- : 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(p(s(x)),y))
[3] times(0,y) -> 0
[4] times(s(x),y) -> plus(y,times(p(s(x)),y))
[5] exp(x,0) -> s(0)
[6] exp(x,s(y)) -> times(x,exp(x,y))
[7] p(s(0)) -> 0
[8] p(s(s(x))) -> s(p(s(x)))
[9] tower(x,y) -> towerIter(x,y,s(0))
[10] towerIter(0,y,z) -> z
[11] towerIter(s(x),y,z) -> towerIter(p(s(x)),y,exp(y,z))


Sub problem: 
guided: 

DP termination of:
<Marked_plus(s(x),y) , Marked_plus(p(s(x)),y)>
<Marked_plus(s(x),y) , Marked_p(s(x))>
<Marked_times(s(x),y) , Marked_plus(y,times(p(s(x)),y))>
<Marked_times(s(x),y) , Marked_times(p(s(x)),y)>
<Marked_times(s(x),y) , Marked_p(s(x))>
<Marked_exp(x,s(y)) , Marked_times(x,exp(x,y))>
<Marked_exp(x,s(y)) , Marked_exp(x,y)>
<Marked_p(s(s(x))) , Marked_p(s(x))>
<Marked_tower(x,y) , Marked_towerIter(x,y,s(0))>
<Marked_towerIter(s(x),y,z) , Marked_towerIter(p(s(x)),y,exp(y,z))>
<Marked_towerIter(s(x),y,z) , Marked_p(s(x))>
<Marked_towerIter(s(x),y,z) , Marked_exp(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

{  <Marked_towerIter(s(x),y,z) , Marked_towerIter(p(s(x)),y,exp(y,z))> 
      --> <Marked_towerIter(s(x),y,z) , Marked_towerIter(p(s(x)),y,exp(y,z))>
}

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

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

{  <Marked_plus(s(x),y) , Marked_plus(p(s(x)),y)> 
      --> <Marked_plus(s(x),y) , Marked_plus(p(s(x)),y)>
}

{  <Marked_p(s(s(x))) , Marked_p(s(x))> 
      --> <Marked_p(s(s(x))) , Marked_p(s(x))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  plus(0,x) >= x ;
  plus(s(x),y) >= s(plus(p(s(x)),y)) ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= plus(y,times(p(s(x)),y)) ;
  exp(x,0) >= s(0) ;
  exp(x,s(y)) >= times(x,exp(x,y)) ;
  towerIter(0,y,z) >= z ;
  towerIter(s(x),y,z) >= towerIter(p(s(x)),y,exp(y,z)) ;
  tower(x,y) >= towerIter(x,y,s(0)) ;
  Marked_towerIter(s(x),y,z) >= Marked_towerIter(p(s(x)),y,exp(y,z)) ;
 }
 + Disjunctions:{ 
{
  Marked_towerIter(s(x),y,z) > Marked_towerIter(p(s(x)),y,exp(y,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 : 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(p(s(x)),y)) ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= plus(y,times(p(s(x)),y)) ;
  exp(x,0) >= s(0) ;
  exp(x,s(y)) >= times(x,exp(x,y)) ;
  towerIter(0,y,z) >= z ;
  towerIter(s(x),y,z) >= towerIter(p(s(x)),y,exp(y,z)) ;
  tower(x,y) >= towerIter(x,y,s(0)) ;
  Marked_towerIter(s(x),y,z) > Marked_towerIter(p(s(x)),y,exp(y,z)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  plus(0,x) >= x ;
  plus(s(x),y) >= s(plus(p(s(x)),y)) ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= plus(y,times(p(s(x)),y)) ;
  exp(x,0) >= s(0) ;
  exp(x,s(y)) >= times(x,exp(x,y)) ;
  towerIter(0,y,z) >= z ;
  towerIter(s(x),y,z) >= towerIter(p(s(x)),y,exp(y,z)) ;
  tower(x,y) >= towerIter(x,y,s(0)) ;
  Marked_towerIter(s(x),y,z) > Marked_towerIter(p(s(x)),y,exp(y,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.(896 bt (805) [306])
=== 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 2.954510 seconds (real time)
Cime Exit Status: 0