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

TRS termination of:
[1] active(zeros) -> mark(cons(0,zeros))
[2] active(tail(cons(X,XS))) -> mark(XS)
[3] active(cons(X1,X2)) -> cons(active(X1),X2)
[4] active(tail(X)) -> tail(active(X))
[5] cons(mark(X1),X2) -> mark(cons(X1,X2))
[6] tail(mark(X)) -> mark(tail(X))
[7] proper(zeros) -> ok(zeros)
[8] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[9] proper(0) -> ok(0)
[10] proper(tail(X)) -> tail(proper(X))
[11] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[12] tail(ok(X)) -> ok(tail(X))
[13] top(mark(X)) -> top(proper(X))
[14] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(zeros) , Marked_cons(0,zeros)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(tail(X)) , Marked_tail(active(X))>
<Marked_active(tail(X)) , Marked_active(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_tail(mark(X)) , Marked_tail(X)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(tail(X)) , Marked_tail(proper(X))>
<Marked_proper(tail(X)) , Marked_proper(X)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_tail(ok(X)) , Marked_tail(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(tail(X)) , Marked_proper(X)> 
      --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(tail(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(tail(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
}

{  <Marked_active(tail(X)) , Marked_active(X)> 
      --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(tail(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(tail(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
}

{  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
      --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}

