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

TRS termination of:
[1] plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
[2] times(X,s(Y)) -> plus(X,times(Y,X))


Sub problem: 
guided: 

DP termination of:
<Marked_plus(plus(X,Y),Z) , Marked_plus(X,plus(Y,Z))>
<Marked_plus(plus(X,Y),Z) , Marked_plus(Y,Z)>
<Marked_times(X,s(Y)) , Marked_plus(X,times(Y,X))>
<Marked_times(X,s(Y)) , Marked_times(Y,X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_times(X,s(Y)) , Marked_times(Y,X)> 
      --> <Marked_times(X,s(Y)) , Marked_times(Y,X)>
}

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

Cime worked for 0.029560 seconds (real time)
Cime Exit Status: 0