Solving ../../benchmarks/smtlib/true/append_equal_elt.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: Some(60.) (sec)
Teacher_type: Checks all clauses every time
Approximation method: remove every clause that can be safely removed



Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}
}
definition:
{
(append, F:
{
append(nil, l2, l2) <= True
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)
}
eq_eltlist(_xs, _ys) <= append(_vs, _ws, _xs) /\ append(_vs, _ws, _ys)
)
}

properties:
{
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)
}


over-approximation: {append}
under-approximation: {}

Clause system for inference is:

{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}


Solving took 6.626337 seconds.
Yes: |_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= _r_1(x_0_1, x_1_1)
  _r_1(nil, cons(x_1_0, x_1_1)) <= _r_3(x_1_0)
  _r_2(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= _r_2(x_0_1, x_1_1)
  _r_2(nil, cons(x_1_0, x_1_1)) <= _r_4(x_1_0)
  _r_3(a) <= True
  _r_4(b) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_0_1, x_2_1) /\ _r_3(x_1_0)
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_0_1, x_2_1) /\ _r_4(x_1_0)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006427 s (model generation: 0.006384,  model checking: 0.000043):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> nil
}

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
No: ()


-------------------------------------------
Step 1, which took 0.006015 s (model generation: 0.005975,  model checking: 0.000040):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(nil, nil, nil) <= True
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(_olb_0, _olb_1)
}

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
Yes: {
_us -> nil  ;  l2 -> nil  ;  t1 -> nil
}


-------------------------------------------
Step 2, which took 0.007695 s (model generation: 0.007644,  model checking: 0.000051):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, nil, nil) <= True
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
Yes: {
_at -> cons(_wlb_0, _wlb_1)  ;  i -> b  ;  j -> a  ;  l1 -> nil
}

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
Yes: {
_us -> cons(_amb_0, _amb_1)  ;  l2 -> cons(_bmb_0, _bmb_1)  ;  t1 -> nil
}


-------------------------------------------
Step 3, which took 0.018011 s (model generation: 0.017927,  model checking: 0.000084):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, nil, nil) <= True
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(a) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(b, _dmb_1)
}

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
Yes: {
_at -> cons(_imb_0, _imb_1)  ;  i -> b  ;  j -> a  ;  l1 -> cons(_lmb_0, _lmb_1)
}

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
No: ()


-------------------------------------------
Step 4, which took 0.018312 s (model generation: 0.018169,  model checking: 0.000143):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, cons(b, nil), cons(b, nil)) <= True
append(nil, nil, nil) <= True
False <= append(cons(a, nil), cons(a, nil), cons(a, nil)) /\ append(cons(a, nil), cons(b, nil), cons(a, nil))
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(a, a) <= True
  _r_1(b, b) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_0, x_2_0)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_0, x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
Yes: {
_us -> cons(b, _pnb_1)  ;  h1 -> a  ;  l2 -> cons(b, _qnb_1)  ;  t1 -> nil
}


-------------------------------------------
Step 5, which took 0.049099 s (model generation: 0.048944,  model checking: 0.000155):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), cons(b, nil), cons(a, cons(b, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, cons(b, nil), cons(b, nil)) <= True
append(nil, nil, nil) <= True
False <= append(cons(a, nil), cons(a, nil), cons(a, nil)) /\ append(cons(a, nil), cons(b, nil), cons(a, nil))
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(a, a) <= True
  _r_1(b, b) <= True
  _r_2(cons(x_0_0, x_0_1)) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_0, x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
Yes: {
_at -> cons(_znb_0, cons(_vob_0, _vob_1))  ;  i -> a  ;  j -> b  ;  l1 -> cons(_cob_0, _cob_1)
}

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
No: ()


-------------------------------------------
Step 6, which took 0.048859 s (model generation: 0.048604,  model checking: 0.000255):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), cons(b, nil), cons(a, cons(b, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, cons(b, nil), cons(b, nil)) <= True
append(nil, nil, nil) <= True
False <= append(cons(a, nil), cons(a, nil), cons(a, nil)) /\ append(cons(a, nil), cons(b, nil), cons(a, nil))
False <= append(cons(a, nil), cons(b, nil), cons(a, cons(a, nil)))
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(a, cons(x_1_0, x_1_1)) <= True
  _r_1(a, nil) <= True
  _r_1(b, cons(x_1_0, x_1_1)) <= _r_2(x_1_0)
  _r_2(b) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_0, x_2_1)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_0, x_2_1)
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
Yes: {
_at -> cons(b, nil)  ;  i -> b  ;  j -> a  ;  l1 -> nil
}

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
Yes: {
_us -> cons(a, cons(b, _xqb_1))  ;  l2 -> cons(b, _pqb_1)  ;  t1 -> nil
}


