- : unit = ()
- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] le(0,y) -> true
[2] le(s(x),0) -> false
[3] le(s(x),s(y)) -> le(x,y)
[4] zero(0) -> true
[5] zero(s(x)) -> false
[6] id(0) -> 0
[7] id(s(x)) -> s(id(x))
[8] minus(x,0) -> x
[9] minus(s(x),s(y)) -> minus(x,y)
[10] mod(x,y) -> if_mod(zero(x),zero(y),le(y,x),id(x),id(y))
[11] if_mod(true,b1,b2,x,y) -> 0
[12] if_mod(false,b1,b2,x,y) -> if2(b1,b2,x,y)
[13] if2(true,b2,x,y) -> 0
[14] if2(false,b2,x,y) -> if3(b2,x,y)
[15] if3(true,x,y) -> mod(minus(x,y),s(y))
[16] if3(false,x,y) -> x


Sub problem: 
guided: 

DP termination of:
<Marked_le(s(x),s(y)) , Marked_le(x,y)>
<Marked_id(s(x)) , Marked_id(x)>
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_mod(x,y) , Marked_if_mod(zero(x),zero(y),le(y,x),id(x),id(y))>
<Marked_mod(x,y) , Marked_zero(x)>
<Marked_mod(x,y) , Marked_zero(y)>
<Marked_mod(x,y) , Marked_le(y,x)>
<Marked_mod(x,y) , Marked_id(x)>
<Marked_mod(x,y) , Marked_id(y)>
<Marked_if_mod(false,b1,b2,x,y) , Marked_if2(b1,b2,x,y)>
<Marked_if2(false,b2,x,y) , Marked_if3(b2,x,y)>
<Marked_if3(true,x,y) , Marked_mod(minus(x,y),s(y))>
<Marked_if3(true,x,y) , Marked_minus(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_if3(true,x,y) , Marked_mod(minus(x,y),s(y))> 
      --> <Marked_mod(x,y) , Marked_if_mod(zero(x),zero(y),le(y,x),id(x),id(y))>
  <Marked_if2(false,b2,x,y) , Marked_if3(b2,x,y)> 
     --> <Marked_if3(true,x,y) , Marked_mod(minus(x,y),s(y))>
  <Marked_if_mod(false,b1,b2,x,y) , Marked_if2(b1,b2,x,y)> 
     --> <Marked_if2(false,b2,x,y) , Marked_if3(b2,x,y)>
  <Marked_mod(x,y) , Marked_if_mod(zero(x),zero(y),le(y,x),id(x),id(y))> 
     --> <Marked_if_mod(false,b1,b2,x,y) , Marked_if2(b1,b2,x,y)>
}

{  <Marked_le(s(x),s(y)) , Marked_le(x,y)> 
      --> <Marked_le(s(x),s(y)) , Marked_le(x,y)>
}

{  <Marked_id(s(x)) , Marked_id(x)> --> <Marked_id(s(x)) , Marked_id(x)>
}

{  <Marked_minus(s(x),s(y)) , Marked_minus(x,y)> 
      --> <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  zero(0) >= true ;
  zero(s(x)) >= false ;
  id(0) >= 0 ;
  id(s(x)) >= s(id(x)) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  if_mod(true,b1,b2,x,y) >= 0 ;
  if_mod(false,b1,b2,x,y) >= if2(b1,b2,x,y) ;
  mod(x,y) >= if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) ;
  if2(true,b2,x,y) >= 0 ;
  if2(false,b2,x,y) >= if3(b2,x,y) ;
  if3(true,x,y) >= mod(minus(x,y),s(y)) ;
  if3(false,x,y) >= x ;
  Marked_if3(true,x,y) >= Marked_mod(minus(x,y),s(y)) ;
  Marked_mod(x,y) >= Marked_if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) ;
  Marked_if2(false,b2,x,y) >= Marked_if3(b2,x,y) ;
  Marked_if_mod(false,b1,b2,x,y) >= Marked_if2(b1,b2,x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_if3(true,x,y) > Marked_mod(minus(x,y),s(y)) ;
 }
{
  Marked_mod(x,y) > Marked_if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) ;
 }
{
  Marked_if2(false,b2,x,y) > Marked_if3(b2,x,y) ;
 }
{
  Marked_if_mod(false,b1,b2,x,y) > Marked_if2(b1,b2,x,y) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  zero(0) >= true ;
  zero(s(x)) >= false ;
  id(0) >= 0 ;
  id(s(x)) >= s(id(x)) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  if_mod(true,b1,b2,x,y) >= 0 ;
  if_mod(false,b1,b2,x,y) >= if2(b1,b2,x,y) ;
  mod(x,y) >= if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) ;
  if2(true,b2,x,y) >= 0 ;
  if2(false,b2,x,y) >= if3(b2,x,y) ;
  if3(true,x,y) >= mod(minus(x,y),s(y)) ;
  if3(false,x,y) >= x ;
  Marked_if3(true,x,y) >= Marked_mod(minus(x,y),s(y)) ;
  Marked_mod(x,y) >= Marked_if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) ;
  Marked_if2(false,b2,x,y) > Marked_if3(b2,x,y) ;
  Marked_if_mod(false,b1,b2,x,y) >= Marked_if2(b1,b2,x,y) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  zero(0) >= true ;
  zero(s(x)) >= false ;
  id(0) >= 0 ;
  id(s(x)) >= s(id(x)) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  if_mod(true,b1,b2,x,y) >= 0 ;
  if_mod(false,b1,b2,x,y) >= if2(b1,b2,x,y) ;
  mod(x,y) >= if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) ;
  if2(true,b2,x,y) >= 0 ;
  if2(false,b2,x,y) >= if3(b2,x,y) ;
  if3(true,x,y) >= mod(minus(x,y),s(y)) ;
  if3(false,x,y) >= x ;
  Marked_if3(true,x,y) >= Marked_mod(minus(x,y),s(y)) ;
  Marked_mod(x,y) >= Marked_if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) ;
  Marked_if2(false,b2,x,y) > Marked_if3(b2,x,y) ;
  Marked_if_mod(false,b1,b2,x,y) >= Marked_if2(b1,b2,x,y) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 78.102359 seconds (real time)
Cime Exit Status: 0