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

TRS termination of:
[1] active(fact(X)) -> mark(if(zero(X),s(0),prod(X,fact(p(X)))))
[2] active(add(0,X)) -> mark(X)
[3] active(add(s(X),Y)) -> mark(s(add(X,Y)))
[4] active(prod(0,X)) -> mark(0)
[5] active(prod(s(X),Y)) -> mark(add(Y,prod(X,Y)))
[6] active(if(true,X,Y)) -> mark(X)
[7] active(if(false,X,Y)) -> mark(Y)
[8] active(zero(0)) -> mark(true)
[9] active(zero(s(X))) -> mark(false)
[10] active(p(s(X))) -> mark(X)
[11] mark(fact(X)) -> active(fact(mark(X)))
[12] mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3))
[13] mark(zero(X)) -> active(zero(mark(X)))
[14] mark(s(X)) -> active(s(mark(X)))
[15] mark(0) -> active(0)
[16] mark(prod(X1,X2)) -> active(prod(mark(X1),mark(X2)))
[17] mark(p(X)) -> active(p(mark(X)))
[18] mark(add(X1,X2)) -> active(add(mark(X1),mark(X2)))
[19] mark(true) -> active(true)
[20] mark(false) -> active(false)
[21] fact(mark(X)) -> fact(X)
[22] fact(active(X)) -> fact(X)
[23] if(mark(X1),X2,X3) -> if(X1,X2,X3)
[24] if(X1,mark(X2),X3) -> if(X1,X2,X3)
[25] if(X1,X2,mark(X3)) -> if(X1,X2,X3)
[26] if(active(X1),X2,X3) -> if(X1,X2,X3)
[27] if(X1,active(X2),X3) -> if(X1,X2,X3)
[28] if(X1,X2,active(X3)) -> if(X1,X2,X3)
[29] zero(mark(X)) -> zero(X)
[30] zero(active(X)) -> zero(X)
[31] s(mark(X)) -> s(X)
[32] s(active(X)) -> s(X)
[33] prod(mark(X1),X2) -> prod(X1,X2)
[34] prod(X1,mark(X2)) -> prod(X1,X2)
[35] prod(active(X1),X2) -> prod(X1,X2)
[36] prod(X1,active(X2)) -> prod(X1,X2)
[37] p(mark(X)) -> p(X)
[38] p(active(X)) -> p(X)
[39] add(mark(X1),X2) -> add(X1,X2)
[40] add(X1,mark(X2)) -> add(X1,X2)
[41] add(active(X1),X2) -> add(X1,X2)
[42] add(X1,active(X2)) -> add(X1,X2)


Sub problem: 
guided: 