-------------------------------------------
Step 7, which took 0.156937 s (model generation: 0.156664,  model checking: 0.000273):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), cons(b, nil), cons(a, cons(b, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, cons(b, nil), cons(b, nil)) <= True
append(nil, nil, nil) <= True
False <= append(cons(a, nil), cons(a, nil), cons(a, nil)) /\ append(cons(a, nil), cons(b, nil), cons(a, nil))
False <= append(cons(a, nil), cons(b, nil), cons(a, cons(a, nil)))
False <= append(nil, cons(a, nil), cons(b, nil))
append(cons(a, nil), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= append(nil, cons(b, nil), cons(a, cons(b, nil)))
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(a, a) <= True
  _r_1(b, b) <= True
  _r_2(cons(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_3(b) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_0, x_2_0)
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_0, x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
Yes: {
_at -> cons(a, cons(b, _jtb_1))  ;  i -> b  ;  j -> a  ;  l1 -> cons(_bsb_0, _bsb_1)
}

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
Yes: {
_us -> cons(a, cons(b, _htb_1))  ;  h1 -> a  ;  l2 -> cons(b, _wsb_1)  ;  t1 -> cons(_xsb_0, _xsb_1)
}


-------------------------------------------
Step 8, which took 0.270573 s (model generation: 0.270277,  model checking: 0.000296):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, cons(a, nil)), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= True
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), cons(b, nil), cons(a, cons(b, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, cons(b, nil), cons(b, nil)) <= True
append(nil, nil, nil) <= True
False <= append(cons(a, nil), cons(a, nil), cons(a, cons(b, nil)))
False <= append(cons(a, nil), cons(a, nil), cons(a, nil)) /\ append(cons(a, nil), cons(b, nil), cons(a, nil))
False <= append(cons(a, nil), cons(b, nil), cons(a, cons(a, nil)))
False <= append(nil, cons(a, nil), cons(b, nil))
append(cons(a, nil), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= append(nil, cons(b, nil), cons(a, cons(b, nil)))
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1), b, cons(x_2_0, x_2_1)) <= True
  _r_1(nil, a, cons(x_2_0, x_2_1)) <= _r_3(x_2_0)
  _r_1(nil, b, cons(x_2_0, x_2_1)) <= _r_2(x_2_0)
  _r_2(b) <= True
  _r_3(a) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_0_1, x_1_0, x_2_1)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_1_0) /\ _r_2(x_2_0)
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
Yes: {
_us -> cons(_dvb_0, cons(a, _pvb_1))  ;  l2 -> cons(a, _evb_1)  ;  t1 -> cons(_fvb_0, nil)
}


-------------------------------------------
Step 9, which took 0.377238 s (model generation: 0.376936,  model checking: 0.000302):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, cons(a, nil)), cons(a, nil), cons(a, cons(a, cons(a, nil)))) <= True
append(cons(a, cons(a, nil)), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= True
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), cons(b, nil), cons(a, cons(b, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, cons(b, nil), cons(b, nil)) <= True
append(nil, nil, nil) <= True
False <= append(cons(a, nil), cons(a, nil), cons(a, cons(b, nil)))
False <= append(cons(a, nil), cons(a, nil), cons(a, nil)) /\ append(cons(a, nil), cons(b, nil), cons(a, nil))
False <= append(cons(a, nil), cons(b, nil), cons(a, cons(a, nil)))
False <= append(nil, cons(a, nil), cons(b, nil))
append(cons(a, nil), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= append(nil, cons(b, nil), cons(a, cons(b, nil)))
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1), a, cons(x_2_0, x_2_1)) <= True
  _r_1(cons(x_0_0, x_0_1), b, cons(x_2_0, x_2_1)) <= True
  _r_1(nil, a, cons(x_2_0, x_2_1)) <= _r_2(x_2_0)
  _r_1(nil, b, cons(x_2_0, x_2_1)) <= _r_3(x_2_0)
  _r_2(a) <= True
  _r_3(b) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_0_1, x_1_0, x_2_1)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_1_0) /\ _r_2(x_2_0)
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
Yes: {
_at -> cons(_xvb_0, cons(_byb_0, _byb_1))  ;  i -> a  ;  j -> b  ;  l1 -> cons(_awb_0, cons(_ayb_0, _ayb_1))
}

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
No: ()


