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

TRS termination of:
[1] f(a,g(y)) -> g(g(y))
[2] f(g(x),a) -> f(x,g(a))
[3] f(g(x),g(y)) -> h(g(y),x,g(y))
[4] h(g(x),y,z) -> f(y,h(x,y,z))
[5] h(a,y,z) -> z


Sub problem: 
guided: 

DP termination of:
<Marked_f(g(x),a) , Marked_f(x,g(a))>
<Marked_f(g(x),g(y)) , Marked_h(g(y),x,g(y))>
<Marked_h(g(x),y,z) , Marked_f(y,h(x,y,z))>
<Marked_h(g(x),y,z) , Marked_h(x,y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_h(g(x),y,z) , Marked_h(x,y,z)> 
      --> <Marked_h(g(x),y,z) , Marked_h(x,y,z)>
  <Marked_h(g(x),y,z) , Marked_h(x,y,z)> 
     --> <Marked_h(g(x),y,z) , Marked_f(y,h(x,y,z))>
  <Marked_h(g(x),y,z) , Marked_f(y,h(x,y,z))> 
     --> <Marked_f(g(x),g(y)) , Marked_h(g(y),x,g(y))>
  <Marked_h(g(x),y,z) , Marked_f(y,h(x,y,z))> 
     --> <Marked_f(g(x),a) , Marked_f(x,g(a))>
  <Marked_f(g(x),g(y)) , Marked_h(g(y),x,g(y))> 
     --> <Marked_h(g(x),y,z) , Marked_h(x,y,z)>
  <Marked_f(g(x),g(y)) , Marked_h(g(y),x,g(y))> 
     --> <Marked_h(g(x),y,z) , Marked_f(y,h(x,y,z))>
  <Marked_f(g(x),a) , Marked_f(x,g(a))> 
     --> <Marked_f(g(x),g(y)) , Marked_h(g(y),x,g(y))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_h -> 2
Marked_f -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_h(g(x),y,z) , Marked_h(x,y,z)> 
      --> <Marked_h(g(x),y,z) , Marked_h(x,y,z)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_h -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(a,g(y)) -> g(g(y))
[2] f(g(x),a) -> f(x,g(a))
[3] f(g(x),g(y)) -> h(g(y),x,g(y))
[4] h(g(x),y,z) -> f(y,h(x,y,z))
[5] h(a,y,z) -> z
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(g(x),a) , Marked_f(x,g(a))>
<Marked_f(g(x),g(y)) , Marked_h(g(y),x,g(y))>
<Marked_h(g(x),y,z) , Marked_f(y,h(x,y,z))>
<Marked_h(g(x),y,z) , Marked_h(x,y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(g(x),a) , Marked_f(x,g(a))>
<Marked_f(g(x),g(y)) , Marked_h(g(y),x,g(y))>
<Marked_h(g(x),y,z) , Marked_f(y,h(x,y,z))>
<Marked_h(g(x),y,z) , Marked_h(x,y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_h(g(x),y,z) , Marked_h(x,y,z)>
<Marked_h(g(x),y,z) , Marked_f(y,h(x,y,z))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_h(g(x),y,z) , Marked_h(x,y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.007955 seconds (real time)
Cime Exit Status: 0