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

TRS termination of:
[1] D(t) -> 1
[2] D(constant) -> 0
[3] D(+(x,y)) -> +(D(x),D(y))
[4] D( *(x,y)) -> +( *(y,D(x)), *(x,D(y)))
[5] D(-(x,y)) -> -(D(x),D(y))


Sub problem: 
guided: 

DP termination of:
<Marked_D(+(x,y)) , Marked_D(x)>
<Marked_D(+(x,y)) , Marked_D(y)>
<Marked_D( *(x,y)) , Marked_D(x)>
<Marked_D( *(x,y)) , Marked_D(y)>
<Marked_D(-(x,y)) , Marked_D(x)>
<Marked_D(-(x,y)) , Marked_D(y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

ST: Marked_D -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] D(t) -> 1
[2] D(constant) -> 0
[3] D(+(x,y)) -> +(D(x),D(y))
[4] D( *(x,y)) -> +( *(y,D(x)), *(x,D(y)))
[5] D(-(x,y)) -> -(D(x),D(y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_D(+(x,y)) , Marked_D(x)>
<Marked_D(+(x,y)) , Marked_D(y)>
<Marked_D( *(x,y)) , Marked_D(x)>
<Marked_D( *(x,y)) , Marked_D(y)>
<Marked_D(-(x,y)) , Marked_D(x)>
<Marked_D(-(x,y)) , Marked_D(y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_D(+(x,y)) , Marked_D(x)>
<Marked_D(+(x,y)) , Marked_D(y)>
<Marked_D( *(x,y)) , Marked_D(x)>
<Marked_D( *(x,y)) , Marked_D(y)>
<Marked_D(-(x,y)) , Marked_D(x)>
<Marked_D(-(x,y)) , Marked_D(y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.005918 seconds (real time)
Cime Exit Status: 0