-------------------------------------------
Step 10, which took 0.442464 s (model generation: 0.441227,  model checking: 0.001237):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, cons(a, nil)), cons(a, nil), cons(a, cons(a, cons(a, nil)))) <= True
append(cons(a, cons(a, nil)), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= True
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), cons(b, nil), cons(a, cons(b, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, cons(b, nil), cons(b, nil)) <= True
append(nil, nil, nil) <= True
False <= append(cons(a, cons(a, nil)), cons(a, nil), cons(a, cons(a, nil))) /\ append(cons(a, cons(a, nil)), cons(b, nil), cons(a, cons(a, nil)))
False <= append(cons(a, nil), cons(a, nil), cons(a, cons(b, nil)))
False <= append(cons(a, nil), cons(a, nil), cons(a, nil)) /\ append(cons(a, nil), cons(b, nil), cons(a, nil))
False <= append(cons(a, nil), cons(b, nil), cons(a, cons(a, nil)))
False <= append(nil, cons(a, nil), cons(b, nil))
append(cons(a, nil), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= append(nil, cons(b, nil), cons(a, cons(b, nil)))
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= _r_1(x_0_1, x_1_1)
  _r_1(nil, cons(x_1_0, x_1_1)) <= _r_2(x_1_0)
  _r_2(a) <= True
  _r_3(b) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_0_1, x_2_1) /\ _r_2(x_1_0)
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ append(x_0_1, x_1_1, x_2_1)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_1_0) /\ _r_2(x_2_0)
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  append(nil, nil, cons(x_2_0, x_2_1)) <= _r_3(x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
Yes: {
_at -> cons(_qyb_0, cons(_egc_0, cons(a, _tcc_1)))  ;  i -> a  ;  j -> b  ;  l1 -> cons(_tyb_0, cons(_dgc_0, nil))
}

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
Yes: {
_us -> cons(b, _ncc_1)  ;  l2 -> cons(b, cons(a, _yfc_1))  ;  t1 -> nil
}


-------------------------------------------
Step 11, which took 0.579645 s (model generation: 0.578329,  model checking: 0.001316):

Clauses:
{
append(nil, l2, l2) <= True -> 0
eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at) -> 0
append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us) -> 0
}

Accumulated learning constraints:
{
append(cons(a, cons(a, nil)), cons(a, nil), cons(a, cons(a, cons(a, nil)))) <= True
append(cons(a, cons(a, nil)), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= True
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), cons(b, nil), cons(a, cons(b, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, cons(b, nil), cons(b, nil)) <= True
append(nil, nil, nil) <= True
False <= append(cons(a, cons(a, nil)), cons(a, nil), cons(a, cons(a, nil))) /\ append(cons(a, cons(a, nil)), cons(b, nil), cons(a, cons(a, nil)))
False <= append(cons(a, cons(a, nil)), cons(b, nil), cons(a, cons(a, cons(a, nil))))
False <= append(cons(a, nil), cons(a, nil), cons(a, cons(b, nil)))
False <= append(cons(a, nil), cons(a, nil), cons(a, nil)) /\ append(cons(a, nil), cons(b, nil), cons(a, nil))
False <= append(cons(a, nil), cons(b, nil), cons(a, cons(a, nil)))
False <= append(nil, cons(a, nil), cons(b, nil))
append(cons(a, nil), cons(b, cons(a, nil)), cons(a, cons(b, nil))) <= append(nil, cons(b, cons(a, nil)), cons(b, nil))
append(cons(a, nil), cons(b, nil), cons(a, cons(a, cons(b, nil)))) <= append(nil, cons(b, nil), cons(a, cons(b, nil)))
False <= append(nil, cons(b, nil), cons(a, nil))
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= _r_1(x_0_1, x_1_1)
  _r_1(nil, cons(x_1_0, x_1_1)) <= _r_2(x_1_0)
  _r_2(b) <= True
  _r_3(a) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_0_1, x_2_1) /\ _r_2(x_1_0)
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ append(x_0_1, x_1_1, x_2_1)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_1_0) /\ _r_2(x_2_0)
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  append(nil, nil, cons(x_2_0, x_2_1)) <= _r_3(x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

eq_elt(i, j) <= append(l1, cons(i, nil), _at) /\ append(l1, cons(j, nil), _at)  :
Yes: {
_at -> cons(_ojc_0, cons(_uqc_0, cons(b, _jnc_1)))  ;  i -> a  ;  j -> b  ;  l1 -> cons(_rjc_0, cons(_tqc_0, nil))
}

append(cons(h1, t1), l2, cons(h1, _us)) <= append(t1, l2, _us)  :
Yes: {
_us -> cons(a, _dnc_1)  ;  l2 -> cons(a, cons(b, _oqc_1))  ;  t1 -> nil
}


Total time: 6.626337
Learner time: 1.977080
Teacher time: 0.004195
Reasons for stopping: Yes: |_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= _r_1(x_0_1, x_1_1)
  _r_1(nil, cons(x_1_0, x_1_1)) <= _r_3(x_1_0)
  _r_2(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= _r_2(x_0_1, x_1_1)
  _r_2(nil, cons(x_1_0, x_1_1)) <= _r_4(x_1_0)
  _r_3(a) <= True
  _r_4(b) <= True
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_0_1, x_2_1) /\ _r_3(x_1_0)
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_0_1, x_2_1) /\ _r_4(x_1_0)
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0)
  append(nil, nil, nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|