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

TRS termination of:
[1] f(s(x),y) -> f(x,s(s(x)))
[2] f(x,s(s(y))) -> f(y,x)


Sub problem: 
guided: 

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

{  <Marked_f(x,s(s(y))) , Marked_f(y,x)> 
      --> <Marked_f(x,s(s(y))) , Marked_f(y,x)>
  <Marked_f(x,s(s(y))) , Marked_f(y,x)> 
     --> <Marked_f(s(x),y) , Marked_f(x,s(s(x)))>
  <Marked_f(s(x),y) , Marked_f(x,s(s(x)))> 
     --> <Marked_f(x,s(s(y))) , Marked_f(y,x)>
  <Marked_f(s(x),y) , Marked_f(x,s(s(x)))> 
     --> <Marked_f(s(x),y) , Marked_f(x,s(s(x)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(x),y) >= f(x,s(s(x))) ;
  f(x,s(s(y))) >= f(y,x) ;
  Marked_f(s(x),y) >= Marked_f(x,s(s(x))) ;
  Marked_f(x,s(s(y))) >= Marked_f(y,x) ;
 }
 + Disjunctions:{ 
{
  Marked_f(s(x),y) > Marked_f(x,s(s(x))) ;
 }
{
  Marked_f(x,s(s(y))) > Marked_f(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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(s(x),y) >= f(x,s(s(x)))
constraint: f(x,s(s(y))) >= f(y,x)
constraint: Marked_f(s(x),y) >= Marked_f(x,s(s(x)))
constraint: Marked_f(x,s(s(y))) >= Marked_f(y,x)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(x,s(s(y))) , Marked_f(y,x)> 
      --> <Marked_f(x,s(s(y))) , Marked_f(y,x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(x),y) >= f(x,s(s(x))) ;
  f(x,s(s(y))) >= f(y,x) ;
  Marked_f(x,s(s(y))) >= Marked_f(y,x) ;
 }
 + Disjunctions:{ 
{
  Marked_f(x,s(s(y))) > Marked_f(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: f(s(x),y) >= f(x,s(s(x)))
constraint: f(x,s(s(y))) >= f(y,x)
constraint: Marked_f(x,s(s(y))) >= Marked_f(y,x)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(s(x),y) -> f(x,s(s(x)))
[2] f(x,s(s(y))) -> f(y,x)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(x),y) , Marked_f(x,s(s(x)))>
<Marked_f(x,s(s(y))) , Marked_f(y,x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(x),y) , Marked_f(x,s(s(x)))>
<Marked_f(x,s(s(y))) , Marked_f(y,x)>
 ,
 CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_f ] (X0,X1) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 1 , 1 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ s ] (X0) = [ [ 1 , 0 , 1 ] [ 1 , 1 , 1 ] [ 1 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 removing <Marked_f(s(x),y),Marked_f(x,s(s(x)))>
 [ {
      
     DP termination of:
     <Marked_f(x,s(s(y))) , Marked_f(y,x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(x,s(s(y))) , Marked_f(y,x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ f ] (X0,X1) = 0; 
 [ Marked_f ] (X0,X1) = 3*X0 + 1*X1 + 0; 
 [ s ] (X0) = 2 + 2*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.253741 seconds (real time)
Cime Exit Status: 0