q_gen_3153, q_gen_3219) -> q_gen_3218
<a, cons, cons>(q_gen_3148, q_gen_3157) -> q_gen_3225
<b, cons, cons>(q_gen_3142, q_gen_3157) -> q_gen_3226
<b, cons, cons>(q_gen_3148, q_gen_3228) -> q_gen_3227
<b, cons, cons>(q_gen_3148, q_gen_3230) -> q_gen_3229
<a, cons, cons>(q_gen_3148, q_gen_3230) -> q_gen_3234
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3236
<b, cons, cons>(q_gen_3153, q_gen_3228) -> q_gen_3241
<b, cons, cons>(q_gen_3148, q_gen_3243) -> q_gen_3242
<a, cons, cons>(q_gen_3153, q_gen_3245) -> q_gen_3244
<a, cons, cons>(q_gen_3153, q_gen_3230) -> q_gen_3252
<a, cons, cons>(q_gen_3142, q_gen_3254) -> q_gen_3253
<b, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3261
<b, cons, cons>(q_gen_3148, q_gen_3263) -> q_gen_3262
<b, cons, cons>(q_gen_3142, q_gen_3187) -> q_gen_3266
<a, cons, cons>(q_gen_3162, q_gen_3141) -> q_gen_3267
<a, cons, cons>(q_gen_3153, q_gen_3280) -> q_gen_3279
<b, cons, cons>(q_gen_3148, q_gen_3288) -> q_gen_3287
<a, cons, cons>(q_gen_3162, q_gen_3230) -> q_gen_3299
<a, cons, cons>(q_gen_3148, q_gen_3303) -> q_gen_3302
<b, cons, cons>(q_gen_3142, q_gen_3314) -> q_gen_3313
<b, cons, cons>(q_gen_3153, q_gen_3322) -> q_gen_3321
<b, cons, cons>(q_gen_3148, q_gen_3314) -> q_gen_3340
<a, cons, cons>(q_gen_3148, q_gen_3254) -> q_gen_3343
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3143, q_gen_3144, q_gen_3145, q_gen_3154, q_gen_3155, q_gen_3163, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3170, q_gen_3171, q_gen_3172, q_gen_3173, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3178, q_gen_3179, q_gen_3180, q_gen_3181, q_gen_3182, q_gen_3183, q_gen_3184, q_gen_3188, q_gen_3189, q_gen_3190, q_gen_3191, q_gen_3192, q_gen_3193, q_gen_3194, q_gen_3195, q_gen_3197, q_gen_3198, q_gen_3199, q_gen_3200, q_gen_3202, q_gen_3203, q_gen_3205, q_gen_3207, q_gen_3211, q_gen_3212, q_gen_3220, q_gen_3221, q_gen_3222, q_gen_3223, q_gen_3224, q_gen_3231, q_gen_3232, q_gen_3233, q_gen_3235, q_gen_3237, q_gen_3238, q_gen_3239, q_gen_3240, q_gen_3246, q_gen_3247, q_gen_3248, q_gen_3249, q_gen_3250, q_gen_3251, q_gen_3256, q_gen_3257, q_gen_3258, q_gen_3259, q_gen_3260, q_gen_3264, q_gen_3265, q_gen_3268, q_gen_3269, q_gen_3270, q_gen_3271, q_gen_3272, q_gen_3273, q_gen_3274, q_gen_3275, q_gen_3276, q_gen_3277, q_gen_3278, q_gen_3282, q_gen_3283, q_gen_3284, q_gen_3285, q_gen_3286, q_gen_3290, q_gen_3291, q_gen_3292, q_gen_3293, q_gen_3294, q_gen_3295, q_gen_3296, q_gen_3297, q_gen_3298, q_gen_3300, q_gen_3301, q_gen_3305, q_gen_3306, q_gen_3307, q_gen_3308, q_gen_3309, q_gen_3310, q_gen_3311, q_gen_3312, q_gen_3317, q_gen_3318, q_gen_3319, q_gen_3320, q_gen_3328, q_gen_3329, q_gen_3330, q_gen_3331, q_gen_3332, q_gen_3333, q_gen_3334, q_gen_3335, q_gen_3336, q_gen_3337, q_gen_3338, q_gen_3339, q_gen_3341, q_gen_3342, q_gen_3344, q_gen_3345, q_gen_3346},
Q_f={},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3193
<s>(q_gen_3177) -> q_gen_3195
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3222
<s>(q_gen_3195) -> q_gen_3224
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3232
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3247
<cons>(q_gen_3165, q_gen_3247) -> q_gen_3249
<s>(q_gen_3224) -> q_gen_3251
<cons>(q_gen_3175, q_gen_3258) -> q_gen_3257
<cons>(q_gen_3175, q_gen_3259) -> q_gen_3258
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3259
<cons>(q_gen_3165, q_gen_3259) -> q_gen_3271
<cons>(q_gen_3165, q_gen_3271) -> q_gen_3283
<cons>(q_gen_3165, q_gen_3292) -> q_gen_3291
<cons>(q_gen_3165, q_gen_3258) -> q_gen_3292
<cons>(q_gen_3165, q_gen_3232) -> q_gen_3294
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3296
<cons>(q_gen_3165, q_gen_3296) -> q_gen_3298
<cons>(q_gen_3175, q_gen_3307) -> q_gen_3306
<cons>(q_gen_3175, q_gen_3189) -> q_gen_3307
<cons>(q_gen_3175, q_gen_3298) -> q_gen_3310
<cons>(q_gen_3175, q_gen_3310) -> q_gen_3312
<cons>(q_gen_3175, q_gen_3319) -> q_gen_3318
<cons>(q_gen_3165, q_gen_3320) -> q_gen_3319
<cons>(q_gen_3165, q_gen_3298) -> q_gen_3320
<cons>(q_gen_3175, q_gen_3330) -> q_gen_3329
<cons>(q_gen_3175, q_gen_3331) -> q_gen_3330
<cons>(q_gen_3165, q_gen_3332) -> q_gen_3331
<cons>(q_gen_3175, q_gen_3193) -> q_gen_3332
<cons>(q_gen_3175, q_gen_3335) -> q_gen_3334
<cons>(q_gen_3175, q_gen_3336) -> q_gen_3335
<cons>(q_gen_3165, q_gen_3337) -> q_gen_3336
<cons>(q_gen_3175, q_gen_3338) -> q_gen_3337
<cons>(q_gen_3175, q_gen_3296) -> q_gen_3338
