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

TRS termination of:
[1] ack(0,y) -> s(y)
[2] ack(s(x),0) -> ack(x,s(0))
[3] ack(s(x),s(y)) -> ack(x,ack(s(x),y))


Sub problem: 
guided: 

DP termination of:
<Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
      --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
     --> <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
  <Marked_ack(s(x),0) , Marked_ack(x,s(0))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),0) , Marked_ack(x,s(0))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_ack -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
      --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_ack -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] ack(0,y) -> s(y)
[2] ack(s(x),0) -> ack(x,s(0))
[3] ack(s(x),s(y)) -> ack(x,ack(s(x),y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.005738 seconds (real time)
Cime Exit Status: 0