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

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


Sub problem: 
guided: 

DP termination of:
<Marked_active(f(X)) , Marked_mark(g(h(f(X))))>
<Marked_active(f(X)) , Marked_g(h(f(X)))>
<Marked_active(f(X)) , Marked_h(f(X))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(g(X)) , Marked_active(g(X))>
<Marked_mark(h(X)) , Marked_active(h(mark(X)))>
<Marked_mark(h(X)) , Marked_h(mark(X))>
<Marked_mark(h(X)) , Marked_mark(X)>
<Marked_f(mark(X)) , Marked_f(X)>
<Marked_f(active(X)) , Marked_f(X)>
<Marked_g(mark(X)) , Marked_g(X)>
<Marked_g(active(X)) , Marked_g(X)>
<Marked_h(mark(X)) , Marked_h(X)>
<Marked_h(active(X)) , Marked_h(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_mark(h(X)) , Marked_mark(X)> 
      --> <Marked_mark(h(X)) , Marked_mark(X)>
  <Marked_mark(h(X)) , Marked_mark(X)> 
     --> <Marked_mark(h(X)) , Marked_active(h(mark(X)))>
  <Marked_mark(h(X)) , Marked_mark(X)> 
     --> <Marked_mark(g(X)) , Marked_active(g(X))>
  <Marked_mark(h(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(h(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(h(X)) , Marked_active(h(mark(X)))> 
     --> <Marked_active(f(X)) , Marked_mark(g(h(f(X))))>
  <Marked_mark(g(X)) , Marked_active(g(X))> 
     --> <Marked_active(f(X)) , Marked_mark(g(h(f(X))))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(h(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(h(X)) , Marked_active(h(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(g(X)) , Marked_active(g(X))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(X)) , Marked_mark(g(h(f(X))))>
  <Marked_active(f(X)) , Marked_mark(g(h(f(X))))> 
     --> <Marked_mark(h(X)) , Marked_mark(X)>
  <Marked_active(f(X)) , Marked_mark(g(h(f(X))))> 
     --> <Marked_mark(h(X)) , Marked_active(h(mark(X)))>
  <Marked_active(f(X)) , Marked_mark(g(h(f(X))))> 
     --> <Marked_mark(g(X)) , Marked_active(g(X))>
  <Marked_active(f(X)) , Marked_mark(g(h(f(X))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(X)) , Marked_mark(g(h(f(X))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}

{  <Marked_f(active(X)) , Marked_f(X)> --> <Marked_f(active(X)) , Marked_f(X)>
  <Marked_f(active(X)) , Marked_f(X)> --> <Marked_f(mark(X)) , Marked_f(X)>
  <Marked_f(mark(X)) , Marked_f(X)> --> <Marked_f(active(X)) , Marked_f(X)>
  <Marked_f(mark(X)) , Marked_f(X)> --> <Marked_f(mark(X)) , Marked_f(X)>
}