<nil, z>() -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3143
<b, z>() -> q_gen_3145
<cons, s>(q_gen_3155, q_gen_3144) -> q_gen_3154
<a, z>() -> q_gen_3155
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3163
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3171, q_gen_3164) -> q_gen_3170
<a, s>(q_gen_3167) -> q_gen_3171
<cons, s>(q_gen_3171, q_gen_3144) -> q_gen_3172
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3173
<b, s>(q_gen_3177) -> q_gen_3176
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3178
<a, s>(q_gen_3177) -> q_gen_3179
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3180
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3181
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3182
<cons, s>(q_gen_3179, q_gen_3184) -> q_gen_3183
<cons, s>(q_gen_3171, q_gen_3189) -> q_gen_3188
<cons, s>(q_gen_3179, q_gen_3190) -> q_gen_3191
<cons, s>(q_gen_3194, q_gen_3193) -> q_gen_3192
<b, s>(q_gen_3195) -> q_gen_3194
<cons, s>(q_gen_3176, q_gen_3189) -> q_gen_3197
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3198
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3199
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3200
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3202
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3203
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3205
<cons, s>(q_gen_3179, q_gen_3189) -> q_gen_3207
<cons, s>(q_gen_3212, q_gen_3184) -> q_gen_3211
<a, s>(q_gen_3195) -> q_gen_3212
<cons, s>(q_gen_3212, q_gen_3144) -> q_gen_3220
<cons, s>(q_gen_3223, q_gen_3222) -> q_gen_3221
<b, s>(q_gen_3224) -> q_gen_3223
<cons, s>(q_gen_3179, q_gen_3232) -> q_gen_3231
<cons, s>(q_gen_3212, q_gen_3189) -> q_gen_3233
<cons, s>(q_gen_3212, q_gen_3232) -> q_gen_3235
<cons, s>(q_gen_3238, q_gen_3164) -> q_gen_3237
<a, s>(q_gen_3224) -> q_gen_3238
<cons, s>(q_gen_3171, q_gen_3174) -> q_gen_3239
<cons, s>(q_gen_3179, q_gen_3193) -> q_gen_3240
<cons, s>(q_gen_3223, q_gen_3247) -> q_gen_3246
<cons, s>(q_gen_3250, q_gen_3249) -> q_gen_3248
<b, s>(q_gen_3251) -> q_gen_3250
<cons, s>(q_gen_3176, q_gen_3257) -> q_gen_3256
<cons, s>(q_gen_3145, q_gen_3232) -> q_gen_3260
<cons, s>(q_gen_3212, q_gen_3174) -> q_gen_3264
<cons, s>(q_gen_3223, q_gen_3193) -> q_gen_3265
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3268
<cons, s>(q_gen_3194, q_gen_3259) -> q_gen_3269
<cons, s>(q_gen_3223, q_gen_3271) -> q_gen_3270
<cons, s>(q_gen_3238, q_gen_3190) -> q_gen_3272
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3273
<cons, s>(q_gen_3171, q_gen_3247) -> q_gen_3274
<cons, s>(q_gen_3238, q_gen_3144) -> q_gen_3275
<cons, s>(q_gen_3238, q_gen_3184) -> q_gen_3276
<cons, s>(q_gen_3278, q_gen_3222) -> q_gen_3277
<a, s>(q_gen_3251) -> q_gen_3278
<cons, s>(q_gen_3171, q_gen_3283) -> q_gen_3282
<cons, s>(q_gen_3166, q_gen_3232) -> q_gen_3284
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3285
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3286
<cons, s>(q_gen_3155, q_gen_3291) -> q_gen_3290
<cons, s>(q_gen_3171, q_gen_3294) -> q_gen_3293
<cons, s>(q_gen_3194, q_gen_3296) -> q_gen_3295
<cons, s>(q_gen_3238, q_gen_3298) -> q_gen_3297
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3300
<cons, s>(q_gen_3212, q_gen_3190) -> q_gen_3301
<cons, s>(q_gen_3212, q_gen_3306) -> q_gen_3305
<cons, s>(q_gen_3155, q_gen_3232) -> q_gen_3308
<cons, s>(q_gen_3179, q_gen_3310) -> q_gen_3309
<cons, s>(q_gen_3212, q_gen_3312) -> q_gen_3311
<cons, s>(q_gen_3194, q_gen_3318) -> q_gen_3317
<cons, s>(q_gen_3212, q_gen_3329) -> q_gen_3328
<cons, s>(q_gen_3145, q_gen_3334) -> q_gen_3333
<cons, s>(q_gen_3238, q_gen_3247) -> q_gen_3339
<cons, s>(q_gen_3179, q_gen_3318) -> q_gen_3341
<cons, s>(q_gen_3166, q_gen_3296) -> q_gen_3342
<cons, s>(q_gen_3212, q_gen_3257) -> q_gen_3344
<cons, s>(q_gen_3179, q_gen_3296) -> q_gen_3345
<cons, s>(q_gen_3212, q_gen_3338) -> q_gen_3346
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3135, q_gen_3146, q_gen_3149},
Q_f={},
Delta=
{
<b, b>() -> q_gen_3134
<a, b>() -> q_gen_3135
<b, a>() -> q_gen_3146
<a, a>() -> q_gen_3149
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.014661 s (model generation: 0.014368,  model checking: 0.000293):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 3
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 1
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 1
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([b, b]), {

