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

TRS termination of:
[1] f(s(X),X) -> f(X,a(X))
[2] f(X,c(X)) -> f(s(X),X)
[3] f(X,X) -> c(X)


Sub problem: 
guided: 

DP termination of:
<Marked_f(s(X),X) , Marked_f(X,a(X))>
<Marked_f(X,c(X)) , Marked_f(s(X),X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(X,c(X)) , Marked_f(s(X),X)> 
      --> <Marked_f(X,c(X)) , Marked_f(s(X),X)>
}

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

Cime worked for 0.029488 seconds (real time)
Cime Exit Status: 0