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

TRS termination of:
[1] active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
[2] mark(f(X1,X2)) -> active(f(mark(X1),X2))
[3] mark(g(X)) -> active(g(mark(X)))
[4] f(mark(X1),X2) -> f(X1,X2)
[5] f(X1,mark(X2)) -> f(X1,X2)
[6] f(active(X1),X2) -> f(X1,X2)
[7] f(X1,active(X2)) -> f(X1,X2)
[8] g(mark(X)) -> g(X)
[9] g(active(X)) -> g(X)


Sub problem: 
guided: 

DP termination of:
<Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))>
<Marked_active(f(g(X),Y)) , Marked_f(X,f(g(X),Y))>
<Marked_mark(f(X1,X2)) , Marked_active(f(mark(X1),X2))>
<Marked_mark(f(X1,X2)) , Marked_f(mark(X1),X2)>
<Marked_mark(f(X1,X2)) , Marked_mark(X1)>
<Marked_mark(g(X)) , Marked_active(g(mark(X)))>
<Marked_mark(g(X)) , Marked_g(mark(X))>
<Marked_mark(g(X)) , Marked_mark(X)>
<Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
<Marked_f(X1,mark(X2)) , Marked_f(X1,X2)>
<Marked_f(active(X1),X2) , Marked_f(X1,X2)>
<Marked_f(X1,active(X2)) , Marked_f(X1,X2)>
<Marked_g(mark(X)) , Marked_g(X)>
<Marked_g(active(X)) , Marked_g(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_mark(g(X)) , Marked_mark(X)> 
      --> <Marked_mark(g(X)) , Marked_mark(X)>
  <Marked_mark(g(X)) , Marked_mark(X)> 
     --> <Marked_mark(g(X)) , Marked_active(g(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_active(f(mark(X1),X2))>
  <Marked_mark(g(X)) , Marked_active(g(mark(X)))> 
     --> <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))>
  <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(g(X)) , Marked_active(g(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_active(f(mark(X1),X2))>
  <Marked_mark(f(X1,X2)) , Marked_active(f(mark(X1),X2))> 
     --> <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))>
  <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))> 
     --> <Marked_mark(g(X)) , Marked_mark(X)>
  <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))> 
     --> <Marked_mark(g(X)) , Marked_active(g(mark(X)))>
  <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))> 
     --> <Marked_mark(f(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))> 
     --> <Marked_mark(f(X1,X2)) , Marked_active(f(mark(X1),X2))>
}

{  <Marked_f(X1,active(X2)) , Marked_f(X1,X2)> 
      --> <Marked_f(X1,active(X2)) , Marked_f(X1,X2)>
  <Marked_f(X1,active(X2)) , Marked_f(X1,X2)> 
     --> <Marked_f(active(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(X1,active(X2)) , Marked_f(X1,X2)> 
     --> <Marked_f(X1,mark(X2)) , Marked_f(X1,X2)>
  <Marked_f(X1,active(X2)) , Marked_f(X1,X2)> 
     --> <Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(active(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(X1,active(X2)) , Marked_f(X1,X2)>
  <Marked_f(active(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(active(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(active(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(X1,mark(X2)) , Marked_f(X1,X2)>
  <Marked_f(active(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(X1,mark(X2)) , Marked_f(X1,X2)> 
     --> <Marked_f(X1,active(X2)) , Marked_f(X1,X2)>
  <Marked_f(X1,mark(X2)) , Marked_f(X1,X2)> 
     --> <Marked_f(active(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(X1,mark(X2)) , Marked_f(X1,X2)> 
     --> <Marked_f(X1,mark(X2)) , Marked_f(X1,X2)>
  <Marked_f(X1,mark(X2)) , Marked_f(X1,X2)> 
     --> <Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(mark(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(X1,active(X2)) , Marked_f(X1,X2)>
  <Marked_f(mark(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(active(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(mark(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(X1,mark(X2)) , Marked_f(X1,X2)>
  <Marked_f(mark(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
}

