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

TRS termination of:
[1] times(x,0) -> 0
[2] times(x,s(y)) -> plus(times(x,y),x)
[3] plus(x,0) -> x
[4] plus(0,x) -> x
[5] plus(x,s(y)) -> s(plus(x,y))
[6] plus(s(x),y) -> s(plus(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_times(x,s(y)) , Marked_plus(times(x,y),x)>
<Marked_times(x,s(y)) , Marked_times(x,y)>
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_times(x,s(y)) , Marked_times(x,y)> 
      --> <Marked_times(x,s(y)) , Marked_times(x,y)>
}

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

ST: Marked_times -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

ST: Marked_plus -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] times(x,0) -> 0
[2] times(x,s(y)) -> plus(times(x,y),x)
[3] plus(x,0) -> x
[4] plus(0,x) -> x
[5] plus(x,s(y)) -> s(plus(x,y))
[6] plus(s(x),y) -> s(plus(x,y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_times(x,s(y)) , Marked_plus(times(x,y),x)>
<Marked_times(x,s(y)) , Marked_times(x,y)>
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_times(x,s(y)) , Marked_times(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_plus(s(x),y) , Marked_plus(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_plus(s(x),y) , Marked_plus(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.008797 seconds (real time)
Cime Exit Status: 0