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

TRS termination of:
[1] f(j(x,y),y) -> g(f(x,k(y)))
[2] f(x,h1(y,z)) -> h2(0,x,h1(y,z))
[3] g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
[4] h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
[5] i(f(x,h(y))) -> y
[6] i(h2(s(x),y,h1(x,z))) -> z
[7] k(h(x)) -> h1(0,x)
[8] k(h1(x,y)) -> h1(s(x),y)


Sub problem: 
guided: 

DP termination of:
<Marked_f(j(x,y),y) , Marked_g(f(x,k(y)))>
<Marked_f(j(x,y),y) , Marked_f(x,k(y))>
<Marked_f(j(x,y),y) , Marked_k(y)>
<Marked_f(x,h1(y,z)) , Marked_h2(0,x,h1(y,z))>
<Marked_g(h2(x,y,h1(z,u))) , Marked_h2(s(x),y,h1(z,u))>
<Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(j(x,y),y) , Marked_f(x,k(y))> 
      --> <Marked_f(j(x,y),y) , Marked_f(x,k(y))>
}

{  <Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))> 
      --> <Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_h2 -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(j(x,y),y) -> g(f(x,k(y)))
[2] f(x,h1(y,z)) -> h2(0,x,h1(y,z))
[3] g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
[4] h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
[5] i(f(x,h(y))) -> y
[6] i(h2(s(x),y,h1(x,z))) -> z
[7] k(h(x)) -> h1(0,x)
[8] k(h1(x,y)) -> h1(s(x),y)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(j(x,y),y) , Marked_g(f(x,k(y)))>
<Marked_f(j(x,y),y) , Marked_f(x,k(y))>
<Marked_f(j(x,y),y) , Marked_k(y)>
<Marked_f(x,h1(y,z)) , Marked_h2(0,x,h1(y,z))>
<Marked_g(h2(x,y,h1(z,u))) , Marked_h2(s(x),y,h1(z,u))>
<Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(j(x,y),y) , Marked_f(x,k(y))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_h2(x,j(y,h1(z,u)),h1(z,u)) , Marked_h2(s(x),y,h1(s(z),u))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.007773 seconds (real time)
Cime Exit Status: 0