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

TRS termination of:
[1] minus(minus(x)) -> x
[2] minus(+(x,y)) ->  *(minus(minus(minus(x))),minus(minus(minus(y))))
[3] minus( *(x,y)) -> +(minus(minus(minus(x))),minus(minus(minus(y))))
[4] f(minus(x)) -> minus(minus(minus(f(x))))


Sub problem: 
guided: 

DP termination of:
<Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
<Marked_minus(+(x,y)) , Marked_minus(minus(x))>
<Marked_minus(+(x,y)) , Marked_minus(x)>
<Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
<Marked_minus(+(x,y)) , Marked_minus(minus(y))>
<Marked_minus(+(x,y)) , Marked_minus(y)>
<Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
<Marked_minus( *(x,y)) , Marked_minus(minus(x))>
<Marked_minus( *(x,y)) , Marked_minus(x)>
<Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
<Marked_minus( *(x,y)) , Marked_minus(minus(y))>
<Marked_minus( *(x,y)) , Marked_minus(y)>
<Marked_f(minus(x)) , Marked_minus(minus(minus(f(x))))>
<Marked_f(minus(x)) , Marked_minus(minus(f(x)))>
<Marked_f(minus(x)) , Marked_minus(f(x))>
<Marked_f(minus(x)) , Marked_f(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(minus(x)) , Marked_f(x)> --> <Marked_f(minus(x)) , Marked_f(x)>
}

