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

TRS termination of:
[1] plus(0,x) -> x
[2] plus(s(x),y) -> s(plus(x,y))
[3] times(0,y) -> 0
[4] times(s(x),y) -> plus(y,times(x,y))
[5] p(s(x)) -> x
[6] p(0) -> 0
[7] minus(x,0) -> x
[8] minus(0,x) -> 0
[9] minus(x,s(y)) -> p(minus(x,y))
[10] isZero(0) -> true
[11] isZero(s(x)) -> false
[12] facIter(x,y) -> if(isZero(x),minus(x,s(0)),y,times(y,x))
[13] if(true,x,y,z) -> y
[14] if(false,x,y,z) -> facIter(x,z)
[15] factorial(x) -> facIter(x,s(0))


Sub problem: 
guided: 

DP termination of:
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_times(s(x),y) , Marked_plus(y,times(x,y))>
<Marked_times(s(x),y) , Marked_times(x,y)>
<Marked_minus(x,s(y)) , Marked_p(minus(x,y))>
<Marked_minus(x,s(y)) , Marked_minus(x,y)>
<Marked_facIter(x,y) , Marked_if(isZero(x),minus(x,s(0)),y,times(y,x))>
<Marked_facIter(x,y) , Marked_isZero(x)>
<Marked_facIter(x,y) , Marked_minus(x,s(0))>
<Marked_facIter(x,y) , Marked_times(y,x)>
<Marked_if(false,x,y,z) , Marked_facIter(x,z)>
<Marked_factorial(x) , Marked_facIter(x,s(0))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_if(false,x,y,z) , Marked_facIter(x,z)> 
      --> <Marked_facIter(x,y) , Marked_if(isZero(x),minus(x,s(0)),y,
                                  times(y,x))>
  <Marked_facIter(x,y) , Marked_if(isZero(x),minus(x,s(0)),y,times(y,x))> 
     --> <Marked_if(false,x,y,z) , Marked_facIter(x,z)>
}

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

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

{  <Marked_plus(s(x),y) , Marked_plus(x,y)> 
      --> <Marked_plus(s(x),y) , Marked_plus(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  plus(0,x) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= plus(y,times(x,y)) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  minus(0,x) >= 0 ;
  minus(x,0) >= x ;
  minus(x,s(y)) >= p(minus(x,y)) ;
  isZero(0) >= true ;
  isZero(s(x)) >= false ;
  if(true,x,y,z) >= y ;
  if(false,x,y,z) >= facIter(x,z) ;
  facIter(x,y) >= if(isZero(x),minus(x,s(0)),y,times(y,x)) ;
  factorial(x) >= facIter(x,s(0)) ;
  Marked_facIter(x,y) >= Marked_if(isZero(x),minus(x,s(0)),y,times(y,x)) ;
  Marked_if(false,x,y,z) >= Marked_facIter(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_facIter(x,y) > Marked_if(isZero(x),minus(x,s(0)),y,times(y,x)) ;
 }
{
  Marked_if(false,x,y,z) > Marked_facIter(x,z) ;
 }
 } 
=== 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 ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== 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:
{
  plus(0,x) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= plus(y,times(x,y)) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  minus(0,x) >= 0 ;
  minus(x,0) >= x ;
  minus(x,s(y)) >= p(minus(x,y)) ;
  isZero(0) >= true ;
  isZero(s(x)) >= false ;
  if(true,x,y,z) >= y ;
  if(false,x,y,z) >= facIter(x,z) ;
  facIter(x,y) >= if(isZero(x),minus(x,s(0)),y,times(y,x)) ;
  factorial(x) >= facIter(x,s(0)) ;
  Marked_facIter(x,y) > Marked_if(isZero(x),minus(x,s(0)),y,times(y,x)) ;
  Marked_if(false,x,y,z) >= Marked_facIter(x,z) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  plus(0,x) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= plus(y,times(x,y)) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  minus(0,x) >= 0 ;
  minus(x,0) >= x ;
  minus(x,s(y)) >= p(minus(x,y)) ;
  isZero(0) >= true ;
  isZero(s(x)) >= false ;
  if(true,x,y,z) >= y ;
  if(false,x,y,z) >= facIter(x,z) ;
  facIter(x,y) >= if(isZero(x),minus(x,s(0)),y,times(y,x)) ;
  factorial(x) >= facIter(x,s(0)) ;
  Marked_facIter(x,y) > Marked_if(isZero(x),minus(x,s(0)),y,times(y,x)) ;
  Marked_if(false,x,y,z) >= Marked_facIter(x,z) ;
 }
 + 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 ===
No solution found for these parameters.(50371 bt (53838) [2160])
=== 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 10.481921 seconds (real time)
Cime Exit Status: 0