DP termination of:
<Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))>
<Marked_active(fact(X)) , Marked_if(zero(X),s(0),prod(X,fact(p(X))))>
<Marked_active(fact(X)) , Marked_zero(X)>
<Marked_active(fact(X)) , Marked_s(0)>
<Marked_active(fact(X)) , Marked_prod(X,fact(p(X)))>
<Marked_active(fact(X)) , Marked_fact(p(X))>
<Marked_active(fact(X)) , Marked_p(X)>
<Marked_active(add(0,X)) , Marked_mark(X)>
<Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))>
<Marked_active(add(s(X),Y)) , Marked_s(add(X,Y))>
<Marked_active(add(s(X),Y)) , Marked_add(X,Y)>
<Marked_active(prod(0,X)) , Marked_mark(0)>
<Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))>
<Marked_active(prod(s(X),Y)) , Marked_add(Y,prod(X,Y))>
<Marked_active(prod(s(X),Y)) , Marked_prod(X,Y)>
<Marked_active(if(true,X,Y)) , Marked_mark(X)>
<Marked_active(if(false,X,Y)) , Marked_mark(Y)>
<Marked_active(zero(0)) , Marked_mark(true)>
<Marked_active(zero(s(X))) , Marked_mark(false)>
<Marked_active(p(s(X))) , Marked_mark(X)>
<Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
<Marked_mark(fact(X)) , Marked_fact(mark(X))>
<Marked_mark(fact(X)) , Marked_mark(X)>
<Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
<Marked_mark(if(X1,X2,X3)) , Marked_if(mark(X1),X2,X3)>
<Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
<Marked_mark(zero(X)) , Marked_zero(mark(X))>
<Marked_mark(zero(X)) , Marked_mark(X)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_s(mark(X))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(0) , Marked_active(0)>
<Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
<Marked_mark(prod(X1,X2)) , Marked_prod(mark(X1),mark(X2))>
<Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
<Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_p(mark(X))>
<Marked_mark(p(X)) , Marked_mark(X)>
<Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
<Marked_mark(add(X1,X2)) , Marked_add(mark(X1),mark(X2))>
<Marked_mark(add(X1,X2)) , Marked_mark(X1)>
<Marked_mark(add(X1,X2)) , Marked_mark(X2)>
<Marked_mark(true) , Marked_active(true)>
<Marked_mark(false) , Marked_active(false)>
<Marked_fact(mark(X)) , Marked_fact(X)>
<Marked_fact(active(X)) , Marked_fact(X)>
<Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)>
<Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)>
<Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)>
<Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)>
<Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)>
<Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)>
<Marked_zero(mark(X)) , Marked_zero(X)>
<Marked_zero(active(X)) , Marked_zero(X)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
<Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)>
<Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)>
<Marked_prod(active(X1),X2) , Marked_prod(X1,X2)>
<Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)>
<Marked_p(mark(X)) , Marked_p(X)>
<Marked_p(active(X)) , Marked_p(X)>
<Marked_add(mark(X1),X2) , Marked_add(X1,X2)>
<Marked_add(X1,mark(X2)) , Marked_add(X1,X2)>
<Marked_add(active(X1),X2) , Marked_add(X1,X2)>
<Marked_add(X1,active(X2)) , Marked_add(X1,X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 8 components:

{  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
      --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))> 
     --> <Marked_active(p(s(X))) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))> 
     --> <Marked_active(if(false,X,Y)) , Marked_mark(Y)>
  <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))> 
     --> <Marked_active(if(true,X,Y)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))> 
     --> <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))>
  <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))> 
     --> <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))>
  <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))> 
     --> <Marked_active(add(0,X)) , Marked_mark(X)>
  <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))> 
     --> <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),
                                                prod(X,fact(p(X)))))>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(p(s(X))) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(if(false,X,Y)) , Marked_mark(Y)>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(if(true,X,Y)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(add(0,X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),
                                                prod(X,fact(p(X)))))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))> 
     --> <Marked_active(p(s(X))) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))> 
     --> <Marked_active(if(false,X,Y)) , Marked_mark(Y)>
  <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))> 
     --> <Marked_active(if(true,X,Y)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))> 
     --> <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))>
  <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))> 
     --> <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))>
  <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))> 
     --> <Marked_active(add(0,X)) , Marked_mark(X)>
  <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))> 
     --> <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),
                                                prod(X,fact(p(X)))))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(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_active(if(mark(X1),X2,X3))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(p(s(X))) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(if(false,X,Y)) , Marked_mark(Y)>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(if(true,X,Y)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(add(0,X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),
                                                prod(X,fact(p(X)))))>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(zero(X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))> 
     --> <Marked_active(p(s(X))) , Marked_mark(X)>
  <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))> 
     --> <Marked_active(if(false,X,Y)) , Marked_mark(Y)>
  <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))> 
     --> <Marked_active(if(true,X,Y)) , Marked_mark(X)>
  <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))> 
     --> <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))>
  <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))> 
     --> <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))>
  <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))> 
     --> <Marked_active(add(0,X)) , Marked_mark(X)>
  <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))> 
     --> <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),
                                                prod(X,fact(p(X)))))>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(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(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(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_active(if(mark(X1),X2,X3))>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))> 
     --> <Marked_active(p(s(X))) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))> 
     --> <Marked_active(if(false,X,Y)) , Marked_mark(Y)>
  <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))> 
     --> <Marked_active(if(true,X,Y)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))> 
     --> <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))>
  <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))> 
     --> <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))>
  <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))> 
     --> <Marked_active(add(0,X)) , Marked_mark(X)>
  <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))> 
     --> <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),
                                                prod(X,fact(p(X)))))>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_mark(fact(X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))> 
     --> <Marked_active(p(s(X))) , Marked_mark(X)>
  <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))> 
     --> <Marked_active(if(false,X,Y)) , Marked_mark(Y)>
  <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))> 
     --> <Marked_active(if(true,X,Y)) , Marked_mark(X)>
  <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))> 
     --> <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))>
  <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))> 
     --> <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))>
  <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))> 
     --> <Marked_active(add(0,X)) , Marked_mark(X)>
  <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))> 
     --> <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),
                                                prod(X,fact(p(X)))))>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_active(p(s(X))) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_active(if(false,X,Y)) , Marked_mark(Y)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_active(if(true,X,Y)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_active(prod(s(X),Y)) , Marked_mark(add(Y,prod(X,Y)))> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_active(add(s(X),Y)) , Marked_mark(s(add(X,Y)))> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_active(add(0,X)) , Marked_mark(X)> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X2)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(add(X1,X2)) , Marked_mark(X1)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(add(X1,X2)) , Marked_active(add(mark(X1),mark(X2)))>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X2)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_mark(X1)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(prod(X1,X2)) , Marked_active(prod(mark(X1),mark(X2)))>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(zero(X)) , Marked_mark(X)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(zero(X)) , Marked_active(zero(mark(X)))>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(if(X1,X2,X3)) , Marked_active(if(mark(X1),X2,X3))>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(fact(X)) , Marked_mark(X)>
  <Marked_active(fact(X)) , Marked_mark(if(zero(X),s(0),prod(X,fact(p(X)))))> 
     --> <Marked_mark(fact(X)) , Marked_active(fact(mark(X)))>
}