{  <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)>
}

{  <Marked_h(active(X)) , Marked_h(X)> --> <Marked_h(active(X)) , Marked_h(X)>
  <Marked_h(active(X)) , Marked_h(X)> --> <Marked_h(mark(X)) , Marked_h(X)>
  <Marked_h(mark(X)) , Marked_h(X)> --> <Marked_h(active(X)) , Marked_h(X)>
  <Marked_h(mark(X)) , Marked_h(X)> --> <Marked_h(mark(X)) , Marked_h(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(g(X)) >= active(g(X)) ;
  mark(h(X)) >= active(h(mark(X))) ;
  mark(f(X)) >= active(f(mark(X))) ;
  g(mark(X)) >= g(X) ;
  g(active(X)) >= g(X) ;
  h(mark(X)) >= h(X) ;
  h(active(X)) >= h(X) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  active(f(X)) >= mark(g(h(f(X)))) ;
  Marked_mark(g(X)) >= Marked_active(g(X)) ;
  Marked_mark(h(X)) >= Marked_mark(X) ;
  Marked_mark(h(X)) >= Marked_active(h(mark(X))) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_active(f(X)) >= Marked_mark(g(h(f(X)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(g(X)) > Marked_active(g(X)) ;
 }
{
  Marked_mark(h(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(h(X)) > Marked_active(h(mark(X))) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_active(f(X)) > Marked_mark(g(h(f(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: mark(g(X)) >= active(g(X))
constraint: mark(h(X)) >= active(h(mark(X)))
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: g(mark(X)) >= g(X)
constraint: g(active(X)) >= g(X)
constraint: h(mark(X)) >= h(X)
constraint: h(active(X)) >= h(X)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: active(f(X)) >= mark(g(h(f(X))))
constraint: Marked_mark(g(X)) >= Marked_active(g(X))
constraint: Marked_mark(h(X)) >= Marked_mark(X)
constraint: Marked_mark(h(X)) >= Marked_active(h(mark(X)))
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_active(f(X)) >= Marked_mark(g(h(f(X))))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(g(X)) >= active(g(X)) ;
  mark(h(X)) >= active(h(mark(X))) ;
  mark(f(X)) >= active(f(mark(X))) ;
  g(mark(X)) >= g(X) ;
  g(active(X)) >= g(X) ;
  h(mark(X)) >= h(X) ;
  h(active(X)) >= h(X) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  active(f(X)) >= mark(g(h(f(X)))) ;
  Marked_f(mark(X)) >= Marked_f(X) ;
  Marked_f(active(X)) >= Marked_f(X) ;
 }
 + Disjunctions:{ 
{
  Marked_f(mark(X)) > Marked_f(X) ;
 }
{
  Marked_f(active(X)) > Marked_f(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: mark(g(X)) >= active(g(X))
constraint: mark(h(X)) >= active(h(mark(X)))
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: g(mark(X)) >= g(X)
constraint: g(active(X)) >= g(X)
constraint: h(mark(X)) >= h(X)
constraint: h(active(X)) >= h(X)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: active(f(X)) >= mark(g(h(f(X))))
constraint: Marked_f(mark(X)) >= Marked_f(X)
constraint: Marked_f(active(X)) >= Marked_f(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(g(X)) >= active(g(X)) ;
  mark(h(X)) >= active(h(mark(X))) ;
  mark(f(X)) >= active(f(mark(X))) ;
  g(mark(X)) >= g(X) ;
  g(active(X)) >= g(X) ;
  h(mark(X)) >= h(X) ;
  h(active(X)) >= h(X) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  active(f(X)) >= mark(g(h(f(X)))) ;
  Marked_g(mark(X)) >= Marked_g(X) ;
  Marked_g(active(X)) >= Marked_g(X) ;
 }
 + Disjunctions:{ 
{
  Marked_g(mark(X)) > Marked_g(X) ;
 }
{
  Marked_g(active(X)) > Marked_g(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: mark(g(X)) >= active(g(X))
constraint: mark(h(X)) >= active(h(mark(X)))
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: g(mark(X)) >= g(X)
constraint: g(active(X)) >= g(X)
constraint: h(mark(X)) >= h(X)
constraint: h(active(X)) >= h(X)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: active(f(X)) >= mark(g(h(f(X))))
constraint: Marked_g(mark(X)) >= Marked_g(X)
constraint: Marked_g(active(X)) >= Marked_g(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(g(X)) >= active(g(X)) ;
  mark(h(X)) >= active(h(mark(X))) ;
  mark(f(X)) >= active(f(mark(X))) ;
  g(mark(X)) >= g(X) ;
  g(active(X)) >= g(X) ;
  h(mark(X)) >= h(X) ;
  h(active(X)) >= h(X) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  active(f(X)) >= mark(g(h(f(X)))) ;
  Marked_h(mark(X)) >= Marked_h(X) ;
  Marked_h(active(X)) >= Marked_h(X) ;
 }
 + Disjunctions:{ 
{
  Marked_h(mark(X)) > Marked_h(X) ;
 }
{
  Marked_h(active(X)) > Marked_h(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: mark(g(X)) >= active(g(X))
constraint: mark(h(X)) >= active(h(mark(X)))
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: g(mark(X)) >= g(X)
constraint: g(active(X)) >= g(X)
constraint: h(mark(X)) >= h(X)
constraint: h(active(X)) >= h(X)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: active(f(X)) >= mark(g(h(f(X))))
constraint: Marked_h(mark(X)) >= Marked_h(X)
constraint: Marked_h(active(X)) >= Marked_h(X)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(h(X)) , Marked_mark(X)> 
      --> <Marked_mark(h(X)) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(g(X)) >= active(g(X)) ;
  mark(h(X)) >= active(h(mark(X))) ;
  mark(f(X)) >= active(f(mark(X))) ;
  g(mark(X)) >= g(X) ;
  g(active(X)) >= g(X) ;
  h(mark(X)) >= h(X) ;
  h(active(X)) >= h(X) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  active(f(X)) >= mark(g(h(f(X)))) ;
  Marked_mark(h(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(h(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: mark(g(X)) >= active(g(X))
constraint: mark(h(X)) >= active(h(mark(X)))
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: g(mark(X)) >= g(X)
constraint: g(active(X)) >= g(X)
constraint: h(mark(X)) >= h(X)
constraint: h(active(X)) >= h(X)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: active(f(X)) >= mark(g(h(f(X))))
constraint: Marked_mark(h(X)) >= Marked_mark(X)
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 0 components:
SOLVED
{
 