})

-------------------------------------------
Step 1, which took 0.009307 s (model generation: 0.009263,  model checking: 0.000044):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134},
Q_f={q_gen_3134},
Delta=
{
<b, b>() -> q_gen_3134
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 1
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 1
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([a, y]), {
y -> b
})

-------------------------------------------
Step 2, which took 0.009784 s (model generation: 0.009710,  model checking: 0.000074):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134},
Q_f={q_gen_3134},
Delta=
{
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 1
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 1
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 3, which took 0.007431 s (model generation: 0.007282,  model checking: 0.000149):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136},
Q_f={q_gen_3136},
Delta=
{
<nil, z>() -> q_gen_3136
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134},
Q_f={q_gen_3134},
Delta=
{
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 1
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 1
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> insert([x, nil, cons(x, nil)]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.010389 s (model generation: 0.008235,  model checking: 0.002154):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136},
Q_f={q_gen_3136},
Delta=
{
<nil, z>() -> q_gen_3136
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134},
Q_f={q_gen_3134},
Delta=
{
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 1
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 1
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 5, which took 0.010629 s (model generation: 0.010519,  model checking: 0.000110):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, b>() -> q_gen_3142
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136},
Q_f={q_gen_3136},
Delta=
{
<nil, z>() -> q_gen_3136
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134},
Q_f={q_gen_3134},
Delta=
{
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 1
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 1
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 6, which took 0.009672 s (model generation: 0.009348,  model checking: 0.000324):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, b>() -> q_gen_3142
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134},
Q_f={q_gen_3134},
Delta=
{
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 1
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 4
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
}
Sat witness: Found: ((insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]), {
_em -> cons(b, nil)  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 7, which took 0.010137 s (model generation: 0.010015,  model checking: 0.000122):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134},
Q_f={q_gen_3134},
Delta=
{
<a, b>() -> q_gen_3134
<b, a>() -> q_gen_3134
<b, b>() -> q_gen_3134
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 2
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 4
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((leq([b, a])) -> BOT, {

})

-------------------------------------------
Step 8, which took 0.008489 s (model generation: 0.008306,  model checking: 0.000183):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 3
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 4
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: (() -> leq([a, y]), {
y -> a
})

-------------------------------------------
Step 9, which took 0.010795 s (model generation: 0.009140,  model checking: 0.001655):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 4
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 4
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: (() -> insert([x, nil, cons(x, nil)]), {
x -> a
})

-------------------------------------------
Step 10, which took 0.010204 s (model generation: 0.009772,  model checking: 0.000432):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 4
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 4
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 11, which took 0.010169 s (model generation: 0.009978,  model checking: 0.000191):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 4
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 4
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 12, which took 0.010689 s (model generation: 0.009713,  model checking: 0.000976):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 4
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 7
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]), {
_em -> cons(a, cons(a, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 13, which took 0.012538 s (model generation: 0.011263,  model checking: 0.001275):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 5
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 5
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 5
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 7
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 6
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 14, which took 0.012593 s (model generation: 0.011707,  model checking: 0.000886):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 6
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 6
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 6
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 7
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 15, which took 0.015198 s (model generation: 0.014565,  model checking: 0.000633):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3165, q_gen_3167},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3144
<nil>() -> q_gen_3144
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, s>(q_gen_3167) -> q_gen_3145
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 6
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 6
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 9
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 7
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> z  ;  _om -> cons(b, nil)  ;  _pm -> s(s(z))  ;  l -> nil  ;  x -> a
})

-------------------------------------------
Step 16, which took 0.016985 s (model generation: 0.015580,  model checking: 0.001405):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3151, q_gen_3168},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<a>() -> q_gen_3151
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<nil, cons>(q_gen_3151, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3151, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3168
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3165, q_gen_3167},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3144
<nil>() -> q_gen_3144
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, s>(q_gen_3167) -> q_gen_3145
<b, z>() -> q_gen_3145
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 8
() -> length([nil, z]) -> 7
() -> leq([a, y]) -> 8
() -> leq([b, b]) -> 7
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 12
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 8
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> z  ;  _om -> cons(b, nil)  ;  _pm -> s(s(z))  ;  l -> nil  ;  x -> b
})

-------------------------------------------
Step 17, which took 0.016165 s (model generation: 0.013772,  model checking: 0.002393):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 9
() -> length([nil, z]) -> 8
() -> leq([a, y]) -> 9
() -> leq([b, b]) -> 8
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 12
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 9
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 9
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 18, which took 0.017344 s (model generation: 0.015670,  model checking: 0.001674):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, s>(q_gen_3167) -> q_gen_3145
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 10
() -> length([nil, z]) -> 9
() -> leq([a, y]) -> 10
() -> leq([b, b]) -> 9
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 15
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 10
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 12
(leq([b, a])) -> BOT -> 10
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> z  ;  _om -> cons(a, nil)  ;  _pm -> s(s(z))  ;  l -> nil  ;  x -> a
})

-------------------------------------------
Step 19, which took 0.017615 s (model generation: 0.015249,  model checking: 0.002366):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 11
() -> length([nil, z]) -> 10
() -> leq([a, y]) -> 11
() -> leq([b, b]) -> 10
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 15
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 11
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 13
(leq([b, a])) -> BOT -> 11
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 20, which took 0.019118 s (model generation: 0.016794,  model checking: 0.002324):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3167) -> q_gen_3167
<z>() -> q_gen_3167
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 12
() -> length([nil, z]) -> 11
() -> leq([a, y]) -> 12
() -> leq([b, b]) -> 11
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 18
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 12
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 14
(leq([b, a])) -> BOT -> 12
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(a, cons(b, nil))  ;  _pm -> s(s(s(z)))  ;  l -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 21, which took 0.020531 s (model generation: 0.018453,  model checking: 0.002078):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, s>(q_gen_3177) -> q_gen_3145
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3177) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 13
() -> length([nil, z]) -> 12
() -> leq([a, y]) -> 13
() -> leq([b, b]) -> 12
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 18
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 13
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 15
(leq([b, a])) -> BOT -> 13
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 22, which took 0.019984 s (model generation: 0.017833,  model checking: 0.002151):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, s>(q_gen_3177) -> q_gen_3145
<a, z>() -> q_gen_3145
<b, s>(q_gen_3177) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 14
() -> length([nil, z]) -> 13
() -> leq([a, y]) -> 14
() -> leq([b, b]) -> 13
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 21
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 14
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 16
(leq([b, a])) -> BOT -> 14
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> z  ;  _om -> cons(a, nil)  ;  _pm -> s(s(s(z)))  ;  l -> nil  ;  x -> a
})

