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

TRS termination of:
[1] a__minus(0,Y) -> 0
[2] a__minus(s(X),s(Y)) -> a__minus(X,Y)
[3] a__geq(X,0) -> true
[4] a__geq(0,s(Y)) -> false
[5] a__geq(s(X),s(Y)) -> a__geq(X,Y)
[6] a__div(0,s(Y)) -> 0
[7] a__div(s(X),s(Y)) -> a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0)
[8] a__if(true,X,Y) -> mark(X)
[9] a__if(false,X,Y) -> mark(Y)
[10] mark(minus(X1,X2)) -> a__minus(X1,X2)
[11] mark(geq(X1,X2)) -> a__geq(X1,X2)
[12] mark(div(X1,X2)) -> a__div(mark(X1),X2)
[13] mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
[14] mark(0) -> 0
[15] mark(s(X)) -> s(mark(X))
[16] mark(true) -> true
[17] mark(false) -> false
[18] a__minus(X1,X2) -> minus(X1,X2)
[19] a__geq(X1,X2) -> geq(X1,X2)
[20] a__div(X1,X2) -> div(X1,X2)
[21] a__if(X1,X2,X3) -> if(X1,X2,X3)


Sub problem: 
guided: 

DP termination of:
<Marked_a__minus(s(X),s(Y)) , Marked_a__minus(X,Y)>
<Marked_a__geq(s(X),s(Y)) , Marked_a__geq(X,Y)>
<Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0)>
<Marked_a__div(s(X),s(Y)) , Marked_a__geq(X,Y)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_mark(minus(X1,X2)) , Marked_a__minus(X1,X2)>
<Marked_mark(geq(X1,X2)) , Marked_a__geq(X1,X2)>
<Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
<Marked_mark(div(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_mark(s(X)) , Marked_mark(X)> 
      --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <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),X2,X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)> 
     --> <Marked_a__if(false,X,Y) , Marked_mark(Y)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
  <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)> 
     --> <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),
                                      s(div(minus(X,Y),s(Y))),0)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <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),X2,X3)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <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),X2,X3)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
  <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),
                               0)> 
     --> <Marked_a__if(false,X,Y) , Marked_mark(Y)>
  <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),
                               0)> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
}

{  <Marked_a__minus(s(X),s(Y)) , Marked_a__minus(X,Y)> 
      --> <Marked_a__minus(s(X),s(Y)) , Marked_a__minus(X,Y)>
}

{  <Marked_a__geq(s(X),s(Y)) , Marked_a__geq(X,Y)> 
      --> <Marked_a__geq(s(X),s(Y)) , Marked_a__geq(X,Y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__minus(0,Y) >= 0 ;
  a__minus(s(X),s(Y)) >= a__minus(X,Y) ;
  a__minus(X1,X2) >= minus(X1,X2) ;
  a__geq(0,s(Y)) >= false ;
  a__geq(s(X),s(Y)) >= a__geq(X,Y) ;
  a__geq(X,0) >= true ;
  a__geq(X1,X2) >= geq(X1,X2) ;
  a__div(0,s(Y)) >= 0 ;
  a__div(s(X),s(Y)) >= a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0) ;
  a__div(X1,X2) >= div(X1,X2) ;
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(mark(X)) ;
  mark(true) >= true ;
  mark(false) >= false ;
  mark(div(X1,X2)) >= a__div(mark(X1),X2) ;
  mark(minus(X1,X2)) >= a__minus(X1,X2) ;
  mark(geq(X1,X2)) >= a__geq(X1,X2) ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ;
  Marked_a__if(true,X,Y) >= Marked_mark(X) ;
  Marked_a__if(false,X,Y) >= Marked_mark(Y) ;
  Marked_a__div(s(X),s(Y)) >= Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),
