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

TRS termination of:
[1] last(nil) -> 0
[2] last(cons(x,nil)) -> x
[3] last(cons(x,cons(y,xs))) -> last(cons(y,xs))
[4] del(x,nil) -> nil
[5] del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
[6] if(true,x,y,xs) -> xs
[7] if(false,x,y,xs) -> cons(y,del(x,xs))
[8] eq(0,0) -> true
[9] eq(0,s(y)) -> false
[10] eq(s(x),0) -> false
[11] eq(s(x),s(y)) -> eq(x,y)
[12] reverse(nil) -> nil
[13] reverse(cons(x,xs)) ->
 cons(last(cons(x,xs)),reverse(del(last(cons(x,xs)),cons(x,xs))))


Sub problem: 
guided: 

DP termination of:
<Marked_last(cons(x,cons(y,xs))) , Marked_last(cons(y,xs))>
<Marked_del(x,cons(y,xs)) , Marked_if(eq(x,y),x,y,xs)>
<Marked_del(x,cons(y,xs)) , Marked_eq(x,y)>
<Marked_if(false,x,y,xs) , Marked_del(x,xs)>
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_reverse(cons(x,xs)) , Marked_last(cons(x,xs))>
<Marked_reverse(cons(x,xs)) , Marked_reverse(del(last(cons(x,xs)),cons(x,xs)))>
<Marked_reverse(cons(x,xs)) , Marked_del(last(cons(x,xs)),cons(x,xs))>
<Marked_reverse(cons(x,xs)) , Marked_last(cons(x,xs))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_reverse(cons(x,xs)) , Marked_reverse(del(last(cons(x,xs)),
                                                 cons(x,xs)))> 
      --> <Marked_reverse(cons(x,xs)) , Marked_reverse(del(last(cons(x,xs)),
                                                        cons(x,xs)))>
}

{  <Marked_if(false,x,y,xs) , Marked_del(x,xs)> 
      --> <Marked_del(x,cons(y,xs)) , Marked_if(eq(x,y),x,y,xs)>
  <Marked_del(x,cons(y,xs)) , Marked_if(eq(x,y),x,y,xs)> 
     --> <Marked_if(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_last(cons(x,cons(y,xs))) , Marked_last(cons(y,xs))> 
      --> <Marked_last(cons(x,cons(y,xs))) , Marked_last(cons(y,xs))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  last(nil) >= 0 ;
  last(cons(x,nil)) >= x ;
  last(cons(x,cons(y,xs))) >= last(cons(y,xs)) ;
  del(x,nil) >= nil ;
  del(x,cons(y,xs)) >= if(eq(x,y),x,y,xs) ;
  if(true,x,y,xs) >= xs ;
  if(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) ;
  reverse(nil) >= nil ;
  reverse(cons(x,xs)) >= cons(last(cons(x,xs)),
                          reverse(del(last(cons(x,xs)),cons(x,xs)))) ;
  Marked_reverse(cons(x,xs)) >= Marked_reverse(del(last(cons(x,xs)),cons(x,xs))) ;
 }
 + Disjunctions:{ 
{
  Marked_reverse(cons(x,xs)) > Marked_reverse(del(last(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 (Simple graph)
Found the following constraints:
{
  last(nil) >= 0 ;
  last(cons(x,nil)) >= x ;
  last(cons(x,cons(y,xs))) >= last(cons(y,xs)) ;
  del(x,nil) >= nil ;
  del(x,cons(y,xs)) >= if(eq(x,y),x,y,xs) ;
  if(true,x,y,xs) >= xs ;
  if(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) ;
  reverse(nil) >= nil ;
  reverse(cons(x,xs)) >= cons(last(cons(x,xs)),
                          reverse(del(last(cons(x,xs)),cons(x,xs)))) ;
  Marked_reverse(cons(x,xs)) > Marked_reverse(del(last(cons(x,xs)),cons(x,xs))) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  last(nil) >= 0 ;
  last(cons(x,nil)) >= x ;
  last(cons(x,cons(y,xs))) >= last(cons(y,xs)) ;
  del(x,nil) >= nil ;
  del(x,cons(y,xs)) >= if(eq(x,y),x,y,xs) ;
  if(true,x,y,xs) >= xs ;
  if(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) ;
  reverse(nil) >= nil ;
  reverse(cons(x,xs)) >= cons(last(cons(x,xs)),
                          reverse(del(last(cons(x,xs)),cons(x,xs)))) ;
  Marked_reverse(cons(x,xs)) > Marked_reverse(del(last(cons(x,xs)),cons(x,xs))) ;
 }
 + 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.(2080 bt (2451) [72])
=== 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 107.672782 seconds (real time)
Cime Exit Status: 0