-------------------------------------------
Step 23, which took 0.025006 s (model generation: 0.019268,  model checking: 0.005738):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3177, q_gen_3179},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3177) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3179
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 15
() -> length([nil, z]) -> 14
() -> leq([a, y]) -> 15
() -> leq([b, b]) -> 14
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 21
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 15
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 15
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(z))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 24, which took 0.025502 s (model generation: 0.021811,  model checking: 0.003691):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 16
() -> length([nil, z]) -> 15
() -> leq([a, y]) -> 16
() -> leq([b, b]) -> 15
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 24
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 16
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 18
(leq([b, a])) -> BOT -> 16
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(s(z)))  ;  _om -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _pm -> s(s(z))  ;  l -> cons(a, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 25, which took 0.033257 s (model generation: 0.028477,  model checking: 0.004780):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 17
() -> length([nil, z]) -> 16
() -> leq([a, y]) -> 17
() -> leq([b, b]) -> 16
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 24
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 17
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 19
(leq([b, a])) -> BOT -> 17
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(z)))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 26, which took 0.040740 s (model generation: 0.037166,  model checking: 0.003574):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 18
() -> length([nil, z]) -> 17
() -> leq([a, y]) -> 18
() -> leq([b, b]) -> 17
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 27
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 18
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 20
(leq([b, a])) -> BOT -> 18
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(s(z)))  ;  _om -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _pm -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 27, which took 0.042890 s (model generation: 0.037290,  model checking: 0.005600):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3164
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 19
() -> length([nil, z]) -> 18
() -> leq([a, y]) -> 19
() -> leq([b, b]) -> 18
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 27
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 19
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 21
(leq([b, a])) -> BOT -> 19
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 28, which took 0.039221 s (model generation: 0.036545,  model checking: 0.002676):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, s>(q_gen_3195) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 20
() -> length([nil, z]) -> 19
() -> leq([a, y]) -> 20
() -> leq([b, b]) -> 19
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 30
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 20
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 22
(leq([b, a])) -> BOT -> 20
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> z  ;  _om -> cons(b, nil)  ;  _pm -> s(s(s(s(z))))  ;  l -> nil  ;  x -> a
})

-------------------------------------------
Step 29, which took 0.045142 s (model generation: 0.039884,  model checking: 0.005258):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3164
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 21
() -> length([nil, z]) -> 20
() -> leq([a, y]) -> 21
() -> leq([b, b]) -> 20
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 30
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 21
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 23
(leq([b, a])) -> BOT -> 21
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 30, which took 0.044142 s (model generation: 0.042266,  model checking: 0.001876):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3159, q_gen_3185},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3159
<cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3159
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3177, q_gen_3179},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, s>(q_gen_3177) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3179
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 22
() -> length([nil, z]) -> 21
() -> leq([a, y]) -> 22
() -> leq([b, b]) -> 21
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 30
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 22
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 26
(leq([b, a])) -> BOT -> 22
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 31, which took 0.049137 s (model generation: 0.045322,  model checking: 0.003815):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3177, q_gen_3179, q_gen_3190},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3164
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3190) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, s>(q_gen_3177) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3179
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 23
() -> length([nil, z]) -> 22
() -> leq([a, y]) -> 23
() -> leq([b, b]) -> 22
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 33
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 23
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 23
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> z  ;  _om -> cons(b, nil)  ;  _pm -> s(s(s(z)))  ;  l -> nil  ;  x -> a
})

-------------------------------------------
Step 32, which took 0.055658 s (model generation: 0.051748,  model checking: 0.003910):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3184
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 24
() -> length([nil, z]) -> 23
() -> leq([a, y]) -> 24
() -> leq([b, b]) -> 23
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 33
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 24
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 28
(leq([b, a])) -> BOT -> 24
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 33, which took 0.054521 s (model generation: 0.049456,  model checking: 0.005065):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3171, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3136
<cons, s>(q_gen_3171, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3171, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3171, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<a, s>(q_gen_3167) -> q_gen_3171
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 25
() -> length([nil, z]) -> 24
() -> leq([a, y]) -> 25
() -> leq([b, b]) -> 24
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 36
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 25
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 29
(leq([b, a])) -> BOT -> 25
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(s(z)))  ;  _om -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _pm -> s(s(z))  ;  l -> cons(a, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 34, which took 0.060569 s (model generation: 0.055370,  model checking: 0.005199):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3196},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, b>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<b, a>() -> q_gen_3148
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3196
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 26
() -> length([nil, z]) -> 25
() -> leq([a, y]) -> 26
() -> leq([b, b]) -> 25
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 39
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 26
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 35
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 30
(leq([b, a])) -> BOT -> 26
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(s(z)))  ;  _om -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _pm -> s(s(s(z)))  ;  l -> cons(a, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 35, which took 0.069915 s (model generation: 0.063399,  model checking: 0.006516):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3177, q_gen_3179, q_gen_3190},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3190) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3177) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3179
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 27
() -> length([nil, z]) -> 26
() -> leq([a, y]) -> 27
() -> leq([b, b]) -> 26
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 39
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 27
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 38
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 31
(leq([b, a])) -> BOT -> 27
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 36, which took 0.064489 s (model generation: 0.062064,  model checking: 0.002425):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3185, q_gen_3186},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<a, b>() -> q_gen_3148
<b, a>() -> q_gen_3148
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3186
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 27
() -> length([nil, z]) -> 27
() -> leq([a, y]) -> 27
() -> leq([b, b]) -> 27
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 39
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 30
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 38
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 31
(leq([b, a])) -> BOT -> 28
}
Sat witness: Found: ((insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]), {
_em -> cons(a, cons(b, cons(b, nil)))  ;  x -> b  ;  y -> a  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 37, which took 0.085716 s (model generation: 0.077763,  model checking: 0.007953):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 28
() -> length([nil, z]) -> 28
() -> leq([a, y]) -> 28
() -> leq([b, b]) -> 28
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 39
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 31
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 41
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 32
(leq([b, a])) -> BOT -> 29
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 38, which took 0.075830 s (model generation: 0.071371,  model checking: 0.004459):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3185, q_gen_3186},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3141
<cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<a, b>() -> q_gen_3148
<b, a>() -> q_gen_3148
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3186
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 29
() -> length([nil, z]) -> 29
() -> leq([a, y]) -> 29
() -> leq([b, b]) -> 29
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 39
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 32
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 41
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 35
(leq([b, a])) -> BOT -> 30
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 39, which took 0.079283 s (model generation: 0.076661,  model checking: 0.002622):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3185, q_gen_3186},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<a, b>() -> q_gen_3148
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3186
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 30
() -> length([nil, z]) -> 30
() -> leq([a, y]) -> 30
() -> leq([b, b]) -> 30
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 39
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 35
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 41
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 35
(leq([b, a])) -> BOT -> 31
}
Sat witness: Found: ((insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]), {
_em -> cons(a, cons(a, cons(b, nil)))  ;  x -> b  ;  y -> a  ;  z -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 40, which took 0.081402 s (model generation: 0.080460,  model checking: 0.000942):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3159, q_gen_3185, q_gen_3186},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3159
<cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3186
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 31
() -> length([nil, z]) -> 31
() -> leq([a, y]) -> 31
() -> leq([b, b]) -> 31
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 39
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 35
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 41
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 38
(leq([b, a])) -> BOT -> 32
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 41, which took 0.085103 s (model generation: 0.082276,  model checking: 0.002827):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3151, q_gen_3168},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<a>() -> q_gen_3151
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<nil, cons>(q_gen_3151, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3151, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3168
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, s>(q_gen_3195) -> q_gen_3145
<a, z>() -> q_gen_3145
<b, s>(q_gen_3195) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 32
() -> length([nil, z]) -> 32
() -> leq([a, y]) -> 32
() -> leq([b, b]) -> 32
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 42
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 36
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 41
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 39
(leq([b, a])) -> BOT -> 33
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> z  ;  _om -> cons(a, nil)  ;  _pm -> s(s(s(s(z))))  ;  l -> nil  ;  x -> a
})