                               0) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(div(X1,X2)) >= Marked_a__div(mark(X1),X2) ;
  Marked_mark(div(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__if(true,X,Y) > Marked_mark(X) ;
 }
{
  Marked_a__if(false,X,Y) > Marked_mark(Y) ;
 }
{
  Marked_a__div(s(X),s(Y)) > Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),
                              0) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(div(X1,X2)) > Marked_a__div(mark(X1),X2) ;
 }
{
  Marked_mark(div(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_a__if(mark(X1),X2,X3) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ;
 }
 } 
=== 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__minus(0,Y) >= 0
constraint: a__minus(s(X),s(Y)) >= a__minus(X,Y)
constraint: a__minus(X1,X2) >= minus(X1,X2)
constraint: a__geq(0,s(Y)) >= false
constraint: a__geq(s(X),s(Y)) >= a__geq(X,Y)
constraint: a__geq(X,0) >= true
constraint: a__geq(X1,X2) >= geq(X1,X2)
constraint: a__div(0,s(Y)) >= 0
constraint: a__div(s(X),s(Y)) >= a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0)
constraint: a__div(X1,X2) >= div(X1,X2)
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(0) >= 0
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(div(X1,X2)) >= a__div(mark(X1),X2)
constraint: mark(minus(X1,X2)) >= a__minus(X1,X2)
constraint: mark(geq(X1,X2)) >= a__geq(X1,X2)
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3)
constraint: Marked_a__if(true,X,Y) >= Marked_mark(X)
constraint: Marked_a__if(false,X,Y) >= Marked_mark(Y)
constraint: Marked_a__div(s(X),s(Y)) >= Marked_a__if(a__geq(X,Y),
                                         s(div(minus(X,Y),s(Y))),0)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(div(X1,X2)) >= Marked_a__div(mark(X1),X2)
constraint: Marked_mark(div(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__minus(0,Y) >= 0 ;
  a__minus(s(X),s(Y)) >= a__minus(X,Y) ;
  a__minus(X1,X2) >= minus(X1,X2) ;
  a__geq(0,s(Y)) >= false ;
  a__geq(s(X),s(Y)) >= a__geq(X,Y) ;
  a__geq(X,0) >= true ;
  a__geq(X1,X2) >= geq(X1,X2) ;
  a__div(0,s(Y)) >= 0 ;
  a__div(s(X),s(Y)) >= a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0) ;
  a__div(X1,X2) >= div(X1,X2) ;
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(mark(X)) ;
  mark(true) >= true ;
  mark(false) >= false ;
  mark(div(X1,X2)) >= a__div(mark(X1),X2) ;
  mark(minus(X1,X2)) >= a__minus(X1,X2) ;
  mark(geq(X1,X2)) >= a__geq(X1,X2) ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ;
  Marked_a__minus(s(X),s(Y)) >= Marked_a__minus(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_a__minus(s(X),s(Y)) > Marked_a__minus(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: a__minus(0,Y) >= 0
constraint: a__minus(s(X),s(Y)) >= a__minus(X,Y)
constraint: a__minus(X1,X2) >= minus(X1,X2)
constraint: a__geq(0,s(Y)) >= false
constraint: a__geq(s(X),s(Y)) >= a__geq(X,Y)
constraint: a__geq(X,0) >= true
constraint: a__geq(X1,X2) >= geq(X1,X2)
constraint: a__div(0,s(Y)) >= 0
constraint: a__div(s(X),s(Y)) >= a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0)
constraint: a__div(X1,X2) >= div(X1,X2)
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(0) >= 0
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(div(X1,X2)) >= a__div(mark(X1),X2)
constraint: mark(minus(X1,X2)) >= a__minus(X1,X2)
constraint: mark(geq(X1,X2)) >= a__geq(X1,X2)
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3)
constraint: Marked_a__minus(s(X),s(Y)) >= Marked_a__minus(X,Y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__minus(0,Y) >= 0 ;
