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

TRS termination of:
[1] s(a) -> a
[2] s(s(x)) -> x
[3] s(f(x,y)) -> f(s(y),s(x))
[4] s(g(x,y)) -> g(s(x),s(y))
[5] f(x,a) -> x
[6] f(a,y) -> y
[7] f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
[8] g(a,a) -> a


Sub problem: 
guided: 

DP termination of:
<Marked_s(f(x,y)) , Marked_f(s(y),s(x))>
<Marked_s(f(x,y)) , Marked_s(y)>
<Marked_s(f(x,y)) , Marked_s(x)>
<Marked_s(g(x,y)) , Marked_g(s(x),s(y))>
<Marked_s(g(x,y)) , Marked_s(x)>
<Marked_s(g(x,y)) , Marked_s(y)>
<Marked_f(g(x,y),g(u,v)) , Marked_g(f(x,u),f(y,v))>
<Marked_f(g(x,y),g(u,v)) , Marked_f(x,u)>
<Marked_f(g(x,y),g(u,v)) , Marked_f(y,v)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_s(g(x,y)) , Marked_s(y)> --> <Marked_s(g(x,y)) , Marked_s(y)>
  <Marked_s(g(x,y)) , Marked_s(y)> --> <Marked_s(g(x,y)) , Marked_s(x)>
  <Marked_s(g(x,y)) , Marked_s(y)> --> <Marked_s(f(x,y)) , Marked_s(x)>
  <Marked_s(g(x,y)) , Marked_s(y)> --> <Marked_s(f(x,y)) , Marked_s(y)>
  <Marked_s(g(x,y)) , Marked_s(x)> --> <Marked_s(g(x,y)) , Marked_s(y)>
  <Marked_s(g(x,y)) , Marked_s(x)> --> <Marked_s(g(x,y)) , Marked_s(x)>
  <Marked_s(g(x,y)) , Marked_s(x)> --> <Marked_s(f(x,y)) , Marked_s(x)>
  <Marked_s(g(x,y)) , Marked_s(x)> --> <Marked_s(f(x,y)) , Marked_s(y)>
  <Marked_s(f(x,y)) , Marked_s(x)> --> <Marked_s(g(x,y)) , Marked_s(y)>
  <Marked_s(f(x,y)) , Marked_s(x)> --> <Marked_s(g(x,y)) , Marked_s(x)>
  <Marked_s(f(x,y)) , Marked_s(x)> --> <Marked_s(f(x,y)) , Marked_s(x)>
  <Marked_s(f(x,y)) , Marked_s(x)> --> <Marked_s(f(x,y)) , Marked_s(y)>
  <Marked_s(f(x,y)) , Marked_s(y)> --> <Marked_s(g(x,y)) , Marked_s(y)>
  <Marked_s(f(x,y)) , Marked_s(y)> --> <Marked_s(g(x,y)) , Marked_s(x)>
  <Marked_s(f(x,y)) , Marked_s(y)> --> <Marked_s(f(x,y)) , Marked_s(x)>
  <Marked_s(f(x,y)) , Marked_s(y)> --> <Marked_s(f(x,y)) , Marked_s(y)>
}

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

ST: Marked_s -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 2

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

Cime worked for 0.008905 seconds (real time)
Cime Exit Status: 0