-------------------------------------------
Step 42, which took 0.098633 s (model generation: 0.088711,  model checking: 0.009922):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 33
() -> length([nil, z]) -> 33
() -> leq([a, y]) -> 33
() -> leq([b, b]) -> 33
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 42
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 37
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 44
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 40
(leq([b, a])) -> BOT -> 34
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 43, which took 0.098095 s (model generation: 0.092304,  model checking: 0.005791):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3153, q_gen_3159, q_gen_3185},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3141
<cons, cons>(q_gen_3153, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, b>() -> q_gen_3142
<b, a>() -> q_gen_3153
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3159
<cons, cons>(q_gen_3153, q_gen_3159) -> q_gen_3159
<a, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3137
<a, cons, cons>(q_gen_3153, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3153, q_gen_3159) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3137
<b, cons, cons>(q_gen_3153, q_gen_3159) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 34
() -> length([nil, z]) -> 34
() -> leq([a, y]) -> 34
() -> leq([b, b]) -> 34
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 42
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 38
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 44
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 43
(leq([b, a])) -> BOT -> 35
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 44, which took 0.107152 s (model generation: 0.104834,  model checking: 0.002318):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3161, q_gen_3196},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3141
<cons, cons>(q_gen_3148, q_gen_3161) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, b>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<b, a>() -> q_gen_3148
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3161
<cons, cons>(q_gen_3142, q_gen_3161) -> q_gen_3161
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3161) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3161) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3161) -> q_gen_3196
<b, cons, cons>(q_gen_3148, q_gen_3161) -> q_gen_3196
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 35
() -> length([nil, z]) -> 35
() -> leq([a, y]) -> 35
() -> leq([b, b]) -> 35
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 42
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 41
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 44
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 43
(leq([b, a])) -> BOT -> 36
}
Sat witness: Found: ((insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]), {
_em -> cons(b, cons(a, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 45, which took 0.118283 s (model generation: 0.114249,  model checking: 0.004034):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3195) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 36
() -> length([nil, z]) -> 36
() -> leq([a, y]) -> 36
() -> leq([b, b]) -> 36
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 45
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 42
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 44
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 43
(leq([b, a])) -> BOT -> 37
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(s(s(z))))  ;  _om -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _pm -> s(s(s(z)))  ;  l -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 46, which took 0.126846 s (model generation: 0.116152,  model checking: 0.010694):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 37
() -> length([nil, z]) -> 37
() -> leq([a, y]) -> 37
() -> leq([b, b]) -> 37
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 48
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 43
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 45
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 38
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(s(s(z))))  ;  _om -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _pm -> s(s(s(s(z))))  ;  l -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 47, which took 0.131645 s (model generation: 0.121438,  model checking: 0.010207):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3195) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 38
() -> length([nil, z]) -> 38
() -> leq([a, y]) -> 38
() -> leq([b, b]) -> 38
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 51
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 44
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 45
(leq([b, a])) -> BOT -> 39
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(a, cons(b, nil))  ;  _pm -> s(s(s(s(s(z)))))  ;  l -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 48, which took 0.210524 s (model generation: 0.202677,  model checking: 0.007847):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3171, q_gen_3174, q_gen_3177, q_gen_3179, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3195) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3171, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3171, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3171, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3171, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3167) -> q_gen_3171
<b, s>(q_gen_3177) -> q_gen_3171
<a, s>(q_gen_3177) -> q_gen_3179
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 39
() -> length([nil, z]) -> 39
() -> leq([a, y]) -> 39
() -> leq([b, b]) -> 39
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 51
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 45
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 46
(leq([b, a])) -> BOT -> 40
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(z))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 49, which took 0.236600 s (model generation: 0.234668,  model checking: 0.001932):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3151, q_gen_3156, q_gen_3157},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<b>() -> q_gen_3139
<a>() -> q_gen_3151
<cons, cons>(q_gen_3142, q_gen_3157) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<a, b>() -> q_gen_3148
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3157
<cons, cons>(q_gen_3148, q_gen_3157) -> q_gen_3157
<nil, cons>(q_gen_3151, q_gen_3138) -> q_gen_3157
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3157) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3157) -> q_gen_3137
<a, nil, cons>(q_gen_3151, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3157) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3156
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3156
<b, cons, cons>(q_gen_3148, q_gen_3157) -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 40
() -> length([nil, z]) -> 40
() -> leq([a, y]) -> 40
() -> leq([b, b]) -> 40
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 51
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 48
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 46
(leq([b, a])) -> BOT -> 41
}
Sat witness: Found: ((insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]), {
_em -> cons(a, cons(b, cons(a, nil)))  ;  x -> b  ;  y -> a  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 50, which took 0.297803 s (model generation: 0.296278,  model checking: 0.001525):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3159, q_gen_3185, q_gen_3186},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<a, b>() -> q_gen_3148
<b, a>() -> q_gen_3148
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3159
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3159
<cons, cons>(q_gen_3148, q_gen_3159) -> q_gen_3159
<cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3186
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3159) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3159) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3185
<a, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
<b, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3177, q_gen_3179},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3177) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3179
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 41
() -> length([nil, z]) -> 41
() -> leq([a, y]) -> 41
() -> leq([b, b]) -> 41
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 51
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 48
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 49
(leq([b, a])) -> BOT -> 42
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 51, which took 0.266166 s (model generation: 0.255237,  model checking: 0.010929):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3224},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3224
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, s>(q_gen_3224) -> q_gen_3145
<a, z>() -> q_gen_3145
<b, s>(q_gen_3224) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 42
() -> length([nil, z]) -> 42
() -> leq([a, y]) -> 42
() -> leq([b, b]) -> 42
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 51
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 49
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 52
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 50
(leq([b, a])) -> BOT -> 43
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(s(s(z)))))  ;  ll -> cons(b, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 52, which took 0.216171 s (model generation: 0.211522,  model checking: 0.004649):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3185, q_gen_3186, q_gen_3187},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<a, b>() -> q_gen_3148
<b, a>() -> q_gen_3148
<cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3187) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3187
<cons, cons>(q_gen_3148, q_gen_3187) -> q_gen_3187
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3187) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3187) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3185
<a, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
<b, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 43
() -> length([nil, z]) -> 43
() -> leq([a, y]) -> 43
() -> leq([b, b]) -> 43
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 51
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 50
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 52
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 44
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 53, which took 0.439485 s (model generation: 0.432344,  model checking: 0.007141):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3195) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 44
() -> length([nil, z]) -> 44
() -> leq([a, y]) -> 44
() -> leq([b, b]) -> 44
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 54
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 51
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 52
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 45
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(b, cons(a, cons(a, cons(a, cons(b, cons(b, nil))))))  ;  _pm -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> a
})