{  <Marked_g(active(X)) , Marked_g(X)> --> <Marked_g(active(X)) , Marked_g(X)>
  <Marked_g(active(X)) , Marked_g(X)> --> <Marked_g(mark(X)) , Marked_g(X)>
  <Marked_g(mark(X)) , Marked_g(X)> --> <Marked_g(active(X)) , Marked_g(X)>
  <Marked_g(mark(X)) , Marked_g(X)> --> <Marked_g(mark(X)) , Marked_g(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(f(X1,X2)) >= active(f(mark(X1),X2)) ;
  mark(g(X)) >= active(g(mark(X))) ;
  f(mark(X1),X2) >= f(X1,X2) ;
  f(active(X1),X2) >= f(X1,X2) ;
  f(X1,mark(X2)) >= f(X1,X2) ;
  f(X1,active(X2)) >= f(X1,X2) ;
  g(mark(X)) >= g(X) ;
  g(active(X)) >= g(X) ;
  active(f(g(X),Y)) >= mark(f(X,f(g(X),Y))) ;
  Marked_mark(f(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(f(X1,X2)) >= Marked_active(f(mark(X1),X2)) ;
  Marked_mark(g(X)) >= Marked_mark(X) ;
  Marked_mark(g(X)) >= Marked_active(g(mark(X))) ;
  Marked_active(f(g(X),Y)) >= Marked_mark(f(X,f(g(X),Y))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(f(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(f(X1,X2)) > Marked_active(f(mark(X1),X2)) ;
 }
{
  Marked_mark(g(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(g(X)) > Marked_active(g(mark(X))) ;
 }
{
  Marked_active(f(g(X),Y)) > Marked_mark(f(X,f(g(X),Y))) ;
 }
 } 
=== 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: mark(f(X1,X2)) >= active(f(mark(X1),X2))
constraint: mark(g(X)) >= active(g(mark(X)))
constraint: f(mark(X1),X2) >= f(X1,X2)
constraint: f(active(X1),X2) >= f(X1,X2)
constraint: f(X1,mark(X2)) >= f(X1,X2)
constraint: f(X1,active(X2)) >= f(X1,X2)
constraint: g(mark(X)) >= g(X)
constraint: g(active(X)) >= g(X)
constraint: active(f(g(X),Y)) >= mark(f(X,f(g(X),Y)))
constraint: Marked_mark(f(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(f(X1,X2)) >= Marked_active(f(mark(X1),X2))
constraint: Marked_mark(g(X)) >= Marked_mark(X)
constraint: Marked_mark(g(X)) >= Marked_active(g(mark(X)))
constraint: Marked_active(f(g(X),Y)) >= Marked_mark(f(X,f(g(X),Y)))
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_g -> 1

