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

TRS termination of:
[1] max(nil) -> 0
[2] max(cons(x,nil)) -> x
[3] max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
[4] if1(true,x,y,xs) -> max(cons(x,xs))
[5] if1(false,x,y,xs) -> max(cons(y,xs))
[6] del(x,nil) -> nil
[7] del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
[8] if2(true,x,y,xs) -> xs
[9] if2(false,x,y,xs) -> cons(y,del(x,xs))
[10] eq(0,0) -> true
[11] eq(0,s(y)) -> false
[12] eq(s(x),0) -> false
[13] eq(s(x),s(y)) -> eq(x,y)
[14] sort(nil) -> nil
[15] sort(cons(x,xs)) ->
 cons(max(cons(x,xs)),sort(h(del(max(cons(x,xs)),cons(x,xs)))))
[16] ge(0,0) -> true
[17] ge(s(x),0) -> true
[18] ge(0,s(x)) -> false
[19] ge(s(x),s(y)) -> ge(x,y)
[20] h(nil) -> nil
[21] h(cons(x,xs)) -> cons(x,h(xs))


Sub problem: 
guided: 

DP termination of:
<Marked_max(cons(x,cons(y,xs))) , Marked_if1(ge(x,y),x,y,xs)>
<Marked_max(cons(x,cons(y,xs))) , Marked_ge(x,y)>
<Marked_if1(true,x,y,xs) , Marked_max(cons(x,xs))>
<Marked_if1(false,x,y,xs) , Marked_max(cons(y,xs))>
<Marked_del(x,cons(y,xs)) , Marked_if2(eq(x,y),x,y,xs)>
<Marked_del(x,cons(y,xs)) , Marked_eq(x,y)>
<Marked_if2(false,x,y,xs) , Marked_del(x,xs)>
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_sort(cons(x,xs)) , Marked_max(cons(x,xs))>
<Marked_sort(cons(x,xs)) , Marked_sort(h(del(max(cons(x,xs)),cons(x,xs))))>
<Marked_sort(cons(x,xs)) , Marked_h(del(max(cons(x,xs)),cons(x,xs)))>
<Marked_sort(cons(x,xs)) , Marked_del(max(cons(x,xs)),cons(x,xs))>
<Marked_sort(cons(x,xs)) , Marked_max(cons(x,xs))>
<Marked_ge(s(x),s(y)) , Marked_ge(x,y)>
<Marked_h(cons(x,xs)) , Marked_h(xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 6 components:

{  <Marked_sort(cons(x,xs)) , Marked_sort(h(del(max(cons(x,xs)),cons(x,xs))))> 
      --> <Marked_sort(cons(x,xs)) , Marked_sort(h(del(max(cons(x,xs)),
                                                    cons(x,xs))))>
}

{  <Marked_if2(false,x,y,xs) , Marked_del(x,xs)> 
      --> <Marked_del(x,cons(y,xs)) , Marked_if2(eq(x,y),x,y,xs)>
  <Marked_del(x,cons(y,xs)) , Marked_if2(eq(x,y),x,y,xs)> 
     --> <Marked_if2(false,x,y,xs) , Marked_del(x,xs)>
}

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

{  <Marked_if1(false,x,y,xs) , Marked_max(cons(y,xs))> 
      --> <Marked_max(cons(x,cons(y,xs))) , Marked_if1(ge(x,y),x,y,xs)>
  <Marked_if1(true,x,y,xs) , Marked_max(cons(x,xs))> 
     --> <Marked_max(cons(x,cons(y,xs))) , Marked_if1(ge(x,y),x,y,xs)>
  <Marked_max(cons(x,cons(y,xs))) , Marked_if1(ge(x,y),x,y,xs)> 
     --> <Marked_if1(false,x,y,xs) , Marked_max(cons(y,xs))>
  <Marked_max(cons(x,cons(y,xs))) , Marked_if1(ge(x,y),x,y,xs)> 
     --> <Marked_if1(true,x,y,xs) , Marked_max(cons(x,xs))>
}

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

{  <Marked_h(cons(x,xs)) , Marked_h(xs)> 
      --> <Marked_h(cons(x,xs)) , Marked_h(xs)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  max(nil) >= 0 ;
  max(cons(x,nil)) >= x ;
  max(cons(x,cons(y,xs))) >= if1(ge(x,y),x,y,xs) ;
  if1(true,x,y,xs) >= max(cons(x,xs)) ;
  if1(false,x,y,xs) >= max(cons(y,xs)) ;
  ge(0,0) >= true ;
  ge(0,s(x)) >= false ;
  ge(s(x),0) >= true ;
  ge(s(x),s(y)) >= ge(x,y) ;
  del(x,nil) >= nil ;
  del(x,cons(y,xs)) >= if2(eq(x,y),x,y,xs) ;
  if2(true,x,y,xs) >= xs ;
  if2(false,x,y,xs) >= cons(y,del(x,xs)) ;
  eq(0,0) >= true ;
  eq(0,s(y)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  sort(nil) >= nil ;
  sort(cons(x,xs)) >= cons(max(cons(x,xs)),
                       sort(h(del(max(cons(x,xs)),cons(x,xs))))) ;
  h(nil) >= nil ;
  h(cons(x,xs)) >= cons(x,h(xs)) ;
  Marked_sort(cons(x,xs)) >= Marked_sort(h(del(max(cons(x,xs)),cons(x,xs)))) ;
 }
 + Disjunctions:{ 
{
  Marked_sort(cons(x,xs)) > Marked_sort(h(del(max(cons(x,xs)),cons(x,xs)))) ;
 }
 } 
=== 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 timeout reached
=== 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 64.541268 seconds (real time)
Cime Exit Status: 0