-------------------------------------------
Step 54, which took 0.285540 s (model generation: 0.283818,  model checking: 0.001722):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3153, q_gen_3159, q_gen_3185, q_gen_3186},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3153, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, b>() -> q_gen_3142
<b, a>() -> q_gen_3153
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3159
<cons, cons>(q_gen_3153, q_gen_3159) -> q_gen_3159
<cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3186
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3137
<a, cons, cons>(q_gen_3153, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3153, q_gen_3159) -> q_gen_3137
<a, cons, cons>(q_gen_3153, q_gen_3186) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3159) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3185
<b, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3185
<b, cons, cons>(q_gen_3153, q_gen_3159) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3177) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 45
() -> length([nil, z]) -> 45
() -> leq([a, y]) -> 45
() -> leq([b, b]) -> 45
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 54
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 54
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 52
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 46
}
Sat witness: Found: ((insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]), {
_em -> cons(b, cons(a, cons(a, nil)))  ;  x -> b  ;  y -> a  ;  z -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 55, which took 0.690233 s (model generation: 0.680752,  model checking: 0.009481):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3179, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3195) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3177) -> q_gen_3179
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 46
() -> length([nil, z]) -> 46
() -> leq([a, y]) -> 46
() -> leq([b, b]) -> 46
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 54
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 54
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 55
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 47
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(s(z))))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 56, which took 0.634402 s (model generation: 0.633475,  model checking: 0.000927):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142, q_gen_3148, q_gen_3185, q_gen_3186, q_gen_3187},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, a>() -> q_gen_3148
<a, b>() -> q_gen_3148
<cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3187) -> q_gen_3186
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3187
<cons, cons>(q_gen_3148, q_gen_3187) -> q_gen_3187
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3186) -> q_gen_3137
<a, cons, cons>(q_gen_3142, q_gen_3187) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3141) -> q_gen_3137
<b, cons, cons>(q_gen_3148, q_gen_3187) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<a, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
<b, cons, cons>(q_gen_3142, q_gen_3187) -> q_gen_3185
<b, cons, cons>(q_gen_3148, q_gen_3186) -> q_gen_3185
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3177) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 47
() -> length([nil, z]) -> 47
() -> leq([a, y]) -> 47
() -> leq([b, b]) -> 47
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 54
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 54
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 55
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 56
(leq([b, a])) -> BOT -> 48
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 57, which took 0.449988 s (model generation: 0.442698,  model checking: 0.007290):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3212},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<cons, s>(q_gen_3212, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3212, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3212, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3212, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3195) -> q_gen_3194
<a, s>(q_gen_3195) -> q_gen_3212
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 48
() -> length([nil, z]) -> 48
() -> leq([a, y]) -> 48
() -> leq([b, b]) -> 48
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 57
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 55
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 55
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 56
(leq([b, a])) -> BOT -> 49
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(b, cons(b, nil))  ;  _pm -> s(s(s(s(z))))  ;  l -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 58, which took 0.818736 s (model generation: 0.812386,  model checking: 0.006350):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 49
() -> length([nil, z]) -> 49
() -> leq([a, y]) -> 49
() -> leq([b, b]) -> 49
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 57
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 55
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 58
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 56
(leq([b, a])) -> BOT -> 50
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 59, which took 1.048355 s (model generation: 1.043530,  model checking: 0.004825):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 50
() -> length([nil, z]) -> 50
() -> leq([a, y]) -> 50
() -> leq([b, b]) -> 50
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 60
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 56
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 58
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 57
(leq([b, a])) -> BOT -> 51
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(z))  ;  _om -> cons(a, cons(b, cons(b, nil)))  ;  _pm -> s(s(s(s(s(z)))))  ;  l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 60, which took 0.977241 s (model generation: 0.968448,  model checking: 0.008793):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3224},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3224) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3224
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, s>(q_gen_3224) -> q_gen_3145
<a, z>() -> q_gen_3145
<b, s>(q_gen_3224) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 51
() -> length([nil, z]) -> 51
() -> leq([a, y]) -> 51
() -> leq([b, b]) -> 51
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 60
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 57
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 61
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 58
(leq([b, a])) -> BOT -> 52
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(z)  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 61, which took 0.811041 s (model generation: 0.808534,  model checking: 0.002507):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3224},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3224) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3224
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, s>(q_gen_3224) -> q_gen_3145
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3224) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 52
() -> length([nil, z]) -> 52
() -> leq([a, y]) -> 52
() -> leq([b, b]) -> 52
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 63
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 58
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 61
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 59
(leq([b, a])) -> BOT -> 53
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> z  ;  _om -> cons(a, nil)  ;  _pm -> s(s(s(s(s(z)))))  ;  l -> nil  ;  x -> a
})

