Solving ../../benchmarks/smtlib/true/isaplanner_prop65.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: {
nat -> {s, z}
}
definition:
{
(plus, F:
{
plus(n, z, n) <= True
plus(n, s(mm), s(_a)) <= plus(n, mm, _a)
}
eq_nat(_d, _e) <= plus(_b, _c, _d) /\ plus(_b, _c, _e)
)
(le, P:
{
le(z, s(nn2)) <= True
le(s(nn1), s(nn2)) <= le(nn1, nn2)
le(nn1, nn2) <= le(s(nn1), s(nn2))
False <= le(s(nn1), z)
False <= le(z, z)
}
)
}

properties:
{
le(i, s(_f)) <= plus(m, i, _f)
}


over-approximation: {plus}
under-approximation: {le}

Clause system for inference is:

{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}


Solving took 0.161388 seconds.
Yes: |_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  _r_1(z, s(x_1_0)) <= True
  _r_1(z, z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0, x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006184 s (model generation: 0.005924,  model checking: 0.000260):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
Yes: {
n -> z
}

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
No: ()

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
No: ()


-------------------------------------------
Step 1, which took 0.006120 s (model generation: 0.006069,  model checking: 0.000051):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
plus(z, z, z) <= True
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
Yes: {
n -> s(_udrk_0)
}

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
Yes: {
_f -> z  ;  i -> z  ;  m -> z
}

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
Yes: {
_a -> z  ;  mm -> z  ;  n -> z
}


-------------------------------------------
Step 2, which took 0.007828 s (model generation: 0.007774,  model checking: 0.000054):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(z, s(z)) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_cerk_0)
}

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
Yes: {
_f -> s(_derk_0)  ;  i -> s(_eerk_0)  ;  m -> z
}

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
Yes: {
_a -> s(_gerk_0)  ;  mm -> z  ;  n -> s(_ierk_0)
}


-------------------------------------------
Step 3, which took 0.010861 s (model generation: 0.010792,  model checking: 0.000069):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= True
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
No: ()

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
No: ()


-------------------------------------------
Step 4, which took 0.009815 s (model generation: 0.009755,  model checking: 0.000060):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
le(z, z) <= le(s(z), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= True
  le(z, s(x_1_0)) <= True
  le(z, z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_nerk_0)  ;  nn2 -> z
}

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
Yes: {

}

le(i, s(_f)) <= plus(m, i, _f)  :
No: ()

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
No: ()


-------------------------------------------
Step 5, which took 0.008161 s (model generation: 0.008047,  model checking: 0.000114):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
le(s(z), z) <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(z, z)
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(s(x_0_0), z) <= True
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
Yes: {

}

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
Yes: {
_f -> s(z)  ;  i -> s(s(z))  ;  m -> s(_bfrk_0)
}

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
No: ()


-------------------------------------------
Step 6, which took 0.009112 s (model generation: 0.008942,  model checking: 0.000170):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, z)
le(s(s(z)), s(s(z))) <= plus(s(z), s(s(z)), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
Yes: {
_f -> s(z)  ;  i -> s(s(z))  ;  m -> z
}

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
Yes: {
_a -> s(z)  ;  mm -> z  ;  n -> s(s(z))
}


-------------------------------------------
Step 7, which took 0.020840 s (model generation: 0.020499,  model checking: 0.000341):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, z)
plus(s(s(z)), s(z), s(s(z))) <= plus(s(s(z)), z, s(z))
le(s(s(z)), s(s(z))) <= plus(s(z), s(s(z)), s(z))
le(s(s(z)), s(s(z))) <= plus(z, s(s(z)), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  _r_1(s(x_0_0)) <= True
  le(s(x_0_0), s(x_1_0)) <= _r_1(x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_ygrk_0)  ;  nn2 -> s(z)
}

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
No: ()

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
No: ()


-------------------------------------------
Step 8, which took 0.023842 s (model generation: 0.023724,  model checking: 0.000118):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(s(z)))
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, z)
plus(s(s(z)), s(z), s(s(z))) <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(s(z)), s(z))
False <= plus(z, s(s(z)), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
No: ()

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
Yes: {
_a -> s(_hirk_0)  ;  mm -> s(z)  ;  n -> z
}


-------------------------------------------
Step 9, which took 0.014551 s (model generation: 0.014380,  model checking: 0.000171):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(s(z)))
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, z)
plus(s(s(z)), s(z), s(s(z))) <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(s(z)), s(z))
False <= plus(z, s(s(z)), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= True
  _r_1(z, s(x_1_0)) <= True
  _r_1(z, z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0, x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
Yes: {
_f -> s(s(z))  ;  i -> s(s(s(z)))  ;  m -> s(_ajrk_0)
}

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
No: ()


-------------------------------------------
Step 10, which took 0.019021 s (model generation: 0.018731,  model checking: 0.000290):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(i, s(_f)) <= plus(m, i, _f) -> 0
plus(n, s(mm), s(_a)) <= plus(n, mm, _a) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(s(z)))
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, z)
plus(s(s(z)), s(z), s(s(z))) <= plus(s(s(z)), z, s(z))
le(s(s(s(z))), s(s(s(z)))) <= plus(s(z), s(s(s(z))), s(s(z)))
False <= plus(s(z), s(s(z)), s(z))
False <= plus(z, s(s(z)), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= True
  _r_1(z, z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0, x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0, x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0, x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(i, s(_f)) <= plus(m, i, _f)  :
Yes: {
_f -> s(z)  ;  i -> s(s(z))  ;  m -> s(s(_elrk_0))
}

plus(n, s(mm), s(_a)) <= plus(n, mm, _a)  :
Yes: {
_a -> s(s(_nlrk_0))  ;  mm -> z  ;  n -> s(s(_mlrk_0))
}


Total time: 0.161388
Learner time: 0.134637
Teacher time: 0.001698
Reasons for stopping: Yes: |_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  _r_1(z, s(x_1_0)) <= True
  _r_1(z, z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0, x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|