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

TRS termination of:
[1] a(c(d(x))) -> c(x)
[2] u(b(d(d(x)))) -> b(x)
[3] v(a(a(x))) -> u(v(x))
[4] v(a(c(x))) -> u(b(d(x)))
[5] v(c(x)) -> b(x)
[6] w(a(a(x))) -> u(w(x))
[7] w(a(c(x))) -> u(b(d(x)))
[8] w(c(x)) -> b(x)


Sub problem: 
guided: 

DP termination of:
<Marked_v(a(a(x))) , Marked_u(v(x))>
<Marked_v(a(a(x))) , Marked_v(x)>
<Marked_v(a(c(x))) , Marked_u(b(d(x)))>
<Marked_w(a(a(x))) , Marked_u(w(x))>
<Marked_w(a(a(x))) , Marked_w(x)>
<Marked_w(a(c(x))) , Marked_u(b(d(x)))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_v(a(a(x))) , Marked_v(x)> --> <Marked_v(a(a(x))) , Marked_v(x)>
}

{  <Marked_w(a(a(x))) , Marked_w(x)> --> <Marked_w(a(a(x))) , Marked_w(x)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_v -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_w -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a(c(d(x))) -> c(x)
[2] u(b(d(d(x)))) -> b(x)
[3] v(a(a(x))) -> u(v(x))
[4] v(a(c(x))) -> u(b(d(x)))
[5] v(c(x)) -> b(x)
[6] w(a(a(x))) -> u(w(x))
[7] w(a(c(x))) -> u(b(d(x)))
[8] w(c(x)) -> b(x)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_v(a(a(x))) , Marked_u(v(x))>
<Marked_v(a(a(x))) , Marked_v(x)>
<Marked_v(a(c(x))) , Marked_u(b(d(x)))>
<Marked_w(a(a(x))) , Marked_u(w(x))>
<Marked_w(a(a(x))) , Marked_w(x)>
<Marked_w(a(c(x))) , Marked_u(b(d(x)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_v(a(a(x))) , Marked_v(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_w(a(a(x))) , Marked_w(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.007247 seconds (real time)
Cime Exit Status: 0