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

TRS termination of:
[1] not(true) -> false
[2] not(false) -> true
[3] odd(0) -> false
[4] odd(s(x)) -> not(odd(x))
[5] +(x,0) -> x
[6] +(x,s(y)) -> s(+(x,y))
[7] +(s(x),y) -> s(+(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_odd(s(x)) , Marked_not(odd(x))>
<Marked_odd(s(x)) , Marked_odd(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_+(s(x),y) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

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

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

ST: Marked_odd -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 2

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

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

ST: Marked_+ -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] not(true) -> false
[2] not(false) -> true
[3] odd(0) -> false
[4] odd(s(x)) -> not(odd(x))
[5] +(x,0) -> x
[6] +(x,s(y)) -> s(+(x,y))
[7] +(s(x),y) -> s(+(x,y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_odd(s(x)) , Marked_not(odd(x))>
<Marked_odd(s(x)) , Marked_odd(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_+(s(x),y) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_odd(s(x)) , Marked_odd(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_+(s(x),y) , Marked_+(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_+(s(x),y) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_+(s(x),y) , Marked_+(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.009176 seconds (real time)
Cime Exit Status: 0