  a__minus(s(X),s(Y)) >= a__minus(X,Y) ;
  a__minus(X1,X2) >= minus(X1,X2) ;
  a__geq(0,s(Y)) >= false ;
  a__geq(s(X),s(Y)) >= a__geq(X,Y) ;
  a__geq(X,0) >= true ;
  a__geq(X1,X2) >= geq(X1,X2) ;
  a__div(0,s(Y)) >= 0 ;
  a__div(s(X),s(Y)) >= a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0) ;
  a__div(X1,X2) >= div(X1,X2) ;
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(mark(X)) ;
  mark(true) >= true ;
  mark(false) >= false ;
  mark(div(X1,X2)) >= a__div(mark(X1),X2) ;
  mark(minus(X1,X2)) >= a__minus(X1,X2) ;
  mark(geq(X1,X2)) >= a__geq(X1,X2) ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ;
  Marked_a__geq(s(X),s(Y)) >= Marked_a__geq(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_a__geq(s(X),s(Y)) > Marked_a__geq(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: a__minus(0,Y) >= 0
constraint: a__minus(s(X),s(Y)) >= a__minus(X,Y)
constraint: a__minus(X1,X2) >= minus(X1,X2)
constraint: a__geq(0,s(Y)) >= false
constraint: a__geq(s(X),s(Y)) >= a__geq(X,Y)
constraint: a__geq(X,0) >= true
constraint: a__geq(X1,X2) >= geq(X1,X2)
constraint: a__div(0,s(Y)) >= 0
constraint: a__div(s(X),s(Y)) >= a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0)
constraint: a__div(X1,X2) >= div(X1,X2)
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(0) >= 0
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(div(X1,X2)) >= a__div(mark(X1),X2)
constraint: mark(minus(X1,X2)) >= a__minus(X1,X2)
constraint: mark(geq(X1,X2)) >= a__geq(X1,X2)
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3)
constraint: Marked_a__geq(s(X),s(Y)) >= Marked_a__geq(X,Y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <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),X2,X3)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)> 
     --> <Marked_a__if(false,X,Y) , Marked_mark(Y)>
  <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(div(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
  <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)> 
     --> <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),
                                      s(div(minus(X,Y),s(Y))),0)>
  <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),X2,X3)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(false,X,Y) , Marked_mark(Y)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),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),X2,X3)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(div(X1,X2)) , Marked_mark(X1)>
  <Marked_a__if(true,X,Y) , Marked_mark(X)> 
     --> <Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
  <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),
                               0)> 
     --> <Marked_a__if(false,X,Y) , Marked_mark(Y)>
  <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),
                               0)> 
     --> <Marked_a__if(true,X,Y) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__minus(0,Y) >= 0 ;
  a__minus(s(X),s(Y)) >= a__minus(X,Y) ;
  a__minus(X1,X2) >= minus(X1,X2) ;
  a__geq(0,s(Y)) >= false ;
  a__geq(s(X),s(Y)) >= a__geq(X,Y) ;
  a__geq(X,0) >= true ;
  a__geq(X1,X2) >= geq(X1,X2) ;
  a__div(0,s(Y)) >= 0 ;
  a__div(s(X),s(Y)) >= a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0) ;
  a__div(X1,X2) >= div(X1,X2) ;
  a__if(true,X,Y) >= mark(X) ;
  a__if(false,X,Y) >= mark(Y) ;
  a__if(X1,X2,X3) >= if(X1,X2,X3) ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(mark(X)) ;
  mark(true) >= true ;
  mark(false) >= false ;
  mark(div(X1,X2)) >= a__div(mark(X1),X2) ;