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

{  <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)> 
      --> <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,active(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,active(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(active(X1),X2,X3) , Marked_if(X1,X2,X3)>
  <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,X2,mark(X3)) , Marked_if(X1,X2,X3)>
  <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(X1,mark(X2),X3) , Marked_if(X1,X2,X3)>
  <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)> 
     --> <Marked_if(mark(X1),X2,X3) , Marked_if(X1,X2,X3)>
}

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

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

{  <Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)> 
      --> <Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)>
  <Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)> 
     --> <Marked_prod(active(X1),X2) , Marked_prod(X1,X2)>
  <Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)> 
     --> <Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)>
  <Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)> 
     --> <Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)>
  <Marked_prod(active(X1),X2) , Marked_prod(X1,X2)> 
     --> <Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)>
  <Marked_prod(active(X1),X2) , Marked_prod(X1,X2)> 
     --> <Marked_prod(active(X1),X2) , Marked_prod(X1,X2)>
  <Marked_prod(active(X1),X2) , Marked_prod(X1,X2)> 
     --> <Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)>
  <Marked_prod(active(X1),X2) , Marked_prod(X1,X2)> 
     --> <Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)>
  <Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)> 
     --> <Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)>
  <Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)> 
     --> <Marked_prod(active(X1),X2) , Marked_prod(X1,X2)>
  <Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)> 
     --> <Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)>
  <Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)> 
     --> <Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)>
  <Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)> 
     --> <Marked_prod(X1,active(X2)) , Marked_prod(X1,X2)>
  <Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)> 
     --> <Marked_prod(active(X1),X2) , Marked_prod(X1,X2)>
  <Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)> 
     --> <Marked_prod(X1,mark(X2)) , Marked_prod(X1,X2)>
  <Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)> 
     --> <Marked_prod(mark(X1),X2) , Marked_prod(X1,X2)>
}

