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

TRS termination of:
[1] empty(nil) -> true
[2] empty(cons(x,y)) -> false
[3] tail(nil) -> nil
[4] tail(cons(x,y)) -> y
[5] head(cons(x,y)) -> x
[6] zero(0) -> true
[7] zero(s(x)) -> false
[8] p(0) -> 0
[9] p(s(0)) -> 0
[10] p(s(s(x))) -> s(p(s(x)))
[11] intlist(x) -> if_intlist(empty(x),x)
[12] if_intlist(true,x) -> nil
[13] if_intlist(false,x) -> cons(s(head(x)),intlist(tail(x)))
[14] int(x,y) -> if_int(zero(x),zero(y),x,y)
[15] if_int(true,b,x,y) -> if1(b,x,y)
[16] if_int(false,b,x,y) -> if2(b,x,y)
[17] if1(true,x,y) -> cons(0,nil)
[18] if1(false,x,y) -> cons(0,int(s(0),y))
[19] if2(true,x,y) -> nil
[20] if2(false,x,y) -> intlist(int(p(x),p(y)))


Sub problem: 
guided: 

DP termination of:
<Marked_p(s(s(x))) , Marked_p(s(x))>
<Marked_intlist(x) , Marked_if_intlist(empty(x),x)>
<Marked_intlist(x) , Marked_empty(x)>
<Marked_if_intlist(false,x) , Marked_head(x)>
<Marked_if_intlist(false,x) , Marked_intlist(tail(x))>
<Marked_if_intlist(false,x) , Marked_tail(x)>
<Marked_int(x,y) , Marked_if_int(zero(x),zero(y),x,y)>
<Marked_int(x,y) , Marked_zero(x)>
<Marked_int(x,y) , Marked_zero(y)>
<Marked_if_int(true,b,x,y) , Marked_if1(b,x,y)>
<Marked_if_int(false,b,x,y) , Marked_if2(b,x,y)>
<Marked_if1(false,x,y) , Marked_int(s(0),y)>
<Marked_if2(false,x,y) , Marked_intlist(int(p(x),p(y)))>
<Marked_if2(false,x,y) , Marked_int(p(x),p(y))>
<Marked_if2(false,x,y) , Marked_p(x)>
<Marked_if2(false,x,y) , Marked_p(y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_if2(false,x,y) , Marked_int(p(x),p(y))> 
      --> <Marked_int(x,y) , Marked_if_int(zero(x),zero(y),x,y)>
  <Marked_if1(false,x,y) , Marked_int(s(0),y)> 
     --> <Marked_int(x,y) , Marked_if_int(zero(x),zero(y),x,y)>
  <Marked_if_int(false,b,x,y) , Marked_if2(b,x,y)> 
     --> <Marked_if2(false,x,y) , Marked_int(p(x),p(y))>
  <Marked_if_int(true,b,x,y) , Marked_if1(b,x,y)> 
     --> <Marked_if1(false,x,y) , Marked_int(s(0),y)>
  <Marked_int(x,y) , Marked_if_int(zero(x),zero(y),x,y)> 
     --> <Marked_if_int(false,b,x,y) , Marked_if2(b,x,y)>
  <Marked_int(x,y) , Marked_if_int(zero(x),zero(y),x,y)> 
     --> <Marked_if_int(true,b,x,y) , Marked_if1(b,x,y)>
}

{  <Marked_if_intlist(false,x) , Marked_intlist(tail(x))> 
      --> <Marked_intlist(x) , Marked_if_intlist(empty(x),x)>
  <Marked_intlist(x) , Marked_if_intlist(empty(x),x)> 
     --> <Marked_if_intlist(false,x) , Marked_intlist(tail(x))>
}

{  <Marked_p(s(s(x))) , Marked_p(s(x))> 
      --> <Marked_p(s(s(x))) , Marked_p(s(x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  empty(nil) >= true ;
  empty(cons(x,y)) >= false ;
  tail(nil) >= nil ;
  tail(cons(x,y)) >= y ;
  head(cons(x,y)) >= x ;
  zero(0) >= true ;
  zero(s(x)) >= false ;
  p(0) >= 0 ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  if_intlist(true,x) >= nil ;
  if_intlist(false,x) >= cons(s(head(x)),intlist(tail(x))) ;
  intlist(x) >= if_intlist(empty(x),x) ;
  if_int(true,b,x,y) >= if1(b,x,y) ;
  if_int(false,b,x,y) >= if2(b,x,y) ;
  int(x,y) >= if_int(zero(x),zero(y),x,y) ;
  if1(true,x,y) >= cons(0,nil) ;
  if1(false,x,y) >= cons(0,int(s(0),y)) ;
  if2(true,x,y) >= nil ;
  if2(false,x,y) >= intlist(int(p(x),p(y))) ;
  Marked_if2(false,x,y) >= Marked_int(p(x),p(y)) ;
  Marked_int(x,y) >= Marked_if_int(zero(x),zero(y),x,y) ;
  Marked_if1(false,x,y) >= Marked_int(s(0),y) ;
  Marked_if_int(true,b,x,y) >= Marked_if1(b,x,y) ;
  Marked_if_int(false,b,x,y) >= Marked_if2(b,x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_if2(false,x,y) > Marked_int(p(x),p(y)) ;
 }
{
  Marked_int(x,y) > Marked_if_int(zero(x),zero(y),x,y) ;
 }
{
  Marked_if1(false,x,y) > Marked_int(s(0),y) ;
 }
{
  Marked_if_int(true,b,x,y) > Marked_if1(b,x,y) ;
 }
{
  Marked_if_int(false,b,x,y) > Marked_if2(b,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 (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 26.420328 seconds (real time)
Cime Exit Status: 0