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

TRS termination of:
[1] a__f(a,X,X) -> a__f(X,a__b,b)
[2] a__b -> a
[3] mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
[4] mark(b) -> a__b
[5] mark(a) -> a
[6] a__f(X1,X2,X3) -> f(X1,X2,X3)
[7] a__b -> b


Sub problem: 
guided: 

DP termination of:
<Marked_a__f(a,X,X) , Marked_a__f(X,a__b,b)>
<Marked_a__f(a,X,X) , Marked_a__b>
<Marked_mark(f(X1,X2,X3)) , Marked_a__f(X1,mark(X2),X3)>
<Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
<Marked_mark(b) , Marked_a__b>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)> 
      --> <Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
}

{  <Marked_a__f(a,X,X) , Marked_a__f(X,a__b,b)> 
      --> <Marked_a__f(a,X,X) , Marked_a__f(X,a__b,b)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_mark -> 1

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__f(a,X,X) >= a__f(X,a__b,b) ;
  a__f(X1,X2,X3) >= f(X1,X2,X3) ;
  a__b >= b ;
  a__b >= a ;
  mark(b) >= a__b ;
  mark(a) >= a ;
  mark(f(X1,X2,X3)) >= a__f(X1,mark(X2),X3) ;
  Marked_a__f(a,X,X) >= Marked_a__f(X,a__b,b) ;
 }
 + Disjunctions:{ 
{
  Marked_a__f(a,X,X) > Marked_a__f(X,a__b,b) ;
 }
 } 
=== 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: a__f(a,X,X) >= a__f(X,a__b,b)
constraint: a__f(X1,X2,X3) >= f(X1,X2,X3)
constraint: a__b >= b
constraint: a__b >= a
constraint: mark(b) >= a__b
constraint: mark(a) >= a
constraint: mark(f(X1,X2,X3)) >= a__f(X1,mark(X2),X3)
constraint: Marked_a__f(a,X,X) >= Marked_a__f(X,a__b,b)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__f(a,X,X) -> a__f(X,a__b,b)
[2] a__b -> a
[3] mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
[4] mark(b) -> a__b
[5] mark(a) -> a
[6] a__f(X1,X2,X3) -> f(X1,X2,X3)
[7] a__b -> b
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__f(a,X,X) , Marked_a__f(X,a__b,b)>
<Marked_a__f(a,X,X) , Marked_a__b>
<Marked_mark(f(X1,X2,X3)) , Marked_a__f(X1,mark(X2),X3)>
<Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
<Marked_mark(b) , Marked_a__b>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_a__f(a,X,X) , Marked_a__f(X,a__b,b)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ a__f ] (X0,X1,X2) = 0; 
 [ mark ] (X0) = 3 + 0; 
 [ b ] () = 0; 
 [ a__b ] () = 3 + 0; 
 [ f ] (X0,X1,X2) = 0; 
 [ a ] () = 3 + 0; 
 [ Marked_a__f ] (X0,X1,X2) = 2*X0 + 2*X2 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.026595 seconds (real time)
Cime Exit Status: 0