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

{  <Marked_add(X1,active(X2)) , Marked_add(X1,X2)> 
      --> <Marked_add(X1,active(X2)) , Marked_add(X1,X2)>
  <Marked_add(X1,active(X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(active(X1),X2) , Marked_add(X1,X2)>
  <Marked_add(X1,active(X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(X1,mark(X2)) , Marked_add(X1,X2)>
  <Marked_add(X1,active(X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(mark(X1),X2) , Marked_add(X1,X2)>
  <Marked_add(active(X1),X2) , Marked_add(X1,X2)> 
     --> <Marked_add(X1,active(X2)) , Marked_add(X1,X2)>
  <Marked_add(active(X1),X2) , Marked_add(X1,X2)> 
     --> <Marked_add(active(X1),X2) , Marked_add(X1,X2)>
  <Marked_add(active(X1),X2) , Marked_add(X1,X2)> 
     --> <Marked_add(X1,mark(X2)) , Marked_add(X1,X2)>
  <Marked_add(active(X1),X2) , Marked_add(X1,X2)> 
     --> <Marked_add(mark(X1),X2) , Marked_add(X1,X2)>
  <Marked_add(X1,mark(X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(X1,active(X2)) , Marked_add(X1,X2)>
  <Marked_add(X1,mark(X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(active(X1),X2) , Marked_add(X1,X2)>
  <Marked_add(X1,mark(X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(X1,mark(X2)) , Marked_add(X1,X2)>
  <Marked_add(X1,mark(X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(mark(X1),X2) , Marked_add(X1,X2)>
  <Marked_add(mark(X1),X2) , Marked_add(X1,X2)> 
     --> <Marked_add(X1,active(X2)) , Marked_add(X1,X2)>
  <Marked_add(mark(X1),X2) , Marked_add(X1,X2)> 
     --> <Marked_add(active(X1),X2) , Marked_add(X1,X2)>
  <Marked_add(mark(X1),X2) , Marked_add(X1,X2)> 
     --> <Marked_add(X1,mark(X2)) , Marked_add(X1,X2)>
  <Marked_add(mark(X1),X2) , Marked_add(X1,X2)> 
     --> <Marked_add(mark(X1),X2) , Marked_add(X1,X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ;
  mark(zero(X)) >= active(zero(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(0) >= active(0) ;
  mark(prod(X1,X2)) >= active(prod(mark(X1),mark(X2))) ;
  mark(fact(X)) >= active(fact(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ;
  mark(true) >= active(true) ;
  mark(false) >= active(false) ;
  if(mark(X1),X2,X3) >= if(X1,X2,X3) ;
  if(active(X1),X2,X3) >= if(X1,X2,X3) ;
  if(X1,mark(X2),X3) >= if(X1,X2,X3) ;
  if(X1,active(X2),X3) >= if(X1,X2,X3) ;
  if(X1,X2,mark(X3)) >= if(X1,X2,X3) ;
  if(X1,X2,active(X3)) >= if(X1,X2,X3) ;
  zero(mark(X)) >= zero(X) ;
  zero(active(X)) >= zero(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  prod(mark(X1),X2) >= prod(X1,X2) ;
  prod(active(X1),X2) >= prod(X1,X2) ;
  prod(X1,mark(X2)) >= prod(X1,X2) ;
  prod(X1,active(X2)) >= prod(X1,X2) ;
  fact(mark(X)) >= fact(X) ;
  fact(active(X)) >= fact(X) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  active(if(true,X,Y)) >= mark(X) ;
  active(if(false,X,Y)) >= mark(Y) ;
  active(zero(s(X))) >= mark(false) ;
  active(zero(0)) >= mark(true) ;
  active(prod(s(X),Y)) >= mark(add(Y,prod(X,Y))) ;
  active(prod(0,X)) >= mark(0) ;
  active(fact(X)) >= mark(if(zero(X),s(0),prod(X,fact(p(X))))) ;
  active(p(s(X))) >= mark(X) ;
  active(add(s(X),Y)) >= mark(s(add(X,Y))) ;
  active(add(0,X)) >= mark(X) ;
  add(mark(X1),X2) >= add(X1,X2) ;
  add(active(X1),X2) >= add(X1,X2) ;
  add(X1,mark(X2)) >= add(X1,X2) ;
  add(X1,active(X2)) >= add(X1,X2) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) ;
  Marked_mark(zero(X)) >= Marked_mark(X) ;
  Marked_mark(zero(X)) >= Marked_active(zero(mark(X))) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(s(X)) >= Marked_active(s(mark(X))) ;
