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

TRS termination of:
[1] merge(nil,y) -> y
[2] merge(x,nil) -> x
[3] merge(.(x,y),.(u,v)) ->
 if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
[4] ++(nil,y) -> y
[5] ++(.(x,y),z) -> .(x,++(y,z))
[6] if(true,x,y) -> x
[7] if(false,x,y) -> x


Sub problem: 
guided: 

DP termination of:
<Marked_merge(.(x,y),.(u,v)) , Marked_if(<(x,u),.(x,merge(y,.(u,v))),
                                .(u,merge(.(x,y),v)))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)> 
      --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)> 
     --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))> 
     --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))> 
     --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
}

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

ST: Marked_merge -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_++ -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))> 
      --> <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_merge -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] merge(nil,y) -> y
[2] merge(x,nil) -> x
[3] merge(.(x,y),.(u,v)) ->
 if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
[4] ++(nil,y) -> y
[5] ++(.(x,y),z) -> .(x,++(y,z))
[6] if(true,x,y) -> x
[7] if(false,x,y) -> x
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_merge(.(x,y),.(u,v)) , Marked_if(<(x,u),.(x,merge(y,.(u,v))),
                                     .(u,merge(.(x,y),v)))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
<Marked_merge(.(x,y),.(u,v)) , Marked_merge(.(x,y),v)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_merge(.(x,y),.(u,v)) , Marked_merge(y,.(u,v))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.010397 seconds (real time)
Cime Exit Status: 0