-------------------------------------------
Step 62, which took 0.746144 s (model generation: 0.738489,  model checking: 0.007655):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3224},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3224) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3224
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, s>(q_gen_3224) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<a, s>(q_gen_3224) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 53
() -> length([nil, z]) -> 53
() -> leq([a, y]) -> 53
() -> leq([b, b]) -> 53
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 63
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 59
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 64
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 60
(leq([b, a])) -> BOT -> 54
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(s(s(z)))))  ;  ll -> cons(a, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 63, which took 2.479175 s (model generation: 2.472276,  model checking: 0.006899):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3212},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<cons, s>(q_gen_3212, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3212, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3212, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3212, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3195) -> q_gen_3194
<a, s>(q_gen_3195) -> q_gen_3212
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 54
() -> length([nil, z]) -> 54
() -> leq([a, y]) -> 54
() -> leq([b, b]) -> 54
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 66
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 60
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 64
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 61
(leq([b, a])) -> BOT -> 55
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(z))  ;  _om -> cons(a, cons(b, cons(b, cons(a, cons(b, cons(b, nil))))))  ;  _pm -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> a
})

-------------------------------------------
Step 64, which took 1.920338 s (model generation: 1.907143,  model checking: 0.013195):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3224},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3224) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3224
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, s>(q_gen_3224) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<a, s>(q_gen_3224) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 55
() -> length([nil, z]) -> 55
() -> leq([a, y]) -> 55
() -> leq([b, b]) -> 55
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 66
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 61
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 67
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 62
(leq([b, a])) -> BOT -> 56
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(z)  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 65, which took 3.426772 s (model generation: 3.419367,  model checking: 0.007405):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3190, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3184
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3184
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 56
() -> length([nil, z]) -> 56
() -> leq([a, y]) -> 56
() -> leq([b, b]) -> 56
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 69
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 62
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 67
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 63
(leq([b, a])) -> BOT -> 57
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(z))  ;  _om -> cons(a, cons(b, cons(b, cons(a, cons(a, cons(b, cons(b, nil)))))))  ;  _pm -> s(z)  ;  l -> cons(a, cons(b, cons(b, cons(b, cons(b, cons(b, nil))))))  ;  x -> b
})

-------------------------------------------
Step 66, which took 2.257770 s (model generation: 2.238837,  model checking: 0.018933):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3189, q_gen_3190, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3189) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 57
() -> length([nil, z]) -> 57
() -> leq([a, y]) -> 57
() -> leq([b, b]) -> 57
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 69
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 63
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 70
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 64
(leq([b, a])) -> BOT -> 58
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 67, which took 4.357514 s (model generation: 4.351358,  model checking: 0.006156):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3224, q_gen_3238},
Q_f={q_gen_3136},
Delta=
{
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<s>(q_gen_3224) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3224
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3224) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3238, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3238, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3238, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3238, q_gen_3184) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
<a, s>(q_gen_3224) -> q_gen_3238
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 58
() -> length([nil, z]) -> 58
() -> leq([a, y]) -> 58
() -> leq([b, b]) -> 58
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 72
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 64
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 70
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 65
(leq([b, a])) -> BOT -> 59
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(s(s(s(z))))  ;  _om -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _pm -> s(s(z))  ;  l -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 68, which took 2.616971 s (model generation: 2.597676,  model checking: 0.019295):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3177, q_gen_3179, q_gen_3189, q_gen_3190, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3179, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3177) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3179, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3179
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 59
() -> length([nil, z]) -> 59
() -> leq([a, y]) -> 59
() -> leq([b, b]) -> 59
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 72
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 65
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 73
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 66
(leq([b, a])) -> BOT -> 60
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(z)))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 69, which took 4.576234 s (model generation: 4.568254,  model checking: 0.007980):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3193, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3193) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3184
<cons>(q_gen_3165, q_gen_3193) -> q_gen_3193
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3193
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3193
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3193) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3193) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3193) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 60
() -> length([nil, z]) -> 60
() -> leq([a, y]) -> 60
() -> leq([b, b]) -> 60
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 75
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 66
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 73
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 67
(leq([b, a])) -> BOT -> 61
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(a, cons(a, cons(a, cons(b, cons(b, cons(b, nil))))))  ;  _pm -> s(s(s(s(z))))  ;  l -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> a
})

-------------------------------------------
Step 70, which took 1.540482 s (model generation: 1.517903,  model checking: 0.022579):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3193, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3193) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3165, q_gen_3193) -> q_gen_3193
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3193
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3193
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3193) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3193) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3193) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 61
() -> length([nil, z]) -> 61
() -> leq([a, y]) -> 61
() -> leq([b, b]) -> 61
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 75
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 67
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 76
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 68
(leq([b, a])) -> BOT -> 62
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(z)))  ;  ll -> cons(a, cons(a, cons(b, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 71, which took 2.288495 s (model generation: 2.277000,  model checking: 0.011495):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3189, q_gen_3190, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3189) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3190
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 62
() -> length([nil, z]) -> 62
() -> leq([a, y]) -> 62
() -> leq([b, b]) -> 62
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 78
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 68
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 76
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 69
(leq([b, a])) -> BOT -> 63
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(b, cons(a, cons(b, cons(b, cons(b, cons(a, nil))))))  ;  _pm -> s(s(s(s(z))))  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 72, which took 2.024686 s (model generation: 2.008949,  model checking: 0.015737):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3189, q_gen_3190, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3189) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 63
() -> length([nil, z]) -> 63
() -> leq([a, y]) -> 63
() -> leq([b, b]) -> 63
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 78
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 69
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 79
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 70
(leq([b, a])) -> BOT -> 64
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(z))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 73, which took 3.597402 s (model generation: 3.589563,  model checking: 0.007839):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3193, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3193) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<cons>(q_gen_3165, q_gen_3193) -> q_gen_3184
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3193
<cons>(q_gen_3175, q_gen_3184) -> q_gen_3193
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3193) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3193) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 64
() -> length([nil, z]) -> 64
() -> leq([a, y]) -> 64
() -> leq([b, b]) -> 64
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 81
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 70
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 79
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 71
(leq([b, a])) -> BOT -> 65
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(a, cons(a, cons(a, cons(b, cons(a, cons(a, cons(a, cons(b, nil))))))))  ;  _pm -> s(s(s(s(z))))  ;  l -> cons(b, cons(a, cons(a, cons(b, cons(a, cons(a, cons(a, nil)))))))  ;  x -> b
})

