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

TRS termination of:
[1] a__and(tt,X) -> mark(X)
[2] a__plus(N,0) -> mark(N)
[3] a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
[4] a__x(N,0) -> 0
[5] a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
[6] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[7] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[8] mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
[9] mark(tt) -> tt
[10] mark(0) -> 0
[11] mark(s(X)) -> s(mark(X))
[12] a__and(X1,X2) -> and(X1,X2)
[13] a__plus(X1,X2) -> plus(X1,X2)
[14] a__x(X1,X2) -> x(X1,X2)


Sub problem: 
guided: 

DP termination of:
<Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__plus(N,s(M)) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_mark(M)>
<Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
<Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))>
<Marked_a__x(N,s(M)) , Marked_mark(N)>
<Marked_a__x(N,s(M)) , Marked_mark(M)>
<Marked_a__x(N,s(M)) , Marked_mark(N)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
<Marked_mark(x(X1,X2)) , Marked_mark(X1)>
<Marked_mark(x(X1,X2)) , Marked_mark(X2)>
<Marked_mark(s(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(s(X)) , Marked_mark(X)> 
      --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,s(M)) , Marked_mark(N)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,s(M)) , Marked_mark(M)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,s(M)) , Marked_mark(N)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(M)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_mark(N)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__x(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,s(M)) , Marked_mark(N)>
  <Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,s(M)) , Marked_mark(M)>
  <Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,s(M)) , Marked_mark(N)>
  <Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))>
  <Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
  <Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(M)>
  <Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(N)>
  <Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
  <Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,0) , Marked_mark(N)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(M)>
  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(N)>
  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,0) , Marked_mark(N)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(mark(X)) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__plus(N,0) >= mark(N) ;
  a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M))) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__x(N,0) >= 0 ;
  a__x(N,s(M)) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  Marked_a__x(N,s(M)) >= Marked_a__x(mark(N),mark(M)) ;
  Marked_a__x(N,s(M)) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  Marked_a__x(N,s(M)) >= Marked_mark(N) ;
  Marked_a__x(N,s(M)) >= Marked_mark(M) ;
  Marked_a__plus(N,0) >= Marked_mark(N) ;
  Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M)) ;
  Marked_a__plus(N,s(M)) >= Marked_mark(N) ;
  Marked_a__plus(N,s(M)) >= Marked_mark(M) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(x(X1,X2)) >= Marked_a__x(mark(X1),mark(X2)) ;
  Marked_mark(x(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(x(X1,X2)) >= Marked_mark(X2) ;
 }
 + Disjunctions:{ 
{
  Marked_a__x(N,s(M)) > Marked_a__x(mark(N),mark(M)) ;
 }
{
  Marked_a__x(N,s(M)) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ;
 }
{
  Marked_a__x(N,s(M)) > Marked_mark(N) ;
 }
{
  Marked_a__x(N,s(M)) > Marked_mark(M) ;
 }
{
  Marked_a__plus(N,0) > Marked_mark(N) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_a__plus(mark(N),mark(M)) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_mark(N) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_mark(M) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(x(X1,X2)) > Marked_a__x(mark(X1),mark(X2)) ;
 }
{
  Marked_mark(x(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(x(X1,X2)) > Marked_mark(X2) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__plus(N,0) >= mark(N)
constraint: a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M)))
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__x(N,0) >= 0
constraint: a__x(N,s(M)) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: Marked_a__x(N,s(M)) >= Marked_a__x(mark(N),mark(M))
constraint: Marked_a__x(N,s(M)) >= Marked_a__plus(a__x(mark(N),mark(M)),
                                    mark(N))
constraint: Marked_a__x(N,s(M)) >= Marked_mark(N)
constraint: Marked_a__x(N,s(M)) >= Marked_mark(M)
constraint: Marked_a__plus(N,0) >= Marked_mark(N)
constraint: Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M))
constraint: Marked_a__plus(N,s(M)) >= Marked_mark(N)
constraint: Marked_a__plus(N,s(M)) >= Marked_mark(M)
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2))
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(x(X1,X2)) >= Marked_a__x(mark(X1),mark(X2))
constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__and(tt,X) -> mark(X)
[2] a__plus(N,0) -> mark(N)
[3] a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
[4] a__x(N,0) -> 0
[5] a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
[6] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[7] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[8] mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
[9] mark(tt) -> tt
[10] mark(0) -> 0
[11] mark(s(X)) -> s(mark(X))
[12] a__and(X1,X2) -> and(X1,X2)
[13] a__plus(X1,X2) -> plus(X1,X2)
[14] a__x(X1,X2) -> x(X1,X2)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__plus(N,s(M)) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_mark(M)>
<Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
<Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))>
<Marked_a__x(N,s(M)) , Marked_mark(N)>
<Marked_a__x(N,s(M)) , Marked_mark(M)>
<Marked_a__x(N,s(M)) , Marked_mark(N)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
<Marked_mark(x(X1,X2)) , Marked_mark(X1)>
<Marked_mark(x(X1,X2)) , Marked_mark(X2)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__plus(N,s(M)) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_mark(M)>
<Marked_a__x(N,s(M)) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
<Marked_a__x(N,s(M)) , Marked_a__x(mark(N),mark(M))>
<Marked_a__x(N,s(M)) , Marked_mark(N)>
<Marked_a__x(N,s(M)) , Marked_mark(M)>
<Marked_a__x(N,s(M)) , Marked_mark(N)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
<Marked_mark(x(X1,X2)) , Marked_mark(X1)>
<Marked_mark(x(X1,X2)) , Marked_mark(X2)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using RPO with AFS = AFS: mark -> 0Marked_mark -> 0
and precedence:
prec (All symbols are Lex.): { a__and  =  and ; a__and  >  Marked_a__and ;
                              a__plus  >  s ; a__plus  <  a__x ;
                              a__plus  =  plus ; a__plus  <  x ;
                              a__plus  <  Marked_a__x ;
                              a__plus  >  Marked_a__plus ; s  <  a__plus ;
                              s  <  a__x ; s  <  plus ; s  <  x ;
                              s  <  Marked_a__x ; a__x  >  a__plus ;
                              a__x  >  s ; a__x  >  plus ; a__x  =  x ;
                              a__x  =  Marked_a__x ; a__x  >  Marked_a__plus ;
                              and  =  a__and ; and  >  Marked_a__and ;
                              plus  =  a__plus ; plus  >  s ; plus  <  a__x ;
                              plus  <  x ; plus  <  Marked_a__x ;
                              plus  >  Marked_a__plus ; x  >  a__plus ;
                              x  >  s ; x  =  a__x ; x  >  plus ;
                              x  =  Marked_a__x ; x  >  Marked_a__plus ;
                              Marked_a__x  >  a__plus ; Marked_a__x  >  s ;
                              Marked_a__x  =  a__x ; Marked_a__x  >  plus ;
                              Marked_a__x  =  x ;
                              Marked_a__x  >  Marked_a__plus ;
                              Marked_a__plus  <  a__plus ;
                              Marked_a__plus  <  a__x ;
                              Marked_a__plus  <  plus ; Marked_a__plus  <  x ;
                              Marked_a__plus  <  Marked_a__x ;
                              Marked_a__and  <  a__and ;
                              Marked_a__and  <  and ; }