{  <Marked_tail(ok(X)) , Marked_tail(X)> 
      --> <Marked_tail(ok(X)) , Marked_tail(X)>
  <Marked_tail(ok(X)) , Marked_tail(X)> 
     --> <Marked_tail(mark(X)) , Marked_tail(X)>
  <Marked_tail(mark(X)) , Marked_tail(X)> 
     --> <Marked_tail(ok(X)) , Marked_tail(X)>
  <Marked_tail(mark(X)) , Marked_tail(X)> 
     --> <Marked_tail(mark(X)) , Marked_tail(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(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
=== 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 : 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(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 (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_proper(cons(X1,X2)) >= Marked_proper(X1) ;
  Marked_proper(cons(X1,X2)) >= Marked_proper(X2) ;
  Marked_proper(tail(X)) >= Marked_proper(X) ;
 }
 + Disjunctions:{ 
{
  Marked_proper(cons(X1,X2)) > Marked_proper(X1) ;
 }
{
  Marked_proper(cons(X1,X2)) > Marked_proper(X2) ;
 }
{
  Marked_proper(tail(X)) > Marked_proper(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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_proper(cons(X1,X2)) >= Marked_proper(X1)
constraint: Marked_proper(cons(X1,X2)) >= Marked_proper(X2)
constraint: Marked_proper(tail(X)) >= Marked_proper(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_active(cons(X1,X2)) >= Marked_active(X1) ;
  Marked_active(tail(X)) >= Marked_active(X) ;
 }
 + Disjunctions:{ 
{
  Marked_active(cons(X1,X2)) > Marked_active(X1) ;
 }
{
  Marked_active(tail(X)) > Marked_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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_active(cons(X1,X2)) >= Marked_active(X1)
constraint: Marked_active(tail(X)) >= Marked_active(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_cons(mark(X1),X2) >= Marked_cons(X1,X2) ;
  Marked_cons(ok(X1),ok(X2)) >= Marked_cons(X1,X2) ;
 }
 + Disjunctions:{ 
{
  Marked_cons(mark(X1),X2) > Marked_cons(X1,X2) ;
 }
{
  Marked_cons(ok(X1),ok(X2)) > Marked_cons(X1,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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_cons(mark(X1),X2) >= Marked_cons(X1,X2)
constraint: Marked_cons(ok(X1),ok(X2)) >= Marked_cons(X1,X2)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_tail(mark(X)) >= Marked_tail(X) ;
  Marked_tail(ok(X)) >= Marked_tail(X) ;
 }
 + Disjunctions:{ 
{
  Marked_tail(mark(X)) > Marked_tail(X) ;
 }
{
  Marked_tail(ok(X)) > Marked_tail(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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_tail(mark(X)) >= Marked_tail(X)
constraint: Marked_tail(ok(X)) >= Marked_tail(X)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_top(ok(X)) >= Marked_top(active(X))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
      --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_proper(cons(X1,X2)) >= Marked_proper(X1) ;
  Marked_proper(cons(X1,X2)) >= Marked_proper(X2) ;
 }
 + Disjunctions:{ 
{
  Marked_proper(cons(X1,X2)) > Marked_proper(X1) ;
 }
{
  Marked_proper(cons(X1,X2)) > Marked_proper(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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_proper(cons(X1,X2)) >= Marked_proper(X1)
constraint: Marked_proper(cons(X1,X2)) >= Marked_proper(X2)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_active(tail(X)) , Marked_active(X)> 
      --> <Marked_active(tail(X)) , Marked_active(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_active(tail(X)) >= Marked_active(X) ;
 }
 + Disjunctions:{ 
{
  Marked_active(tail(X)) > Marked_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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_active(tail(X)) >= Marked_active(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
      --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_cons(mark(X1),X2) >= Marked_cons(X1,X2) ;
 }
 + Disjunctions:{ 
{
  Marked_cons(mark(X1),X2) > Marked_cons(X1,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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_cons(mark(X1),X2) >= Marked_cons(X1,X2)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_tail(ok(X)) , Marked_tail(X)> 
      --> <Marked_tail(ok(X)) , Marked_tail(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(zeros) >= mark(cons(0,zeros)) ;
  active(tail(cons(X,XS))) >= mark(XS) ;
  active(tail(X)) >= tail(active(X)) ;
  tail(mark(X)) >= mark(tail(X)) ;
  tail(ok(X)) >= ok(tail(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(zeros) >= ok(zeros) ;
  proper(tail(X)) >= tail(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_tail(ok(X)) >= Marked_tail(X) ;
 }
 + Disjunctions:{ 
{
  Marked_tail(ok(X)) > Marked_tail(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: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(zeros) >= mark(cons(0,zeros))
constraint: active(tail(cons(X,XS))) >= mark(XS)
constraint: active(tail(X)) >= tail(active(X))
constraint: tail(mark(X)) >= mark(tail(X))
constraint: tail(ok(X)) >= ok(tail(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(zeros) >= ok(zeros)
constraint: proper(tail(X)) >= tail(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_tail(ok(X)) >= Marked_tail(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] active(zeros) -> mark(cons(0,zeros))
[2] active(tail(cons(X,XS))) -> mark(XS)
[3] active(cons(X1,X2)) -> cons(active(X1),X2)
[4] active(tail(X)) -> tail(active(X))
[5] cons(mark(X1),X2) -> mark(cons(X1,X2))
[6] tail(mark(X)) -> mark(tail(X))
[7] proper(zeros) -> ok(zeros)
[8] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[9] proper(0) -> ok(0)
[10] proper(tail(X)) -> tail(proper(X))
[11] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[12] tail(ok(X)) -> ok(tail(X))
[13] top(mark(X)) -> top(proper(X))
[14] top(ok(X)) -> top(active(X))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(zeros) , Marked_cons(0,zeros)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(tail(X)) , Marked_tail(active(X))>
<Marked_active(tail(X)) , Marked_active(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_tail(mark(X)) , Marked_tail(X)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(tail(X)) , Marked_tail(proper(X))>
<Marked_proper(tail(X)) , Marked_proper(X)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_tail(ok(X)) , Marked_tail(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: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ mark ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ top ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ active ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ ok ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ cons ] (X0,X1) = [ [ 0 , 1 , 1 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_top ] (X0) = [ [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ tail ] (X0) = [ [ 1 , 1 , 1 ] [ 1 , 1 , 1 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ zeros ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ proper ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 removing <Marked_top(mark(X)),Marked_top(proper(X))>
 [ {
      
     DP termination of:
     <Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 2 + 0; 
 [ top ] (X0) = 0; 
 [ active ] (X0) = 2*X0 + 0; 
 [ 0 ] () = 2 + 0; 
 [ ok ] (X0) = 3 + 2*X0 + 0; 
 [ cons ] (X0,X1) = 2 + 2*X0 + 0; 
 [ Marked_top ] (X0) = 2*X0 + 0; 
 [ tail ] (X0) = 1*X0 + 0; 
 [ zeros ] () = 1 + 0; 
 [ proper ] (X0) = 2 + 3*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(tail(X)) , Marked_proper(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ top ] (X0) = 0; 
 [ active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ ok ] (X0) = 0; 
 [ cons ] (X0,X1) = 2*X1 + 2*X0; 
 [ tail ] (X0) = 2*X0 + 1; 
 [ zeros ] () = 0; 
 [ Marked_proper ] (X0) = 3*X0; 
 [ proper ] (X0) = 1*X0; 
 removing <Marked_proper(tail(X)),Marked_proper(X)>
 [ {
      
