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

TRS termination of:
[1] isEmpty(cons(x,xs)) -> false
[2] isEmpty(nil) -> true
[3] isZero(0) -> true
[4] isZero(s(x)) -> false
[5] head(cons(x,xs)) -> x
[6] tail(cons(x,xs)) -> xs
[7] tail(nil) -> nil
[8] p(s(s(x))) -> s(p(s(x)))
[9] p(s(0)) -> 0
[10] p(0) -> 0
[11] inc(s(x)) -> s(inc(x))
[12] inc(0) -> s(0)
[13] sumList(xs,y) ->
 if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
[14] if(true,b,y,xs,ys,x) -> y
[15] if(false,true,y,xs,ys,x) -> sumList(xs,y)
[16] if(false,false,y,xs,ys,x) -> sumList(ys,x)
[17] sum(xs) -> sumList(xs,0)


Sub problem: 
guided: 

DP termination of:
<Marked_p(s(s(x))) , Marked_p(s(x))>
<Marked_inc(s(x)) , Marked_inc(x)>
<Marked_sumList(xs,y) , Marked_if(isEmpty(xs),isZero(head(xs)),y,tail(xs),
                         cons(p(head(xs)),tail(xs)),inc(y))>
<Marked_sumList(xs,y) , Marked_isEmpty(xs)>
<Marked_sumList(xs,y) , Marked_isZero(head(xs))>
<Marked_sumList(xs,y) , Marked_head(xs)>
<Marked_sumList(xs,y) , Marked_tail(xs)>
<Marked_sumList(xs,y) , Marked_p(head(xs))>
<Marked_sumList(xs,y) , Marked_head(xs)>
<Marked_sumList(xs,y) , Marked_tail(xs)>
<Marked_sumList(xs,y) , Marked_inc(y)>
<Marked_if(false,true,y,xs,ys,x) , Marked_sumList(xs,y)>
<Marked_if(false,false,y,xs,ys,x) , Marked_sumList(ys,x)>
<Marked_sum(xs) , Marked_sumList(xs,0)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_if(false,false,y,xs,ys,x) , Marked_sumList(ys,x)> 
      --> <Marked_sumList(xs,y) , Marked_if(isEmpty(xs),isZero(head(xs)),
                                   y,tail(xs),cons(p(head(xs)),tail(xs)),
                                   inc(y))>
  <Marked_if(false,true,y,xs,ys,x) , Marked_sumList(xs,y)> 
     --> <Marked_sumList(xs,y) , Marked_if(isEmpty(xs),isZero(head(xs)),
                                  y,tail(xs),cons(p(head(xs)),tail(xs)),
                                  inc(y))>
  <Marked_sumList(xs,y) , Marked_if(isEmpty(xs),isZero(head(xs)),y,tail(xs),
                           cons(p(head(xs)),tail(xs)),inc(y))> 
     --> <Marked_if(false,false,y,xs,ys,x) , Marked_sumList(ys,x)>
  <Marked_sumList(xs,y) , Marked_if(isEmpty(xs),isZero(head(xs)),y,tail(xs),
                           cons(p(head(xs)),tail(xs)),inc(y))> 
     --> <Marked_if(false,true,y,xs,ys,x) , Marked_sumList(xs,y)>
}

{  <Marked_p(s(s(x))) , Marked_p(s(x))> 
      --> <Marked_p(s(s(x))) , Marked_p(s(x))>
}

{  <Marked_inc(s(x)) , Marked_inc(x)> --> <Marked_inc(s(x)) , Marked_inc(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  isEmpty(cons(x,xs)) >= false ;
  isEmpty(nil) >= true ;
  isZero(0) >= true ;
  isZero(s(x)) >= false ;
  head(cons(x,xs)) >= x ;
  tail(cons(x,xs)) >= xs ;
  tail(nil) >= nil ;
  p(0) >= 0 ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  inc(0) >= s(0) ;
  inc(s(x)) >= s(inc(x)) ;
  if(false,false,y,xs,ys,x) >= sumList(ys,x) ;
  if(false,true,y,xs,ys,x) >= sumList(xs,y) ;
  if(true,b,y,xs,ys,x) >= y ;
  sumList(xs,y) >= if(isEmpty(xs),isZero(head(xs)),y,tail(xs),
                    cons(p(head(xs)),tail(xs)),inc(y)) ;
  sum(xs) >= sumList(xs,0) ;
  Marked_sumList(xs,y) >= Marked_if(isEmpty(xs),isZero(head(xs)),y,tail(xs),
                           cons(p(head(xs)),tail(xs)),inc(y)) ;
  Marked_if(false,false,y,xs,ys,x) >= Marked_sumList(ys,x) ;
  Marked_if(false,true,y,xs,ys,x) >= Marked_sumList(xs,y) ;
 }
 + Disjunctions:{ 
{
  Marked_sumList(xs,y) > Marked_if(isEmpty(xs),isZero(head(xs)),y,tail(xs),
                          cons(p(head(xs)),tail(xs)),inc(y)) ;
 }
{
  Marked_if(false,false,y,xs,ys,x) > Marked_sumList(ys,x) ;
 }
{
  Marked_if(false,true,y,xs,ys,x) > Marked_sumList(xs,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 ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== 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
=== STOPING TIMER virtual ===
Time out 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 79.109342 seconds (real time)
Cime Exit Status: 0