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

TRS termination of:
[1] ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
[2] u21(ackout(X),Y) -> u22(ackin(Y,X))


Sub problem: 
guided: 

DP termination of:
<Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
<Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
<Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)> 
      --> <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
  <Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)> 
     --> <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
  <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)> 
     --> <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
  <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)> 
     --> <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
  <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)> 
     --> <Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_u21 -> 2
Marked_ackin -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)> 
      --> <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_ackin -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
[2] u21(ackout(X),Y) -> u22(ackin(Y,X))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
<Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
<Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
<Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
<Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
<Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.007285 seconds (real time)
Cime Exit Status: 0