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

TRS termination of:
[1] a__f(X) -> a__if(mark(X),c,f(true))
[2] a__if(true,X,Y) -> mark(X)
[3] a__if(false,X,Y) -> mark(Y)
[4] mark(f(X)) -> a__f(mark(X))
[5] mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
[6] mark(c) -> c
[7] mark(true) -> true
[8] mark(false) -> false
[9] a__f(X) -> f(X)
[10] a__if(X1,X2,X3) -> if(X1,X2,X3)


Sub problem: 
guided: 

DP termination of:
<Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))>
<Marked_a__f(X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
      --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)> 
     --> <Marked_a__if(false,X,Y) , Marked_mark(Y)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <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_a__f(mark(X))>
  <Marked_mark(f(X)) , Marked_a__f(mark(X))> 
     --> <Marked_a__f(X) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_a__f(mark(X))> 
     --> <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_a__f(X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_a__f(X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__f(X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_a__f(X) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_a__f(X) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))> 
     --> <Marked_a__if(false,X,Y) , Marked_mark(Y)>
  <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  mark(c) >= c ;
  mark(f(X)) >= a__f(mark(X)) ;
  mark(true) >= true ;
  mark(false) >= false ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),mark(X2),X3) ;
  a__f(X) >= a__if(mark(X),c,f(true)) ;
  a__f(X) >= f(X) ;
  Marked_a__if(true,X,Y) >= Marked_mark(X) ;
  Marked_a__if(false,X,Y) >= Marked_mark(Y) ;
  Marked_a__f(X) >= Marked_a__if(mark(X),c,f(true)) ;
  Marked_a__f(X) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_a__f(mark(X)) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),mark(X2),X3) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X2) ;
 }
 + Disjunctions:{ 
{
  Marked_a__if(true,X,Y) > Marked_mark(X) ;
 }
{
  Marked_a__if(false,X,Y) > Marked_mark(Y) ;
 }
{
  Marked_a__f(X) > Marked_a__if(mark(X),c,f(true)) ;
 }
{
  Marked_a__f(X) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_a__f(mark(X)) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_a__if(mark(X1),mark(X2),X3) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X2) ;
 }
 } 
=== 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__if(true,X,Y) >= mark(X)
constraint: a__if(false,X,Y) >= mark(Y)
constraint: a__if(X1,X2,X3) >= if(X1,X2,X3)
constraint: mark(c) >= c
constraint: mark(f(X)) >= a__f(mark(X))
constraint: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),mark(X2),X3)
constraint: a__f(X) >= a__if(mark(X),c,f(true))
constraint: a__f(X) >= f(X)
constraint: Marked_a__if(true,X,Y) >= Marked_mark(X)
constraint: Marked_a__if(false,X,Y) >= Marked_mark(Y)
constraint: Marked_a__f(X) >= Marked_a__if(mark(X),c,f(true))
constraint: Marked_a__f(X) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_a__f(mark(X))
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),mark(X2),X3)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X2)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
      --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <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_a__f(mark(X))>
  <Marked_mark(f(X)) , Marked_a__f(mark(X))> 
     --> <Marked_a__f(X) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_a__f(mark(X))> 
     --> <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_a__f(X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_a__f(X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__f(X) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_a__f(X) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_a__f(X) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_a__f(mark(X))>
  <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  mark(c) >= c ;
  mark(f(X)) >= a__f(mark(X)) ;
  mark(true) >= true ;
  mark(false) >= false ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),mark(X2),X3) ;
  a__f(X) >= a__if(mark(X),c,f(true)) ;
  a__f(X) >= f(X) ;
  Marked_a__if(true,X,Y) >= Marked_mark(X) ;
  Marked_a__f(X) >= Marked_a__if(mark(X),c,f(true)) ;
  Marked_a__f(X) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_a__f(mark(X)) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),mark(X2),X3) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X2) ;
 }
 + Disjunctions:{ 
{
  Marked_a__if(true,X,Y) > Marked_mark(X) ;
 }
{
  Marked_a__f(X) > Marked_a__if(mark(X),c,f(true)) ;
 }
{
  Marked_a__f(X) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_a__f(mark(X)) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_a__if(mark(X1),mark(X2),X3) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X2) ;
 }
 } 
=== 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__if(true,X,Y) >= mark(X)
constraint: a__if(false,X,Y) >= mark(Y)
constraint: a__if(X1,X2,X3) >= if(X1,X2,X3)
constraint: mark(c) >= c
constraint: mark(f(X)) >= a__f(mark(X))
constraint: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),mark(X2),X3)
constraint: a__f(X) >= a__if(mark(X),c,f(true))
constraint: a__f(X) >= f(X)
constraint: Marked_a__if(true,X,Y) >= Marked_mark(X)
constraint: Marked_a__f(X) >= Marked_a__if(mark(X),c,f(true))
constraint: Marked_a__f(X) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_a__f(mark(X))
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),mark(X2),X3)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X2)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
      --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  mark(c) >= c ;
  mark(f(X)) >= a__f(mark(X)) ;
  mark(true) >= true ;
  mark(false) >= false ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),mark(X2),X3) ;
  a__f(X) >= a__if(mark(X),c,f(true)) ;
  a__f(X) >= f(X) ;
  Marked_a__if(true,X,Y) >= Marked_mark(X) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),mark(X2),X3) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X2) ;
 }
 + Disjunctions:{ 
{
  Marked_a__if(true,X,Y) > Marked_mark(X) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_a__if(mark(X1),mark(X2),X3) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X2) ;
 }
 } 
=== 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__if(true,X,Y) >= mark(X)
constraint: a__if(false,X,Y) >= mark(Y)
constraint: a__if(X1,X2,X3) >= if(X1,X2,X3)
constraint: mark(c) >= c
constraint: mark(f(X)) >= a__f(mark(X))
constraint: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),mark(X2),X3)
constraint: a__f(X) >= a__if(mark(X),c,f(true))
constraint: a__f(X) >= f(X)
constraint: Marked_a__if(true,X,Y) >= Marked_mark(X)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),mark(X2),X3)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X2)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__f(X) -> a__if(mark(X),c,f(true))
[2] a__if(true,X,Y) -> mark(X)
[3] a__if(false,X,Y) -> mark(Y)
[4] mark(f(X)) -> a__f(mark(X))
[5] mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
[6] mark(c) -> c
[7] mark(true) -> true
[8] mark(false) -> false
[9] a__f(X) -> f(X)
[10] a__if(X1,X2,X3) -> if(X1,X2,X3)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))>
<Marked_a__f(X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))>
<Marked_a__f(X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a__if ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; 
 [ Marked_a__if ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; 
 [ true ] () = 0; 
 [ c ] () = 0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ false ] () = 1; 
 [ mark ] (X0) = 1*X0; 
 [ Marked_a__f ] (X0) = 2*X0; 
 [ a__f ] (X0) = 1*X0; 
 [ f ] (X0) = 1*X0; 
 [ if ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; 
 removing <Marked_a__if(false,X,Y),Marked_mark(Y)>
 [ {
      