 removing <Marked_a__and(tt,X),Marked_mark(X)><Marked_a__plus(N,0),Marked_mark(
                                                                    N)><
Marked_a__plus(N,s(M)),Marked_a__plus(mark(N),mark(M))><Marked_a__plus(N,s(M)),
Marked_mark(N)><Marked_a__plus(N,s(M)),Marked_mark(M)><Marked_a__x(N,s(M)),
Marked_a__plus(a__x(mark(N),mark(M)),mark(N))><Marked_a__x(N,s(M)),Marked_a__x(
                                                                    mark(
                                                                    N),
                                                                    mark(M))><
Marked_a__x(N,s(M)),Marked_mark(N)><Marked_a__x(N,s(M)),Marked_mark(M)><
Marked_a__x(N,s(M)),Marked_mark(N)><Marked_mark(and(X1,X2)),Marked_a__and(
                                                             mark(X1),
                                                             X2)><Marked_mark(
                                                                   and(
                                                                    X1,
                                                                    X2)),
Marked_mark(X1)><Marked_mark(plus(X1,X2)),Marked_a__plus(mark(X1),mark(X2))><
Marked_mark(plus(X1,X2)),Marked_mark(X1)><Marked_mark(plus(X1,X2)),Marked_mark(
                                                                    X2)><
Marked_mark(x(X1,X2)),Marked_mark(X1)><Marked_mark(x(X1,X2)),Marked_mark(X2)><
Marked_mark(s(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.191291 seconds (real time)
Cime Exit Status: 0