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

TRS termination of:
[1] flatten(nil) -> nil
[2] flatten(unit(x)) -> flatten(x)
[3] flatten(++(x,y)) -> ++(flatten(x),flatten(y))
[4] flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
[5] flatten(flatten(x)) -> flatten(x)
[6] rev(nil) -> nil
[7] rev(unit(x)) -> unit(x)
[8] rev(++(x,y)) -> ++(rev(y),rev(x))
[9] rev(rev(x)) -> x
[10] ++(x,nil) -> x
[11] ++(nil,y) -> y
[12] ++(++(x,y),z) -> ++(x,++(y,z))


Sub problem: 
guided: 

DP termination of:
<Marked_flatten(unit(x)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_++(flatten(x),flatten(y))>
<Marked_flatten(++(x,y)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_flatten(y)>
<Marked_flatten(++(unit(x),y)) , Marked_++(flatten(x),flatten(y))>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
<Marked_rev(++(x,y)) , Marked_++(rev(y),rev(x))>
<Marked_rev(++(x,y)) , Marked_rev(y)>
<Marked_rev(++(x,y)) , Marked_rev(x)>
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
      --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
}

{  <Marked_rev(++(x,y)) , Marked_rev(x)> 
      --> <Marked_rev(++(x,y)) , Marked_rev(x)>
  <Marked_rev(++(x,y)) , Marked_rev(x)> 
     --> <Marked_rev(++(x,y)) , Marked_rev(y)>
  <Marked_rev(++(x,y)) , Marked_rev(y)> 
     --> <Marked_rev(++(x,y)) , Marked_rev(x)>
  <Marked_rev(++(x,y)) , Marked_rev(y)> 
     --> <Marked_rev(++(x,y)) , Marked_rev(y)>
}

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

ST: Marked_flatten -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_rev -> 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] flatten(nil) -> nil
[2] flatten(unit(x)) -> flatten(x)
[3] flatten(++(x,y)) -> ++(flatten(x),flatten(y))
[4] flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
[5] flatten(flatten(x)) -> flatten(x)
[6] rev(nil) -> nil
[7] rev(unit(x)) -> unit(x)
[8] rev(++(x,y)) -> ++(rev(y),rev(x))
[9] rev(rev(x)) -> x
[10] ++(x,nil) -> x
[11] ++(nil,y) -> y
[12] ++(++(x,y),z) -> ++(x,++(y,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_flatten(unit(x)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_++(flatten(x),flatten(y))>
<Marked_flatten(++(x,y)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_flatten(y)>
<Marked_flatten(++(unit(x),y)) , Marked_++(flatten(x),flatten(y))>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
<Marked_rev(++(x,y)) , Marked_++(rev(y),rev(x))>
<Marked_rev(++(x,y)) , Marked_rev(y)>
<Marked_rev(++(x,y)) , Marked_rev(x)>
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_flatten(unit(x)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_flatten(y)>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_rev(++(x,y)) , Marked_rev(y)>
<Marked_rev(++(x,y)) , Marked_rev(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.014436 seconds (real time)
Cime Exit Status: 0