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

TRS termination of:
[1] app(id,x) -> x
[2] app(plus,0) -> id
[3] app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(plus,app(s,x)),y) , Marked_app(s,app(app(plus,x),y))>
<Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
<Marked_app(app(plus,app(s,x)),y) , Marked_app(plus,x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)> 
      --> <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) ;
  app(id,x) >= x ;
  app(plus,0) >= id ;
  Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(plus,app(s,x)),y) > Marked_app(app(plus,x),y) ;
 }
 } 
=== 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(app(plus,app(s,x)),y) >= app(s,app(app(plus,x),y))
constraint: app(id,x) >= x
constraint: app(plus,0) >= id
constraint: Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] app(id,x) -> x
[2] app(plus,0) -> id
[3] app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_app(app(plus,app(s,x)),y) , Marked_app(s,app(app(plus,x),y))>
<Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
<Marked_app(app(plus,app(s,x)),y) , Marked_app(plus,x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(plus,app(s,x)),y) , Marked_app(app(plus,x),y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ app ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; 
 [ s ] () = 0; 
 [ plus ] () = 0; 
 [ id ] () = 0; 
 [ Marked_app ] (X0,X1) = 2*X0 + 0; 
 [ 0 ] () = 3 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.034034 seconds (real time)
Cime Exit Status: 0