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

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


Sub problem: 
guided: 

DP termination of:
<Marked_g(f(x,y),z) , Marked_g(y,z)>
<Marked_g(h(x,y),z) , Marked_g(x,f(y,z))>
<Marked_g(x,h(y,z)) , Marked_g(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_g(x,h(y,z)) , Marked_g(x,y)> 
      --> <Marked_g(x,h(y,z)) , Marked_g(x,y)>
  <Marked_g(x,h(y,z)) , Marked_g(x,y)> 
     --> <Marked_g(h(x,y),z) , Marked_g(x,f(y,z))>
  <Marked_g(x,h(y,z)) , Marked_g(x,y)> --> <Marked_g(f(x,y),z) , Marked_g(y,z)>
  <Marked_g(h(x,y),z) , Marked_g(x,f(y,z))> 
     --> <Marked_g(h(x,y),z) , Marked_g(x,f(y,z))>
  <Marked_g(h(x,y),z) , Marked_g(x,f(y,z))> 
     --> <Marked_g(f(x,y),z) , Marked_g(y,z)>
  <Marked_g(f(x,y),z) , Marked_g(y,z)> --> <Marked_g(x,h(y,z)) , Marked_g(x,y)>
  <Marked_g(f(x,y),z) , Marked_g(y,z)> 
     --> <Marked_g(h(x,y),z) , Marked_g(x,f(y,z))>
  <Marked_g(f(x,y),z) , Marked_g(y,z)> --> <Marked_g(f(x,y),z) , Marked_g(y,z)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_g -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_g(x,h(y,z)) , Marked_g(x,y)> 
      --> <Marked_g(x,h(y,z)) , Marked_g(x,y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_g -> 2

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

Cime worked for 0.006129 seconds (real time)
Cime Exit Status: 0