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

TRS termination of:
[1] f(0,y) -> y
[2] f(x,0) -> x
[3] f(i(x),y) -> i(x)
[4] f(f(x,y),z) -> f(x,f(y,z))
[5] f(g(x,y),z) -> g(f(x,z),f(y,z))
[6] f(1,g(x,y)) -> x
[7] f(2,g(x,y)) -> y


Sub problem: 
guided: 

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

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

ST: Marked_f -> 1

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

Cime worked for 0.006976 seconds (real time)
Cime Exit Status: 0