  mark(minus(X1,X2)) >= a__minus(X1,X2) ;
  mark(geq(X1,X2)) >= a__geq(X1,X2) ;
  mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ;
  Marked_a__if(true,X,Y) >= Marked_mark(X) ;
  Marked_a__if(false,X,Y) >= Marked_mark(Y) ;
  Marked_a__div(s(X),s(Y)) >= Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),
                               0) ;
  Marked_mark(div(X1,X2)) >= Marked_a__div(mark(X1),X2) ;
  Marked_mark(div(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__if(true,X,Y) > Marked_mark(X) ;
 }
{
  Marked_a__if(false,X,Y) > Marked_mark(Y) ;
 }
{
  Marked_a__div(s(X),s(Y)) > Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),
                              0) ;
 }
{
  Marked_mark(div(X1,X2)) > Marked_a__div(mark(X1),X2) ;
 }
{
  Marked_mark(div(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_a__if(mark(X1),X2,X3) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ;
 }
 } 
=== 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__minus(0,Y) >= 0
constraint: a__minus(s(X),s(Y)) >= a__minus(X,Y)
constraint: a__minus(X1,X2) >= minus(X1,X2)
constraint: a__geq(0,s(Y)) >= false
constraint: a__geq(s(X),s(Y)) >= a__geq(X,Y)
constraint: a__geq(X,0) >= true
constraint: a__geq(X1,X2) >= geq(X1,X2)
constraint: a__div(0,s(Y)) >= 0
constraint: a__div(s(X),s(Y)) >= a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0)
constraint: a__div(X1,X2) >= div(X1,X2)
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(0) >= 0
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(true) >= true
constraint: mark(false) >= false
constraint: mark(div(X1,X2)) >= a__div(mark(X1),X2)
constraint: mark(minus(X1,X2)) >= a__minus(X1,X2)
constraint: mark(geq(X1,X2)) >= a__geq(X1,X2)
constraint: mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3)
constraint: Marked_a__if(true,X,Y) >= Marked_mark(X)
constraint: Marked_a__if(false,X,Y) >= Marked_mark(Y)
constraint: Marked_a__div(s(X),s(Y)) >= Marked_a__if(a__geq(X,Y),
                                         s(div(minus(X,Y),s(Y))),0)
constraint: Marked_mark(div(X1,X2)) >= Marked_a__div(mark(X1),X2)
constraint: Marked_mark(div(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1)
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] a__minus(0,Y) -> 0
[2] a__minus(s(X),s(Y)) -> a__minus(X,Y)
[3] a__geq(X,0) -> true
[4] a__geq(0,s(Y)) -> false
[5] a__geq(s(X),s(Y)) -> a__geq(X,Y)
[6] a__div(0,s(Y)) -> 0
[7] a__div(s(X),s(Y)) -> a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0)
[8] a__if(true,X,Y) -> mark(X)
[9] a__if(false,X,Y) -> mark(Y)
[10] mark(minus(X1,X2)) -> a__minus(X1,X2)
[11] mark(geq(X1,X2)) -> a__geq(X1,X2)
[12] mark(div(X1,X2)) -> a__div(mark(X1),X2)
[13] mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
[14] mark(0) -> 0
[15] mark(s(X)) -> s(mark(X))
[16] mark(true) -> true
[17] mark(false) -> false
[18] a__minus(X1,X2) -> minus(X1,X2)
[19] a__geq(X1,X2) -> geq(X1,X2)
[20] a__div(X1,X2) -> div(X1,X2)
[21] a__if(X1,X2,X3) -> if(X1,X2,X3)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__minus(s(X),s(Y)) , Marked_a__minus(X,Y)>
<Marked_a__geq(s(X),s(Y)) , Marked_a__geq(X,Y)>
<Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0)>
<Marked_a__div(s(X),s(Y)) , Marked_a__geq(X,Y)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_mark(minus(X1,X2)) , Marked_a__minus(X1,X2)>
<Marked_mark(geq(X1,X2)) , Marked_a__geq(X1,X2)>
<Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
<Marked_mark(div(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),
