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

TRS termination of:
[1] null(nil) -> true
[2] null(add(n,x)) -> false
[3] tail(add(n,x)) -> x
[4] tail(nil) -> nil
[5] head(add(n,x)) -> n
[6] app(nil,y) -> y
[7] app(add(n,x),y) -> add(n,app(x,y))
[8] reverse(nil) -> nil
[9] reverse(add(n,x)) -> app(reverse(x),add(n,nil))
[10] shuffle(x) -> shuff(x,nil)
[11] shuff(x,y) -> if(null(x),x,y,app(y,add(head(x),nil)))
[12] if(true,x,y,z) -> y
[13] if(false,x,y,z) -> shuff(reverse(tail(x)),z)


Sub problem: 
guided: 

DP termination of:
<Marked_app(add(n,x),y) , Marked_app(x,y)>
<Marked_reverse(add(n,x)) , Marked_app(reverse(x),add(n,nil))>
<Marked_reverse(add(n,x)) , Marked_reverse(x)>
<Marked_shuffle(x) , Marked_shuff(x,nil)>
<Marked_shuff(x,y) , Marked_if(null(x),x,y,app(y,add(head(x),nil)))>
<Marked_shuff(x,y) , Marked_null(x)>
<Marked_shuff(x,y) , Marked_app(y,add(head(x),nil))>
<Marked_shuff(x,y) , Marked_head(x)>
<Marked_if(false,x,y,z) , Marked_shuff(reverse(tail(x)),z)>
<Marked_if(false,x,y,z) , Marked_reverse(tail(x))>
<Marked_if(false,x,y,z) , Marked_tail(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_if(false,x,y,z) , Marked_shuff(reverse(tail(x)),z)> 
      --> <Marked_shuff(x,y) , Marked_if(null(x),x,y,app(y,add(head(x),nil)))>
  <Marked_shuff(x,y) , Marked_if(null(x),x,y,app(y,add(head(x),nil)))> 
     --> <Marked_if(false,x,y,z) , Marked_shuff(reverse(tail(x)),z)>
}

{  <Marked_reverse(add(n,x)) , Marked_reverse(x)> 
      --> <Marked_reverse(add(n,x)) , Marked_reverse(x)>
}

{  <Marked_app(add(n,x),y) , Marked_app(x,y)> 
      --> <Marked_app(add(n,x),y) , Marked_app(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  null(nil) >= true ;
  null(add(n,x)) >= false ;
  tail(nil) >= nil ;
  tail(add(n,x)) >= x ;
  head(add(n,x)) >= n ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuff(x,y) >= if(null(x),x,y,app(y,add(head(x),nil))) ;
  shuffle(x) >= shuff(x,nil) ;
  if(true,x,y,z) >= y ;
  if(false,x,y,z) >= shuff(reverse(tail(x)),z) ;
  Marked_if(false,x,y,z) >= Marked_shuff(reverse(tail(x)),z) ;
  Marked_shuff(x,y) >= Marked_if(null(x),x,y,app(y,add(head(x),nil))) ;
 }
 + Disjunctions:{ 
{
  Marked_if(false,x,y,z) > Marked_shuff(reverse(tail(x)),z) ;
 }
{
  Marked_shuff(x,y) > Marked_if(null(x),x,y,app(y,add(head(x),nil))) ;
 }
 } 
=== 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 : 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:
{
  null(nil) >= true ;
  null(add(n,x)) >= false ;
  tail(nil) >= nil ;
  tail(add(n,x)) >= x ;
  head(add(n,x)) >= n ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuff(x,y) >= if(null(x),x,y,app(y,add(head(x),nil))) ;
  shuffle(x) >= shuff(x,nil) ;
  if(true,x,y,z) >= y ;
  if(false,x,y,z) >= shuff(reverse(tail(x)),z) ;
  Marked_if(false,x,y,z) >= Marked_shuff(reverse(tail(x)),z) ;
  Marked_shuff(x,y) > Marked_if(null(x),x,y,app(y,add(head(x),nil))) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  null(nil) >= true ;
  null(add(n,x)) >= false ;
  tail(nil) >= nil ;
  tail(add(n,x)) >= x ;
  head(add(n,x)) >= n ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuff(x,y) >= if(null(x),x,y,app(y,add(head(x),nil))) ;
  shuffle(x) >= shuff(x,nil) ;
  if(true,x,y,z) >= y ;
  if(false,x,y,z) >= shuff(reverse(tail(x)),z) ;
  Marked_if(false,x,y,z) >= Marked_shuff(reverse(tail(x)),z) ;
  Marked_shuff(x,y) > Marked_if(null(x),x,y,app(y,add(head(x),nil))) ;
 }
 + 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.(32437 bt (34047) [2040])
=== 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 9.283891 seconds (real time)
Cime Exit Status: 0