Solving ../../benchmarks/smtlib/true/plus_succ_le_2.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(_wb)) <= plus(n, mm, _wb)
}
eq_nat(_zb, _ac) <= plus(_xb, _yb, _ac) /\ plus(_xb, _yb, _zb)
)
(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(n, _bc) <= plus(n, s(m), _bc)
}


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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 0
}


Solving took 0.220757 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, z) <= True
  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)) <= _r_1(x_0_0, x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.015122 s (model generation: 0.015002,  model checking: 0.000120):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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: ()

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

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


-------------------------------------------
Step 1, which took 0.008091 s (model generation: 0.008041,  model checking: 0.000050):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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(_pnsba_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: ()

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

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


-------------------------------------------
Step 2, which took 0.006630 s (model generation: 0.006571,  model checking: 0.000059):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 0
}

Accumulated learning constraints:
{
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>
{
  
}
]


;
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)  :
No: ()

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

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

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

plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb)  :
Yes: {
_wb -> s(_tnsba_0)  ;  mm -> z  ;  n -> s(_vnsba_0)
}

le(n, _bc) <= plus(n, s(m), _bc)  :
Yes: {
_bc -> s(_wnsba_0)  ;  n -> z
}


-------------------------------------------
Step 3, which took 0.017509 s (model generation: 0.017398,  model checking: 0.000111):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 0
}

Accumulated learning constraints:
{
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(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)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_znsba_0)
}

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

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

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

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

le(n, _bc) <= plus(n, s(m), _bc)  :
Yes: {
_bc -> s(_aosba_0)  ;  n -> s(_bosba_0)
}


-------------------------------------------
Step 4, which took 0.012867 s (model generation: 0.012819,  model checking: 0.000048):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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), s(z)) <= plus(s(z), 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
}
]


;
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: ()

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

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


-------------------------------------------
Step 5, which took 0.010258 s (model generation: 0.010173,  model checking: 0.000085):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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))
le(s(z), s(z)) <= plus(s(z), 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(_gosba_0)  ;  nn2 -> z
}

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

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

}

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

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


-------------------------------------------
Step 6, which took 0.017195 s (model generation: 0.016988,  model checking: 0.000207):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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)
False <= plus(s(z), 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(s(x_0_0), z) <= True
  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(s(x_0_0), z) <= True
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(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)) <= 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: ()

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

le(n, _bc) <= plus(n, s(m), _bc)  :
Yes: {
_bc -> s(z)  ;  m -> s(_dpsba_0)  ;  n -> s(z)
}


-------------------------------------------
Step 7, which took 0.011353 s (model generation: 0.011188,  model checking: 0.000165):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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)
False <= plus(s(z), s(s(z)), s(z))
False <= plus(s(z), 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: ()

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

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


-------------------------------------------
Step 8, which took 0.013997 s (model generation: 0.013826,  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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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))
False <= plus(s(z), s(s(z)), s(z))
False <= plus(s(z), 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_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)) <= 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: ()

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

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


-------------------------------------------
Step 9, which took 0.020277 s (model generation: 0.020160,  model checking: 0.000117):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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(s(z)), s(z), s(s(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(s(z), 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>
{
  _r_1(s(x_0_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(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))  :
Yes: {
nn1 -> s(_cssba_0)  ;  nn2 -> s(z)
}

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

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

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

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


-------------------------------------------
Step 10, which took 0.016121 s (model generation: 0.015932,  model checking: 0.000189):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 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)
False <= plus(s(s(z)), s(z), s(s(z)))
False <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(s(z)), s(z))
False <= plus(s(z), 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, z) <= True
  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)) <= _r_1(x_0_0, x_2_0)
  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  :
Yes: {
n -> s(s(_ktsba_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: ()

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

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


-------------------------------------------
Step 11, which took 0.020055 s (model generation: 0.019831,  model checking: 0.000224):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(s(z)), z, s(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)
False <= plus(s(s(z)), s(z), s(s(z)))
False <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(s(z)), s(z))
False <= plus(s(z), 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
  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)) <= _r_1(x_0_0, x_1_0) /\ le(x_0_0, x_2_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)) <= 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: ()

plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb)  :
Yes: {
_wb -> s(s(_pusba_0))  ;  mm -> z  ;  n -> s(s(_ousba_0))
}

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


-------------------------------------------
Step 12, which took 0.026327 s (model generation: 0.026146,  model checking: 0.000181):

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
plus(n, s(mm), s(_wb)) <= plus(n, mm, _wb) -> 0
le(n, _bc) <= plus(n, s(m), _bc) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(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)
False <= plus(s(s(z)), s(z), s(s(z)))
False <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(s(z)), s(z))
False <= plus(s(z), 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
  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)) <= _r_1(x_0_0, x_2_0)
  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: ()

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

le(n, _bc) <= plus(n, s(m), _bc)  :
No: ()


Total time: 0.220757
Learner time: 0.194075
Teacher time: 0.001726
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, z) <= True
  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)) <= _r_1(x_0_0, x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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