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

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


Sub problem: 
guided: 

DP termination of:
<Marked_f(a,a) , Marked_f(a,b)>
<Marked_f(a,b) , Marked_f(s(a),c)>
<Marked_f(s(X),c) , Marked_f(X,c)>
<Marked_f(c,c) , Marked_f(a,a)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(c,c) , Marked_f(a,a)> --> <Marked_f(a,a) , Marked_f(a,b)>
  <Marked_f(s(X),c) , Marked_f(X,c)> --> <Marked_f(c,c) , Marked_f(a,a)>
  <Marked_f(s(X),c) , Marked_f(X,c)> --> <Marked_f(s(X),c) , Marked_f(X,c)>
  <Marked_f(a,b) , Marked_f(s(a),c)> --> <Marked_f(s(X),c) , Marked_f(X,c)>
  <Marked_f(a,a) , Marked_f(a,b)> --> <Marked_f(a,b) , Marked_f(s(a),c)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(a,a) >= f(a,b) ;
  f(a,b) >= f(s(a),c) ;
  f(s(X),c) >= f(X,c) ;
  f(c,c) >= f(a,a) ;
  Marked_f(a,a) >= Marked_f(a,b) ;
  Marked_f(a,b) >= Marked_f(s(a),c) ;
  Marked_f(s(X),c) >= Marked_f(X,c) ;
  Marked_f(c,c) >= Marked_f(a,a) ;
 }
 + Disjunctions:{ 
{
  Marked_f(a,a) > Marked_f(a,b) ;
 }
{
  Marked_f(a,b) > Marked_f(s(a),c) ;
 }
{
  Marked_f(s(X),c) > Marked_f(X,c) ;
 }
{
  Marked_f(c,c) > Marked_f(a,a) ;
 }
 } 
=== 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(a,a) >= f(a,b)
constraint: f(a,b) >= f(s(a),c)
constraint: f(s(X),c) >= f(X,c)
constraint: f(c,c) >= f(a,a)
constraint: Marked_f(a,a) >= Marked_f(a,b)
constraint: Marked_f(a,b) >= Marked_f(s(a),c)
constraint: Marked_f(s(X),c) >= Marked_f(X,c)
constraint: Marked_f(c,c) >= Marked_f(a,a)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(s(X),c) , Marked_f(X,c)> --> <Marked_f(s(X),c) , Marked_f(X,c)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(a,a) -> f(a,b)
[2] f(a,b) -> f(s(a),c)
[3] f(s(X),c) -> f(X,c)
[4] f(c,c) -> f(a,a)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(a,a) , Marked_f(a,b)>
<Marked_f(a,b) , Marked_f(s(a),c)>
<Marked_f(s(X),c) , Marked_f(X,c)>
<Marked_f(c,c) , Marked_f(a,a)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(a,a) , Marked_f(a,b)>
<Marked_f(a,b) , Marked_f(s(a),c)>
<Marked_f(s(X),c) , Marked_f(X,c)>
<Marked_f(c,c) , Marked_f(a,a)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ f ] (X0,X1) = 0; 
 [ c ] () = 1; 
 [ b ] () = 0; 
 [ a ] () = 0; 
 [ Marked_f ] (X0,X1) = 2*X0; 
 [ s ] (X0) = 1*X0; 
 removing <Marked_f(c,c),Marked_f(a,a)>
 [ {
      
     DP termination of:
     <Marked_f(a,a) , Marked_f(a,b)>
<Marked_f(a,b) , Marked_f(s(a),c)>
<Marked_f(s(X),c) , Marked_f(X,c)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(X),c) , Marked_f(X,c)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.033155 seconds (real time)
Cime Exit Status: 0