     DP termination of:
     <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))>
<Marked_a__f(X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))>
<Marked_a__f(X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a__if ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; 
 [ Marked_a__if ] (X0,X1,X2) = 2*X1; 
 [ true ] () = 0; 
 [ c ] () = 0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ false ] () = 0; 
 [ mark ] (X0) = 1*X0; 
 [ Marked_a__f ] (X0) = 2*X0; 
 [ a__f ] (X0) = 2*X0 + 2; 
 [ f ] (X0) = 2*X0 + 2; 
 [ if ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; 
 removing <Marked_mark(f(X)),Marked_a__f(mark(X))><Marked_mark(f(X)),
Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_a__f(X) , Marked_a__if(mark(X),c,f(true))>
<Marked_a__f(X) , Marked_mark(X)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),mark(X2),X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a__if ] (X0,X1,X2) = 1*X2*X0 + 1*X1 + 1*X0 + 1; 
 [ Marked_a__if ] (X0,X1,X2) = 1*X2*X0 + 1*X1; 
 [ true ] () = 0; 
 [ c ] () = 0; 
 [ Marked_mark ] (X0) = 1*X0; 
 [ false ] () = 1; 
 [ mark ] (X0) = 1*X0; 
 [ a__f ] (X0) = 2*X0 + 1; 
 [ f ] (X0) = 2*X0 + 1; 
 [ if ] (X0,X1,X2) = 1*X2*X0 + 1*X1 + 1*X0 + 1; 
 removing <Marked_mark(if(X1,X2,X3)),Marked_a__if(mark(X1),mark(X2),X3)><
Marked_mark(if(X1,X2,X3)),Marked_mark(X1)><Marked_mark(if(X1,X2,X3)),
Marked_mark(X2)>
 [ {
      
     DP termination of:
     <Marked_a__if(true,X,Y) , Marked_mark(X)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.348758 seconds (real time)
Cime Exit Status: 0