{  <Marked_minus( *(x,y)) , Marked_minus(y)> 
      --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(y))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(x))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(y)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(y))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(x)>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(x))>
  <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))> 
     --> <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(minus(x)) >= x ;
  minus( *(x,y)) >= +(minus(minus(minus(x))),minus(minus(minus(y)))) ;
  minus(+(x,y)) >=  *(minus(minus(minus(x))),minus(minus(minus(y)))) ;
  f(minus(x)) >= minus(minus(minus(f(x)))) ;
  Marked_minus( *(x,y)) >= Marked_minus(minus(minus(x))) ;
  Marked_minus( *(x,y)) >= Marked_minus(minus(minus(y))) ;
  Marked_minus( *(x,y)) >= Marked_minus(minus(x)) ;
  Marked_minus( *(x,y)) >= Marked_minus(minus(y)) ;
  Marked_minus( *(x,y)) >= Marked_minus(x) ;
  Marked_minus( *(x,y)) >= Marked_minus(y) ;
  Marked_minus(+(x,y)) >= Marked_minus(minus(minus(x))) ;
  Marked_minus(+(x,y)) >= Marked_minus(minus(minus(y))) ;
  Marked_minus(+(x,y)) >= Marked_minus(minus(x)) ;
  Marked_minus(+(x,y)) >= Marked_minus(minus(y)) ;
  Marked_minus(+(x,y)) >= Marked_minus(x) ;
  Marked_minus(+(x,y)) >= Marked_minus(y) ;
 }
 + Disjunctions:{ 
{
  Marked_minus( *(x,y)) > Marked_minus(minus(minus(x))) ;
 }
{
  Marked_minus( *(x,y)) > Marked_minus(minus(minus(y))) ;
 }
{
  Marked_minus( *(x,y)) > Marked_minus(minus(x)) ;
 }
{
  Marked_minus( *(x,y)) > Marked_minus(minus(y)) ;
 }
{
  Marked_minus( *(x,y)) > Marked_minus(x) ;
 }
{
  Marked_minus( *(x,y)) > Marked_minus(y) ;
 }
{
  Marked_minus(+(x,y)) > Marked_minus(minus(minus(x))) ;
 }
{
  Marked_minus(+(x,y)) > Marked_minus(minus(minus(y))) ;
 }
{
  Marked_minus(+(x,y)) > Marked_minus(minus(x)) ;
 }
{
  Marked_minus(+(x,y)) > Marked_minus(minus(y)) ;
 }
{
  Marked_minus(+(x,y)) > Marked_minus(x) ;
 }
{
  Marked_minus(+(x,y)) > Marked_minus(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: minus(minus(x)) >= x
constraint: minus( *(x,y)) >= +(minus(minus(minus(x))),minus(minus(minus(y))))
constraint: minus(+(x,y)) >=  *(minus(minus(minus(x))),minus(minus(minus(y))))
constraint: f(minus(x)) >= minus(minus(minus(f(x))))
constraint: Marked_minus( *(x,y)) >= Marked_minus(minus(minus(x)))
constraint: Marked_minus( *(x,y)) >= Marked_minus(minus(minus(y)))
constraint: Marked_minus( *(x,y)) >= Marked_minus(minus(x))
constraint: Marked_minus( *(x,y)) >= Marked_minus(minus(y))
constraint: Marked_minus( *(x,y)) >= Marked_minus(x)
constraint: Marked_minus( *(x,y)) >= Marked_minus(y)
constraint: Marked_minus(+(x,y)) >= Marked_minus(minus(minus(x)))
constraint: Marked_minus(+(x,y)) >= Marked_minus(minus(minus(y)))
constraint: Marked_minus(+(x,y)) >= Marked_minus(minus(x))
constraint: Marked_minus(+(x,y)) >= Marked_minus(minus(y))
constraint: Marked_minus(+(x,y)) >= Marked_minus(x)
constraint: Marked_minus(+(x,y)) >= Marked_minus(y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] minus(minus(x)) -> x
[2] minus(+(x,y)) ->  *(minus(minus(minus(x))),minus(minus(minus(y))))
[3] minus( *(x,y)) -> +(minus(minus(minus(x))),minus(minus(minus(y))))
[4] f(minus(x)) -> minus(minus(minus(f(x))))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
<Marked_minus(+(x,y)) , Marked_minus(minus(x))>
<Marked_minus(+(x,y)) , Marked_minus(x)>
<Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
<Marked_minus(+(x,y)) , Marked_minus(minus(y))>
<Marked_minus(+(x,y)) , Marked_minus(y)>
<Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
<Marked_minus( *(x,y)) , Marked_minus(minus(x))>
<Marked_minus( *(x,y)) , Marked_minus(x)>
<Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
<Marked_minus( *(x,y)) , Marked_minus(minus(y))>
<Marked_minus( *(x,y)) , Marked_minus(y)>
<Marked_f(minus(x)) , Marked_minus(minus(minus(f(x))))>
<Marked_f(minus(x)) , Marked_minus(minus(f(x)))>
<Marked_f(minus(x)) , Marked_minus(f(x))>
<Marked_f(minus(x)) , Marked_f(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(minus(x)) , Marked_f(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_minus(+(x,y)) , Marked_minus(minus(minus(x)))>
<Marked_minus(+(x,y)) , Marked_minus(minus(x))>
<Marked_minus(+(x,y)) , Marked_minus(x)>
<Marked_minus(+(x,y)) , Marked_minus(minus(minus(y)))>
<Marked_minus(+(x,y)) , Marked_minus(minus(y))>
<Marked_minus(+(x,y)) , Marked_minus(y)>
<Marked_minus( *(x,y)) , Marked_minus(minus(minus(x)))>
<Marked_minus( *(x,y)) , Marked_minus(minus(x))>
<Marked_minus( *(x,y)) , Marked_minus(x)>
<Marked_minus( *(x,y)) , Marked_minus(minus(minus(y)))>
<Marked_minus( *(x,y)) , Marked_minus(minus(y))>
<Marked_minus( *(x,y)) , Marked_minus(y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0) = 1*X0 + 0; 
 [ + ] (X0,X1) = 3 + 2*X0 + 2*X1 + 0; 
 [ * ] (X0,X1) = 3 + 2*X0 + 2*X1 + 0; 
 [ Marked_minus ] (X0) = 2*X0 + 0; 
 [ f ] (X0) = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.109190 seconds (real time)
Cime Exit Status: 0