-------------------------------------------
Step 74, which took 2.730444 s (model generation: 2.723013,  model checking: 0.007431):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3176, q_gen_3177, q_gen_3184, q_gen_3194, q_gen_3195, q_gen_3224, q_gen_3238},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3184) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<a>() -> q_gen_3165
<b>() -> q_gen_3165
<s>(q_gen_3224) -> q_gen_3167
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3174
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3184
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3224
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3184) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, s>(q_gen_3224) -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3184) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3238, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3238, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3238, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3238, q_gen_3184) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
<a, s>(q_gen_3224) -> q_gen_3238
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 65
() -> length([nil, z]) -> 65
() -> leq([a, y]) -> 65
() -> leq([b, b]) -> 65
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 81
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 71
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 82
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 72
(leq([b, a])) -> BOT -> 66
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 75, which took 3.067717 s (model generation: 3.059288,  model checking: 0.008429):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3189, q_gen_3190, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<cons>(q_gen_3175, q_gen_3189) -> q_gen_3190
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 66
() -> length([nil, z]) -> 66
() -> leq([a, y]) -> 66
() -> leq([b, b]) -> 66
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 84
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 72
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 82
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 73
(leq([b, a])) -> BOT -> 67
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(a, cons(a, cons(b, cons(b, cons(b, cons(a, nil))))))  ;  _pm -> s(s(s(z)))  ;  l -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 76, which took 2.564340 s (model generation: 2.547819,  model checking: 0.016521):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3189, q_gen_3190, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3189) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 67
() -> length([nil, z]) -> 67
() -> leq([a, y]) -> 67
() -> leq([b, b]) -> 67
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 84
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 73
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 85
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 74
(leq([b, a])) -> BOT -> 68
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 77, which took 4.929747 s (model generation: 4.920086,  model checking: 0.009661):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3189, q_gen_3190, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3189) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3164
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 68
() -> length([nil, z]) -> 68
() -> leq([a, y]) -> 68
() -> leq([b, b]) -> 68
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 87
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 74
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 85
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 75
(leq([b, a])) -> BOT -> 69
}
Sat witness: Found: ((insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]), {
_nm -> s(z)  ;  _om -> cons(a, cons(a, cons(a, cons(a, cons(b, cons(b, nil))))))  ;  _pm -> s(s(s(s(z))))  ;  l -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> a
})

-------------------------------------------
Step 78, which took 5.042818 s (model generation: 5.033077,  model checking: 0.009741):

Model:
|_
{
insert -> 
{{{
Q={q_gen_3137, q_gen_3138, q_gen_3139, q_gen_3141, q_gen_3142},
Q_f={q_gen_3137},
Delta=
{
<nil>() -> q_gen_3138
<a>() -> q_gen_3139
<b>() -> q_gen_3139
<cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3141
<nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3141
<a, a>() -> q_gen_3142
<a, b>() -> q_gen_3142
<b, a>() -> q_gen_3142
<b, b>() -> q_gen_3142
<a, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<a, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
<b, cons, cons>(q_gen_3142, q_gen_3141) -> q_gen_3137
<b, nil, cons>(q_gen_3139, q_gen_3138) -> q_gen_3137
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3136, q_gen_3144, q_gen_3145, q_gen_3164, q_gen_3165, q_gen_3166, q_gen_3167, q_gen_3169, q_gen_3174, q_gen_3175, q_gen_3176, q_gen_3177, q_gen_3189, q_gen_3190, q_gen_3193, q_gen_3194, q_gen_3195},
Q_f={q_gen_3136},
Delta=
{
<cons>(q_gen_3165, q_gen_3189) -> q_gen_3144
<cons>(q_gen_3175, q_gen_3193) -> q_gen_3144
<nil>() -> q_gen_3144
<cons>(q_gen_3165, q_gen_3144) -> q_gen_3164
<b>() -> q_gen_3165
<z>() -> q_gen_3167
<cons>(q_gen_3165, q_gen_3174) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3164) -> q_gen_3174
<cons>(q_gen_3175, q_gen_3190) -> q_gen_3174
<a>() -> q_gen_3175
<s>(q_gen_3167) -> q_gen_3177
<cons>(q_gen_3165, q_gen_3190) -> q_gen_3189
<cons>(q_gen_3165, q_gen_3164) -> q_gen_3190
<cons>(q_gen_3165, q_gen_3193) -> q_gen_3193
<cons>(q_gen_3175, q_gen_3144) -> q_gen_3193
<cons>(q_gen_3175, q_gen_3174) -> q_gen_3193
<cons>(q_gen_3175, q_gen_3189) -> q_gen_3193
<s>(q_gen_3177) -> q_gen_3195
<s>(q_gen_3195) -> q_gen_3195
<cons, s>(q_gen_3145, q_gen_3144) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3164) -> q_gen_3136
<cons, s>(q_gen_3166, q_gen_3193) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3190) -> q_gen_3136
<cons, s>(q_gen_3176, q_gen_3193) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3174) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3189) -> q_gen_3136
<cons, s>(q_gen_3194, q_gen_3193) -> q_gen_3136
<nil, z>() -> q_gen_3136
<a, z>() -> q_gen_3145
<b, z>() -> q_gen_3145
<a, s>(q_gen_3167) -> q_gen_3166
<b, s>(q_gen_3167) -> q_gen_3166
<cons, s>(q_gen_3145, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3145, q_gen_3193) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3174) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3166, q_gen_3190) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3176, q_gen_3189) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3144) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3164) -> q_gen_3169
<cons, s>(q_gen_3194, q_gen_3190) -> q_gen_3169
<a, s>(q_gen_3177) -> q_gen_3176
<b, s>(q_gen_3177) -> q_gen_3176
<a, s>(q_gen_3195) -> q_gen_3194
<b, s>(q_gen_3195) -> q_gen_3194
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3134, q_gen_3146},
Q_f={q_gen_3134},
Delta=
{
<a, a>() -> q_gen_3134
<a, b>() -> q_gen_3134
<b, b>() -> q_gen_3134
<b, a>() -> q_gen_3146
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 69
() -> length([nil, z]) -> 69
() -> leq([a, y]) -> 69
() -> leq([b, b]) -> 69
(insert([x, l, _om]) /\ length([_om, _pm]) /\ length([l, _nm])) -> eq_nat([s(_nm), _pm]) -> 87
(insert([x, z, _em]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _em)]) -> 75
(length([ll, _jm])) -> length([cons(x, ll), s(_jm)]) -> 88
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 76
(leq([b, a])) -> BOT -> 70
}
Sat witness: Found: ((length([ll, _jm])) -> length([cons(x, ll), s(_jm)]), {
_jm -> s(s(s(z)))  ;  ll -> cons(a, cons(a, nil))  ;  x -> a
})

Total time: 64.992189
Reason for stopping: DontKnow. Stopped because: timeout