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

TRS termination of:
[1] from(X) -> cons(X,from(s(X)))
[2] 2ndspos(0,Z) -> rnil
[3] 2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z))
[4] 2ndsneg(0,Z) -> rnil
[5] 2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z))
[6] pi(X) -> 2ndspos(X,from(0))
[7] plus(0,Y) -> Y
[8] plus(s(X),Y) -> s(plus(X,Y))
[9] times(0,Y) -> 0
[10] times(s(X),Y) -> plus(Y,times(X,Y))
[11] square(X) -> times(X,X)


Sub problem: 
guided: 

DP termination of:
<Marked_from(X) , Marked_from(s(X))>
<Marked_2ndspos(s(N),cons(X,cons(Y,Z))) , Marked_2ndsneg(N,Z)>
<Marked_2ndsneg(s(N),cons(X,cons(Y,Z))) , Marked_2ndspos(N,Z)>
<Marked_pi(X) , Marked_2ndspos(X,from(0))>
<Marked_pi(X) , Marked_from(0)>
<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_square(X) , Marked_times(X,X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_2ndsneg(s(N),cons(X,cons(Y,Z))) , Marked_2ndspos(N,Z)> 
      --> <Marked_2ndspos(s(N),cons(X,cons(Y,Z))) , Marked_2ndsneg(N,Z)>
  <Marked_2ndspos(s(N),cons(X,cons(Y,Z))) , Marked_2ndsneg(N,Z)> 
     --> <Marked_2ndsneg(s(N),cons(X,cons(Y,Z))) , Marked_2ndspos(N,Z)>
}

{  <Marked_from(X) , Marked_from(s(X))> 
      --> <Marked_from(X) , Marked_from(s(X))>
}

{  <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)

ST: Marked_2ndsneg -> 2
Marked_2ndspos -> 2

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  from(X) >= cons(X,from(s(X))) ;
  2ndspos(s(N),cons(X,cons(Y,Z))) >= rcons(posrecip(Y),2ndsneg(N,Z)) ;
  2ndspos(0,Z) >= rnil ;
  2ndsneg(s(N),cons(X,cons(Y,Z))) >= rcons(negrecip(Y),2ndspos(N,Z)) ;
  2ndsneg(0,Z) >= rnil ;
  pi(X) >= 2ndspos(X,from(0)) ;
  plus(s(X),Y) >= s(plus(X,Y)) ;
  plus(0,Y) >= Y ;
  times(s(X),Y) >= plus(Y,times(X,Y)) ;
  times(0,Y) >= 0 ;
  square(X) >= times(X,X) ;
  Marked_from(X) >= Marked_from(s(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_from(X) > Marked_from(s(X)) ;
 }
 } 
=== 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:
{
  from(X) >= cons(X,from(s(X))) ;
  2ndspos(s(N),cons(X,cons(Y,Z))) >= rcons(posrecip(Y),2ndsneg(N,Z)) ;
  2ndspos(0,Z) >= rnil ;
  2ndsneg(s(N),cons(X,cons(Y,Z))) >= rcons(negrecip(Y),2ndspos(N,Z)) ;
  2ndsneg(0,Z) >= rnil ;
  pi(X) >= 2ndspos(X,from(0)) ;
  plus(s(X),Y) >= s(plus(X,Y)) ;
  plus(0,Y) >= Y ;
  times(s(X),Y) >= plus(Y,times(X,Y)) ;
  times(0,Y) >= 0 ;
  square(X) >= times(X,X) ;
  Marked_from(X) > Marked_from(s(X)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  from(X) >= cons(X,from(s(X))) ;
  2ndspos(s(N),cons(X,cons(Y,Z))) >= rcons(posrecip(Y),2ndsneg(N,Z)) ;
  2ndspos(0,Z) >= rnil ;
  2ndsneg(s(N),cons(X,cons(Y,Z))) >= rcons(negrecip(Y),2ndspos(N,Z)) ;
  2ndsneg(0,Z) >= rnil ;
  pi(X) >= 2ndspos(X,from(0)) ;
  plus(s(X),Y) >= s(plus(X,Y)) ;
  plus(0,Y) >= Y ;
  times(s(X),Y) >= plus(Y,times(X,Y)) ;
  times(0,Y) >= 0 ;
  square(X) >= times(X,X) ;
  Marked_from(X) > Marked_from(s(X)) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
=== 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.(2349 bt (3402) [163])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
=== 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
=== 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 0.685340 seconds (real time)
Cime Exit Status: 0