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

TRS termination of:
[1] a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
[2] mark(f(X1,X2)) -> a__f(mark(X1),X2)
[3] mark(g(X)) -> g(mark(X))
[4] a__f(X1,X2) -> f(X1,X2)


Sub problem: 
guided: 

DP termination of:
<Marked_a__f(g(X),Y) , Marked_a__f(mark(X),f(g(X),Y))>
<Marked_a__f(g(X),Y) , Marked_mark(X)>
<Marked_mark(f(X1,X2)) , Marked_a__f(mark(X1),X2)>
<Marked_mark(f(X1,X2)) , Marked_mark(X1)>
<Marked_mark(g(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

Cime worked for 0.042853 seconds (real time)
Cime Exit Status: 0