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

TRS termination of:
[1] sum(0) -> 0
[2] sum(s(x)) -> +(sum(x),s(x))
[3] sum1(0) -> 0
[4] sum1(s(x)) -> s(+(sum1(x),+(x,x)))


Sub problem: 
guided: 

DP termination of:
<Marked_sum(s(x)) , Marked_sum(x)>
<Marked_sum1(s(x)) , Marked_sum1(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_sum(s(x)) , Marked_sum(x)> --> <Marked_sum(s(x)) , Marked_sum(x)>
}

{  <Marked_sum1(s(x)) , Marked_sum1(x)> 
      --> <Marked_sum1(s(x)) , Marked_sum1(x)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_sum -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_sum1 -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] sum(0) -> 0
[2] sum(s(x)) -> +(sum(x),s(x))
[3] sum1(0) -> 0
[4] sum1(s(x)) -> s(+(sum1(x),+(x,x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_sum(s(x)) , Marked_sum(x)>
<Marked_sum1(s(x)) , Marked_sum1(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sum(s(x)) , Marked_sum(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_sum1(s(x)) , Marked_sum1(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.006837 seconds (real time)
Cime Exit Status: 0