  Marked_mark(prod(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(prod(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(prod(X1,X2)) >= Marked_active(prod(mark(X1),mark(X2))) ;
  Marked_mark(fact(X)) >= Marked_mark(X) ;
  Marked_mark(fact(X)) >= Marked_active(fact(mark(X))) ;
  Marked_mark(p(X)) >= Marked_mark(X) ;
  Marked_mark(p(X)) >= Marked_active(p(mark(X))) ;
  Marked_mark(add(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(add(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),mark(X2))) ;
  Marked_active(if(true,X,Y)) >= Marked_mark(X) ;
  Marked_active(if(false,X,Y)) >= Marked_mark(Y) ;
  Marked_active(prod(s(X),Y)) >= Marked_mark(add(Y,prod(X,Y))) ;
  Marked_active(fact(X)) >= Marked_mark(if(zero(X),s(0),prod(X,fact(p(X))))) ;
  Marked_active(p(s(X))) >= Marked_mark(X) ;
  Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ;
  Marked_active(add(0,X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(if(X1,X2,X3)) > Marked_active(if(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(zero(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(zero(X)) > Marked_active(zero(mark(X))) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(s(X)) > Marked_active(s(mark(X))) ;
 }
{
  Marked_mark(prod(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(prod(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(prod(X1,X2)) > Marked_active(prod(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(fact(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(fact(X)) > Marked_active(fact(mark(X))) ;
 }
{
  Marked_mark(p(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(p(X)) > Marked_active(p(mark(X))) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),mark(X2))) ;
 }
{
  Marked_active(if(true,X,Y)) > Marked_mark(X) ;
 }
{
  Marked_active(if(false,X,Y)) > Marked_mark(Y) ;
 }
{
  Marked_active(prod(s(X),Y)) > Marked_mark(add(Y,prod(X,Y))) ;
 }
{
  Marked_active(fact(X)) > Marked_mark(if(zero(X),s(0),prod(X,fact(p(X))))) ;
 }
{
  Marked_active(p(s(X))) > Marked_mark(X) ;
 }
{
  Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ;
 }
{
  Marked_active(add(0,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(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3))
constraint: mark(zero(X)) >= active(zero(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(0) >= active(0)
constraint: mark(prod(X1,X2)) >= active(prod(mark(X1),mark(X2)))
constraint: mark(fact(X)) >= active(fact(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2)))
constraint: mark(true) >= active(true)
constraint: mark(false) >= active(false)
constraint: if(mark(X1),X2,X3) >= if(X1,X2,X3)
constraint: if(active(X1),X2,X3) >= if(X1,X2,X3)
constraint: if(X1,mark(X2),X3) >= if(X1,X2,X3)
constraint: if(X1,active(X2),X3) >= if(X1,X2,X3)
constraint: if(X1,X2,mark(X3)) >= if(X1,X2,X3)
constraint: if(X1,X2,active(X3)) >= if(X1,X2,X3)
constraint: zero(mark(X)) >= zero(X)
constraint: zero(active(X)) >= zero(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: prod(mark(X1),X2) >= prod(X1,X2)
constraint: prod(active(X1),X2) >= prod(X1,X2)
constraint: prod(X1,mark(X2)) >= prod(X1,X2)
constraint: prod(X1,active(X2)) >= prod(X1,X2)
constraint: fact(mark(X)) >= fact(X)
constraint: fact(active(X)) >= fact(X)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: active(if(true,X,Y)) >= mark(X)
constraint: active(if(false,X,Y)) >= mark(Y)
constraint: active(zero(s(X))) >= mark(false)
constraint: active(zero(0)) >= mark(true)
constraint: active(prod(s(X),Y)) >= mark(add(Y,prod(X,Y)))