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_active(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_active(f(mark(X1),X2))>
  <Marked_mark(f(X1,X2)) , Marked_active(f(mark(X1),X2))> 
     --> <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))>
  <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))> 
     --> <Marked_mark(g(X)) , Marked_mark(X)>
  <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))> 
     --> <Marked_mark(f(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))> 
     --> <Marked_mark(f(X1,X2)) , Marked_active(f(mark(X1),X2))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(f(X1,X2)) >= active(f(mark(X1),X2)) ;
  mark(g(X)) >= active(g(mark(X))) ;
  f(mark(X1),X2) >= f(X1,X2) ;
  f(active(X1),X2) >= f(X1,X2) ;
  f(X1,mark(X2)) >= f(X1,X2) ;
  f(X1,active(X2)) >= f(X1,X2) ;
  g(mark(X)) >= g(X) ;
  g(active(X)) >= g(X) ;
  active(f(g(X),Y)) >= mark(f(X,f(g(X),Y))) ;
  Marked_mark(f(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(f(X1,X2)) >= Marked_active(f(mark(X1),X2)) ;
  Marked_mark(g(X)) >= Marked_mark(X) ;
  Marked_active(f(g(X),Y)) >= Marked_mark(f(X,f(g(X),Y))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(f(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(f(X1,X2)) > Marked_active(f(mark(X1),X2)) ;
 }
{
  Marked_mark(g(X)) > Marked_mark(X) ;
 }
{
  Marked_active(f(g(X),Y)) > Marked_mark(f(X,f(g(X),Y))) ;
 }
 } 
=== 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: mark(f(X1,X2)) >= active(f(mark(X1),X2))
constraint: mark(g(X)) >= active(g(mark(X)))
constraint: f(mark(X1),X2) >= f(X1,X2)
constraint: f(active(X1),X2) >= f(X1,X2)
constraint: f(X1,mark(X2)) >= f(X1,X2)
constraint: f(X1,active(X2)) >= f(X1,X2)
constraint: g(mark(X)) >= g(X)
constraint: g(active(X)) >= g(X)
constraint: active(f(g(X),Y)) >= mark(f(X,f(g(X),Y)))
constraint: Marked_mark(f(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(f(X1,X2)) >= Marked_active(f(mark(X1),X2))
constraint: Marked_mark(g(X)) >= Marked_mark(X)
constraint: Marked_active(f(g(X),Y)) >= Marked_mark(f(X,f(g(X),Y)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(mark(X1),X2) , Marked_f(X1,X2)> 
      --> <Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(mark(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(active(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(active(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
  <Marked_f(active(X1),X2) , Marked_f(X1,X2)> 
     --> <Marked_f(active(X1),X2) , Marked_f(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
[2] mark(f(X1,X2)) -> active(f(mark(X1),X2))
[3] mark(g(X)) -> active(g(mark(X)))
[4] f(mark(X1),X2) -> f(X1,X2)
[5] f(X1,mark(X2)) -> f(X1,X2)
[6] f(active(X1),X2) -> f(X1,X2)
[7] f(X1,active(X2)) -> f(X1,X2)
[8] g(mark(X)) -> g(X)
[9] g(active(X)) -> g(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))>
<Marked_active(f(g(X),Y)) , Marked_f(X,f(g(X),Y))>
<Marked_mark(f(X1,X2)) , Marked_active(f(mark(X1),X2))>
<Marked_mark(f(X1,X2)) , Marked_f(mark(X1),X2)>
<Marked_mark(f(X1,X2)) , Marked_mark(X1)>
<Marked_mark(g(X)) , Marked_active(g(mark(X)))>
<Marked_mark(g(X)) , Marked_g(mark(X))>
<Marked_mark(g(X)) , Marked_mark(X)>
<Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
<Marked_f(X1,mark(X2)) , Marked_f(X1,X2)>
<Marked_f(active(X1),X2) , Marked_f(X1,X2)>
<Marked_f(X1,active(X2)) , Marked_f(X1,X2)>
<Marked_g(mark(X)) , Marked_g(X)>
<Marked_g(active(X)) , Marked_g(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))>
<Marked_mark(f(X1,X2)) , Marked_active(f(mark(X1),X2))>
<Marked_mark(f(X1,X2)) , Marked_mark(X1)>
<Marked_mark(g(X)) , Marked_active(g(mark(X)))>
<Marked_mark(g(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ g ] (X0) = 0; 
 [ Marked_mark ] (X0) = 1; 
 [ f ] (X0,X1) = 1; 
 [ active ] (X0) = 0; 
 [ Marked_active ] (X0) = 1*X0; 
 removing <Marked_mark(g(X)),Marked_active(g(mark(X)))>
 [ {
      
     DP termination of:
     <Marked_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))>
<Marked_mark(f(X1,X2)) , Marked_active(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_active(f(g(X),Y)) , Marked_mark(f(X,f(g(X),Y)))>
<Marked_mark(f(X1,X2)) , Marked_active(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 = 
      [ mark ] (X0) = 1*X0 + 0; 
 [ g ] (X0) = 2 + 2*X0 + 0; 
 [ Marked_mark ] (X0) = 2 + 3*X0 + 0; 
 [ f ] (X0,X1) = 2 + 2*X0 + 0; 
 [ active ] (X0) = 1*X0 + 0; 
 [ Marked_active ] (X0) = 2 + 2*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
<Marked_f(X1,mark(X2)) , Marked_f(X1,X2)>
<Marked_f(active(X1),X2) , Marked_f(X1,X2)>
<Marked_f(X1,active(X2)) , Marked_f(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_f(active(X1),X2) , Marked_f(X1,X2)>
<Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(active(X1),X2) , Marked_f(X1,X2)>
<Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_g(mark(X)) , Marked_g(X)>
<Marked_g(active(X)) , Marked_g(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.167497 seconds (real time)
Cime Exit Status: 0