                                  s(div(minus(X,Y),s(Y))),0)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
<Marked_mark(div(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ 0 ] () = 0; 
 [ div ] (X0,X1) = 2*X0; 
 [ a__geq ] (X0,X1) = 0; 
 [ if ] (X0,X1,X2) = 2*X2 + 1*X1 + 2*X0; 
 [ s ] (X0) = 2*X0 + 2; 
 [ mark ] (X0) = 1*X0; 
 [ a__div ] (X0,X1) = 2*X0; 
 [ Marked_a__div ] (X0,X1) = 1*X0; 
 [ a__minus ] (X0,X1) = 0; 
 [ Marked_mark ] (X0) = 1*X0; 
 [ minus ] (X0,X1) = 0; 
 [ false ] () = 0; 
 [ Marked_a__if ] (X0,X1,X2) = 2*X2 + 1*X1; 
 [ true ] () = 0; 
 [ geq ] (X0,X1) = 0; 
 [ a__if ] (X0,X1,X2) = 2*X2 + 1*X1 + 2*X0; 
 removing <Marked_mark(s(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),
                                  s(div(minus(X,Y),s(Y))),0)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
<Marked_mark(div(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),
                                  s(div(minus(X,Y),s(Y))),0)>
<Marked_a__if(true,X,Y) , Marked_mark(X)>
<Marked_a__if(false,X,Y) , Marked_mark(Y)>
<Marked_mark(div(X1,X2)) , Marked_a__div(mark(X1),X2)>
<Marked_mark(div(X1,X2)) , Marked_mark(X1)>
<Marked_mark(if(X1,X2,X3)) , Marked_a__if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ 0 ] () = 0; 
 [ div ] (X0,X1) = 3*X1 + 2*X0 + 3; 
 [ a__geq ] (X0,X1) = 3; 
 [ if ] (X0,X1,X2) = 2*X2 + 3*X1 + 1*X0 + 2; 
 [ s ] (X0) = 2; 
 [ mark ] (X0) = 2*X0 + 1; 
 [ a__div ] (X0,X1) = 3*X1 + 2*X0 + 3; 
 [ Marked_a__div ] (X0,X1) = 2*X1 + 1*X0 + 3; 
 [ a__minus ] (X0,X1) = 0; 
 [ Marked_mark ] (X0) = 3*X0 + 1; 
 [ minus ] (X0,X1) = 0; 
 [ false ] () = 2; 
 [ Marked_a__if ] (X0,X1,X2) = 3*X2 + 3*X1 + 1*X0; 
 [ true ] () = 2; 
 [ geq ] (X0,X1) = 1; 
 [ a__if ] (X0,X1,X2) = 2*X2 + 3*X1 + 1*X0 + 2; 
 removing <Marked_a__if(true,X,Y),Marked_mark(X)><Marked_a__if(false,X,Y),
Marked_mark(Y)><Marked_mark(div(X1,X2)),Marked_a__div(mark(X1),X2)><Marked_mark(
                                                                    div(
                                                                    X1,
                                                                    X2)),
Marked_mark(X1)><Marked_mark(if(X1,X2,X3)),Marked_a__if(mark(X1),X2,X3)><
Marked_mark(if(X1,X2,X3)),Marked_mark(X1)>
 [ {
      
     DP termination of:
     <Marked_a__div(s(X),s(Y)) , Marked_a__if(a__geq(X,Y),
                                  s(div(minus(X,Y),s(Y))),0)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_a__minus(s(X),s(Y)) , Marked_a__minus(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ Marked_a__minus ] (X0,X1) = 1*X1 + 0; 
 [ div ] (X0,X1) = 2*X0 + 0; 
 [ a__geq ] (X0,X1) = 0; 
 [ if ] (X0,X1,X2) = 1*X1 + 2*X2 + 0; 
 [ s ] (X0) = 2 + 2*X0 + 0; 
 [ mark ] (X0) = 2*X0 + 0; 
 [ a__div ] (X0,X1) = 2*X0 + 0; 
 [ a__minus ] (X0,X1) = 0; 
 [ minus ] (X0,X1) = 0; 
 [ false ] () = 0; 
 [ true ] () = 0; 
 [ geq ] (X0,X1) = 0; 
 [ a__if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; 
 ]} 
{
 
DP termination of:
<Marked_a__geq(s(X),s(Y)) , Marked_a__geq(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ div ] (X0,X1) = 2*X0 + 0; 
 [ a__geq ] (X0,X1) = 0; 
 [ if ] (X0,X1,X2) = 2*X1 + 1*X2 + 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ mark ] (X0) = 2*X0 + 0; 
 [ a__div ] (X0,X1) = 2*X0 + 0; 
 [ a__minus ] (X0,X1) = 0; 
 [ minus ] (X0,X1) = 0; 
 [ false ] () = 0; 
 [ true ] () = 0; 
 [ geq ] (X0,X1) = 0; 
 [ a__if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; 
 [ Marked_a__geq ] (X0,X1) = 1*X1 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.399877 seconds (real time)
Cime Exit Status: 0