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

TRS termination of:
[1] double(0) -> 0
[2] double(s(x)) -> s(s(double(x)))
[3] half(0) -> 0
[4] half(s(0)) -> 0
[5] half(s(s(x))) -> s(half(x))
[6] -(x,0) -> x
[7] -(s(x),s(y)) -> -(x,y)
[8] if(0,y,z) -> y
[9] if(s(x),y,z) -> z
[10] half(double(x)) -> x


Sub problem: 
guided: 

DP termination of:
<Marked_double(s(x)) , Marked_double(x)>
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

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

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

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

ST: Marked_double -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_half -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_- -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] double(0) -> 0
[2] double(s(x)) -> s(s(double(x)))
[3] half(0) -> 0
[4] half(s(0)) -> 0
[5] half(s(s(x))) -> s(half(x))
[6] -(x,0) -> x
[7] -(s(x),s(y)) -> -(x,y)
[8] if(0,y,z) -> y
[9] if(s(x),y,z) -> z
[10] half(double(x)) -> x
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_double(s(x)) , Marked_double(x)>
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_double(s(x)) , Marked_double(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_half(s(s(x))) , Marked_half(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.010226 seconds (real time)
Cime Exit Status: 0