TRS termination of:
[1] active(f(X)) -> mark(g(h(f(X))))
[2] mark(f(X)) -> active(f(mark(X)))
[3] mark(g(X)) -> active(g(X))
[4] mark(h(X)) -> active(h(mark(X)))
[5] f(mark(X)) -> f(X)
[6] f(active(X)) -> f(X)
[7] g(mark(X)) -> g(X)
[8] g(active(X)) -> g(X)
[9] h(mark(X)) -> h(X)
[10] h(active(X)) -> h(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(f(X)) , Marked_mark(g(h(f(X))))>
<Marked_active(f(X)) , Marked_g(h(f(X)))>
<Marked_active(f(X)) , Marked_h(f(X))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(g(X)) , Marked_active(g(X))>
<Marked_mark(h(X)) , Marked_active(h(mark(X)))>
<Marked_mark(h(X)) , Marked_h(mark(X))>
<Marked_mark(h(X)) , Marked_mark(X)>
<Marked_f(mark(X)) , Marked_f(X)>
<Marked_f(active(X)) , Marked_f(X)>
<Marked_g(mark(X)) , Marked_g(X)>
<Marked_g(active(X)) , Marked_g(X)>
<Marked_h(mark(X)) , Marked_h(X)>
<Marked_h(active(X)) , Marked_h(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(X)) , Marked_mark(g(h(f(X))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(g(X)) , Marked_active(g(X))>
<Marked_mark(h(X)) , Marked_active(h(mark(X)))>
<Marked_mark(h(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 3*X0 + 3; 
 [ active ] (X0) = 1*X0; 
 [ h ] (X0) = 2*X0; 
 [ g ] (X0) = 0; 
 [ Marked_active ] (X0) = 3*X0 + 3; 
 [ f ] (X0) = 2*X0 + 2; 
 removing <Marked_active(f(X)),Marked_mark(g(h(f(X))))><Marked_mark(f(X)),
Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(g(X)) , Marked_active(g(X))>
<Marked_mark(h(X)) , Marked_active(h(mark(X)))>
<Marked_mark(h(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(h(X)) , Marked_mark(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 2*X0 + 0; 
 [ Marked_mark ] (X0) = 3*X0 + 0; 
 [ active ] (X0) = 1*X0 + 0; 
 [ h ] (X0) = 1 + 2*X0 + 0; 
 [ g ] (X0) = 0; 
 [ f ] (X0) = 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_f(mark(X)) , Marked_f(X)>
<Marked_f(active(X)) , Marked_f(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 1 + 1*X0 + 0; 
 [ active ] (X0) = 1 + 1*X0 + 0; 
 [ h ] (X0) = 1 + 0; 
 [ g ] (X0) = 0; 
 [ f ] (X0) = 0; 
 [ Marked_f ] (X0) = 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_g(mark(X)) , Marked_g(X)>
<Marked_g(active(X)) , Marked_g(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 1 + 1*X0 + 0; 
 [ active ] (X0) = 1 + 2*X0 + 0; 
 [ h ] (X0) = 0; 
 [ Marked_g ] (X0) = 3*X0 + 0; 
 [ g ] (X0) = 0; 
 [ f ] (X0) = 0; 
 ]} 
{
 
DP termination of:
<Marked_h(mark(X)) , Marked_h(X)>
<Marked_h(active(X)) , Marked_h(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 1 + 1*X0 + 0; 
 [ active ] (X0) = 1 + 2*X0 + 0; 
 [ h ] (X0) = 0; 
 [ g ] (X0) = 0; 
 [ Marked_h ] (X0) = 3*X0 + 0; 
 [ f ] (X0) = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.206321 seconds (real time)
Cime Exit Status: 0