- : 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] active(f(X1,X2)) -> f(active(X1),X2)
[3] active(g(X)) -> g(active(X))
[4] f(mark(X1),X2) -> mark(f(X1,X2))
[5] g(mark(X)) -> mark(g(X))
[6] proper(f(X1,X2)) -> f(proper(X1),proper(X2))
[7] proper(g(X)) -> g(proper(X))
[8] f(ok(X1),ok(X2)) -> ok(f(X1,X2))
[9] g(ok(X)) -> ok(g(X))
[10] top(mark(X)) -> top(proper(X))
[11] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(f(g(X),Y)) , Marked_f(X,f(g(X),Y))>
<Marked_active(f(X1,X2)) , Marked_f(active(X1),X2)>
<Marked_active(f(X1,X2)) , Marked_active(X1)>
<Marked_active(g(X)) , Marked_g(active(X))>
<Marked_active(g(X)) , Marked_active(X)>
<Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
<Marked_g(mark(X)) , Marked_g(X)>
<Marked_proper(f(X1,X2)) , Marked_f(proper(X1),proper(X2))>
<Marked_proper(f(X1,X2)) , Marked_proper(X1)>
<Marked_proper(f(X1,X2)) , Marked_proper(X2)>
<Marked_proper(g(X)) , Marked_g(proper(X))>
<Marked_proper(g(X)) , Marked_proper(X)>
<Marked_f(ok(X1),ok(X2)) , Marked_f(X1,X2)>
<Marked_g(ok(X)) , Marked_g(X)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(ok(X)) , Marked_top(active(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
}

{  <Marked_proper(g(X)) , Marked_proper(X)> 
      --> <Marked_proper(g(X)) , Marked_proper(X)>
  <Marked_proper(g(X)) , Marked_proper(X)> 
     --> <Marked_proper(f(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(g(X)) , Marked_proper(X)> 
     --> <Marked_proper(f(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(f(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(g(X)) , Marked_proper(X)>
  <Marked_proper(f(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(f(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(f(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(f(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(f(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(g(X)) , Marked_proper(X)>
  <Marked_proper(f(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(f(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(f(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(f(X1,X2)) , Marked_proper(X1)>
}

{  <Marked_active(g(X)) , Marked_active(X)> 
      --> <Marked_active(g(X)) , Marked_active(X)>
  <Marked_active(g(X)) , Marked_active(X)> 
     --> <Marked_active(f(X1,X2)) , Marked_active(X1)>
  <Marked_active(f(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(g(X)) , Marked_active(X)>
  <Marked_active(f(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(f(X1,X2)) , Marked_active(X1)>
}

{  <Marked_f(ok(X1),ok(X2)) , Marked_f(X1,X2)> 
      --> <Marked_f(ok(X1),ok(X2)) , Marked_f(X1,X2)>
  <Marked_f(ok(X1),ok(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(ok(X1),ok(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(ok(X)) , Marked_g(X)> --> <Marked_g(ok(X)) , Marked_g(X)>
  <Marked_g(ok(X)) , Marked_g(X)> --> <Marked_g(mark(X)) , Marked_g(X)>
  <Marked_g(mark(X)) , Marked_g(X)> --> <Marked_g(ok(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:
{
  f(mark(X1),X2) >= mark(f(X1,X2)) ;
  f(ok(X1),ok(X2)) >= ok(f(X1,X2)) ;
  g(mark(X)) >= mark(g(X)) ;
  g(ok(X)) >= ok(g(X)) ;
  active(f(g(X),Y)) >= mark(f(X,f(g(X),Y))) ;
  active(f(X1,X2)) >= f(active(X1),X2) ;
  active(g(X)) >= g(active(X)) ;
  proper(f(X1,X2)) >= f(proper(X1),proper(X2)) ;
  proper(g(X)) >= g(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(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(mark(X1),X2) >= mark(f(X1,X2))
constraint: f(ok(X1),ok(X2)) >= ok(f(X1,X2))
constraint: g(mark(X)) >= mark(g(X))
constraint: g(ok(X)) >= ok(g(X))
constraint: active(f(g(X),Y)) >= mark(f(X,f(g(X),Y)))
constraint: active(f(X1,X2)) >= f(active(X1),X2)
constraint: active(g(X)) >= g(active(X))
constraint: proper(f(X1,X2)) >= f(proper(X1),proper(X2))
constraint: proper(g(X)) >= g(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_top(mark(X)) >= Marked_top(proper(X))
constraint: Marked_top(ok(X)) >= Marked_top(active(X))
APPLY CRITERIA (Subterm criterion)

ST: Marked_proper -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_active -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_g -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
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)>
}
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] active(f(X1,X2)) -> f(active(X1),X2)
[3] active(g(X)) -> g(active(X))
[4] f(mark(X1),X2) -> mark(f(X1,X2))
[5] g(mark(X)) -> mark(g(X))
[6] proper(f(X1,X2)) -> f(proper(X1),proper(X2))
[7] proper(g(X)) -> g(proper(X))
[8] f(ok(X1),ok(X2)) -> ok(f(X1,X2))
[9] g(ok(X)) -> ok(g(X))
[10] top(mark(X)) -> top(proper(X))
[11] top(ok(X)) -> top(active(X))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(f(g(X),Y)) , Marked_f(X,f(g(X),Y))>
<Marked_active(f(X1,X2)) , Marked_f(active(X1),X2)>
<Marked_active(f(X1,X2)) , Marked_active(X1)>
<Marked_active(g(X)) , Marked_g(active(X))>
<Marked_active(g(X)) , Marked_active(X)>
<Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
<Marked_g(mark(X)) , Marked_g(X)>
<Marked_proper(f(X1,X2)) , Marked_f(proper(X1),proper(X2))>
<Marked_proper(f(X1,X2)) , Marked_proper(X1)>
<Marked_proper(f(X1,X2)) , Marked_proper(X2)>
<Marked_proper(g(X)) , Marked_g(proper(X))>
<Marked_proper(g(X)) , Marked_proper(X)>
<Marked_f(ok(X1),ok(X2)) , Marked_f(X1,X2)>
<Marked_g(ok(X)) , Marked_g(X)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 2 + 2*X0 + 0; 
 [ proper ] (X0) = 1 + 2*X0 + 0; 
 [ g ] (X0) = 2 + 3*X0 + 0; 
 [ top ] (X0) = 2*X0 + 0; 
 [ f ] (X0,X1) = 2 + 2*X0 + 0; 
 [ ok ] (X0) = 3 + 2*X0 + 0; 
 [ active ] (X0) = 1*X0 + 0; 
 [ Marked_top ] (X0) = 2*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_proper(f(X1,X2)) , Marked_proper(X1)>
<Marked_proper(f(X1,X2)) , Marked_proper(X2)>
<Marked_proper(g(X)) , Marked_proper(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_active(f(X1,X2)) , Marked_active(X1)>
<Marked_active(g(X)) , Marked_active(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
<Marked_f(ok(X1),ok(X2)) , Marked_f(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_f(mark(X1),X2) , Marked_f(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <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(ok(X)) , Marked_g(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.074063 seconds (real time)
Cime Exit Status: 0