     DP termination of:
     <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 0; 
 [ top ] (X0) = 0; 
 [ active ] (X0) = 1*X0 + 0; 
 [ 0 ] () = 0; 
 [ ok ] (X0) = 0; 
 [ cons ] (X0,X1) = 1 + 2*X0 + 2*X1 + 0; 
 [ tail ] (X0) = 2 + 0; 
 [ zeros ] () = 2 + 0; 
 [ Marked_proper ] (X0) = 3*X0 + 0; 
 [ proper ] (X0) = 1*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(tail(X)) , Marked_active(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 2; 
 [ top ] (X0) = 0; 
 [ active ] (X0) = 1*X0; 
 [ 0 ] () = 3; 
 [ Marked_active ] (X0) = 3*X0; 
 [ ok ] (X0) = 0; 
 [ cons ] (X0,X1) = 1*X0 + 1; 
 [ tail ] (X0) = 2*X0; 
 [ zeros ] () = 2; 
 [ proper ] (X0) = 2*X0; 
 removing <Marked_active(cons(X1,X2)),Marked_active(X1)>
 [ {
      
     DP termination of:
     <Marked_active(tail(X)) , Marked_active(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(tail(X)) , Marked_active(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 0; 
 [ top ] (X0) = 0; 
 [ active ] (X0) = 2*X0 + 0; 
 [ 0 ] () = 2 + 0; 
 [ Marked_active ] (X0) = 3*X0 + 0; 
 [ ok ] (X0) = 3 + 0; 
 [ cons ] (X0,X1) = 3*X0 + 0; 
 [ tail ] (X0) = 1 + 2*X0 + 0; 
 [ zeros ] () = 2 + 0; 
 [ proper ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1; 
 [ top ] (X0) = 2*X0; 
 [ active ] (X0) = 1; 
 [ 0 ] () = 0; 
 [ ok ] (X0) = 2*X0 + 1; 
 [ cons ] (X0,X1) = 1*X0; 
 [ tail ] (X0) = 1*X0; 
 [ Marked_cons ] (X0,X1) = 1*X1; 
 [ zeros ] () = 0; 
 [ proper ] (X0) = 1; 
 removing <Marked_cons(ok(X1),ok(X2)),Marked_cons(X1,X2)>
 [ {
      
     DP termination of:
     <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 2 + 1*X0 + 0; 
 [ top ] (X0) = 0; 
 [ active ] (X0) = 2 + 1*X0 + 0; 
 [ 0 ] () = 0; 
 [ ok ] (X0) = 0; 
 [ cons ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ tail ] (X0) = 1*X0 + 0; 
 [ Marked_cons ] (X0,X1) = 3*X0 + 0; 
 [ zeros ] () = 0; 
 [ proper ] (X0) = 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_tail(mark(X)) , Marked_tail(X)>
<Marked_tail(ok(X)) , Marked_tail(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0 + 1; 
 [ top ] (X0) = 0; 
 [ active ] (X0) = 3*X0; 
 [ Marked_tail ] (X0) = 3*X0; 
 [ 0 ] () = 0; 
 [ ok ] (X0) = 1*X0; 
 [ cons ] (X0,X1) = 2*X1 + 2*X0; 
 [ tail ] (X0) = 3*X0 + 3; 
 [ zeros ] () = 2; 
 [ proper ] (X0) = 1*X0; 
 removing <Marked_tail(mark(X)),Marked_tail(X)>
 [ {
      
     DP termination of:
     <Marked_tail(ok(X)) , Marked_tail(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_tail(ok(X)) , Marked_tail(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 2 + 0; 
 [ top ] (X0) = 0; 
 [ active ] (X0) = 2*X0 + 0; 
 [ Marked_tail ] (X0) = 3*X0 + 0; 
 [ 0 ] () = 2 + 0; 
 [ ok ] (X0) = 3 + 2*X0 + 0; 
 [ cons ] (X0,X1) = 2 + 2*X0 + 0; 
 [ tail ] (X0) = 2 + 3*X0 + 0; 
 [ zeros ] () = 1 + 0; 
 [ proper ] (X0) = 2 + 3*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 1.928350 seconds (real time)
Cime Exit Status: 0