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

TRS termination of:
[1] app(nil,y) -> y
[2] app(add(n,x),y) -> add(n,app(x,y))
[3] reverse(nil) -> nil
[4] reverse(add(n,x)) -> app(reverse(x),add(n,nil))
[5] shuffle(nil) -> nil
[6] shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))


Sub problem: 
guided: 

DP termination of:
<Marked_app(add(n,x),y) , Marked_app(x,y)>
<Marked_reverse(add(n,x)) , Marked_app(reverse(x),add(n,nil))>
<Marked_reverse(add(n,x)) , Marked_reverse(x)>
<Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))>
<Marked_shuffle(add(n,x)) , Marked_reverse(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))> 
      --> <Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))>
}

{  <Marked_reverse(add(n,x)) , Marked_reverse(x)> 
      --> <Marked_reverse(add(n,x)) , Marked_reverse(x)>
}

{  <Marked_app(add(n,x),y) , Marked_app(x,y)> 
      --> <Marked_app(add(n,x),y) , Marked_app(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  reverse(nil) >= nil ;
  reverse(add(n,x)) >= app(reverse(x),add(n,nil)) ;
  shuffle(nil) >= nil ;
  shuffle(add(n,x)) >= add(n,shuffle(reverse(x))) ;
  Marked_shuffle(add(n,x)) >= Marked_shuffle(reverse(x)) ;
 }
 + Disjunctions:{ 
{
  Marked_shuffle(add(n,x)) > Marked_shuffle(reverse(x)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: app(nil,y) >= y
constraint: app(add(n,x),y) >= add(n,app(x,y))
constraint: reverse(nil) >= nil
constraint: reverse(add(n,x)) >= app(reverse(x),add(n,nil))
constraint: shuffle(nil) >= nil
constraint: shuffle(add(n,x)) >= add(n,shuffle(reverse(x)))
constraint: Marked_shuffle(add(n,x)) >= Marked_shuffle(reverse(x))
APPLY CRITERIA (Subterm criterion)

ST: Marked_reverse -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_app -> 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] app(nil,y) -> y
[2] app(add(n,x),y) -> add(n,app(x,y))
[3] reverse(nil) -> nil
[4] reverse(add(n,x)) -> app(reverse(x),add(n,nil))
[5] shuffle(nil) -> nil
[6] shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_app(add(n,x),y) , Marked_app(x,y)>
<Marked_reverse(add(n,x)) , Marked_app(reverse(x),add(n,nil))>
<Marked_reverse(add(n,x)) , Marked_reverse(x)>
<Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))>
<Marked_shuffle(add(n,x)) , Marked_reverse(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_shuffle(add(n,x)) , Marked_shuffle(reverse(x))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ app ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ shuffle ] (X0) = 2*X0 + 0; 
 [ add ] (X0,X1) = 1 + 1*X1 + 0; 
 [ nil ] () = 0; 
 [ Marked_shuffle ] (X0) = 1*X0 + 0; 
 [ reverse ] (X0) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_reverse(add(n,x)) , Marked_reverse(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_app(add(n,x),y) , Marked_app(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.036953 seconds (real time)
Cime Exit Status: 0