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

TRS termination of:
[1] +(x,0) -> x
[2] +(x,s(y)) -> s(+(x,y))
[3] +(0,s(y)) -> s(y)
[4] s(+(0,y)) -> s(y)


Sub problem: 
guided: 

DP termination of:
<Marked_+(x,s(y)) , Marked_s(+(x,y))>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_s(+(0,y)) , Marked_s(y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_+(x,s(y)) , Marked_+(x,y)> --> <Marked_+(x,s(y)) , Marked_+(x,y)>
}

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

Cime worked for 0.021768 seconds (real time)
Cime Exit Status: 0