constraint: active(prod(0,X)) >= mark(0)
constraint: active(fact(X)) >= mark(if(zero(X),s(0),prod(X,fact(p(X)))))
constraint: active(p(s(X))) >= mark(X)
constraint: active(add(s(X),Y)) >= mark(s(add(X,Y)))
constraint: active(add(0,X)) >= mark(X)
constraint: add(mark(X1),X2) >= add(X1,X2)
constraint: add(active(X1),X2) >= add(X1,X2)
constraint: add(X1,mark(X2)) >= add(X1,X2)
constraint: add(X1,active(X2)) >= add(X1,X2)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3))
constraint: Marked_mark(zero(X)) >= Marked_mark(X)
constraint: Marked_mark(zero(X)) >= Marked_active(zero(mark(X)))
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X)))
constraint: Marked_mark(prod(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(prod(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(prod(X1,X2)) >= Marked_active(prod(mark(X1),mark(X2)))
constraint: Marked_mark(fact(X)) >= Marked_mark(X)
constraint: Marked_mark(fact(X)) >= Marked_active(fact(mark(X)))
constraint: Marked_mark(p(X)) >= Marked_mark(X)
constraint: Marked_mark(p(X)) >= Marked_active(p(mark(X)))
constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),mark(X2)))
constraint: Marked_active(if(true,X,Y)) >= Marked_mark(X)
constraint: Marked_active(if(false,X,Y)) >= Marked_mark(Y)
constraint: Marked_active(prod(s(X),Y)) >= Marked_mark(add(Y,prod(X,Y)))
constraint: Marked_active(fact(X)) >= Marked_mark(if(zero(X),s(0),
                                                   prod(X,fact(p(X)))))
constraint: Marked_active(p(s(X))) >= Marked_mark(X)
constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y)))
constraint: Marked_active(add(0,X)) >= Marked_mark(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ;
  mark(zero(X)) >= active(zero(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(0) >= active(0) ;
  mark(prod(X1,X2)) >= active(prod(mark(X1),mark(X2))) ;
  mark(fact(X)) >= active(fact(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ;
  mark(true) >= active(true) ;
  mark(false) >= active(false) ;
  if(mark(X1),X2,X3) >= if(X1,X2,X3) ;
  if(active(X1),X2,X3) >= if(X1,X2,X3) ;
  if(X1,mark(X2),X3) >= if(X1,X2,X3) ;
  if(X1,active(X2),X3) >= if(X1,X2,X3) ;
  if(X1,X2,mark(X3)) >= if(X1,X2,X3) ;
  if(X1,X2,active(X3)) >= if(X1,X2,X3) ;
  zero(mark(X)) >= zero(X) ;
  zero(active(X)) >= zero(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  prod(mark(X1),X2) >= prod(X1,X2) ;
  prod(active(X1),X2) >= prod(X1,X2) ;
  prod(X1,mark(X2)) >= prod(X1,X2) ;
  prod(X1,active(X2)) >= prod(X1,X2) ;
  fact(mark(X)) >= fact(X) ;
  fact(active(X)) >= fact(X) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  active(if(true,X,Y)) >= mark(X) ;
  active(if(false,X,Y)) >= mark(Y) ;
  active(zero(s(X))) >= mark(false) ;
  active(zero(0)) >= mark(true) ;
  active(prod(s(X),Y)) >= mark(add(Y,prod(X,Y))) ;
  active(prod(0,X)) >= mark(0) ;
  active(fact(X)) >= mark(if(zero(X),s(0),prod(X,fact(p(X))))) ;
  active(p(s(X))) >= mark(X) ;
  active(add(s(X),Y)) >= mark(s(add(X,Y))) ;
  active(add(0,X)) >= mark(X) ;
  add(mark(X1),X2) >= add(X1,X2) ;
  add(active(X1),X2) >= add(X1,X2) ;
  add(X1,mark(X2)) >= add(X1,X2) ;
  add(X1,active(X2)) >= add(X1,X2) ;
  Marked_fact(mark(X)) >= Marked_fact(X) ;
  Marked_fact(active(X)) >= Marked_fact(X) ;
 }
 + Disjunctions:{ 
{
  Marked_fact(mark(X)) > Marked_fact(X) ;
 }
{
  Marked_fact(active(X)) > Marked_fact(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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 39.616993 seconds (real time)
Cime Exit Status: 0