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

TRS termination of:
[1] a__U11(tt,N) -> mark(N)
[2] a__U21(tt,M,N) -> s(a__plus(mark(N),mark(M)))
[3] a__U31(tt) -> 0
[4] a__U41(tt,M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
[5] a__and(tt,X) -> mark(X)
[6] a__isNat(0) -> tt
[7] a__isNat(plus(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
[8] a__isNat(s(V1)) -> a__isNat(V1)
[9] a__isNat(x(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
[10] a__plus(N,0) -> a__U11(a__isNat(N),N)
[11] a__plus(N,s(M)) -> a__U21(a__and(a__isNat(M),isNat(N)),M,N)
[12] a__x(N,0) -> a__U31(a__isNat(N))
[13] a__x(N,s(M)) -> a__U41(a__and(a__isNat(M),isNat(N)),M,N)
[14] mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
[15] mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
[16] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[17] mark(U31(X)) -> a__U31(mark(X))
[18] mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
[19] mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
[20] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[21] mark(isNat(X)) -> a__isNat(X)
[22] mark(tt) -> tt
[23] mark(s(X)) -> s(mark(X))
[24] mark(0) -> 0
[25] a__U11(X1,X2) -> U11(X1,X2)
[26] a__U21(X1,X2,X3) -> U21(X1,X2,X3)
[27] a__plus(X1,X2) -> plus(X1,X2)
[28] a__U31(X) -> U31(X)
[29] a__U41(X1,X2,X3) -> U41(X1,X2,X3)
[30] a__x(X1,X2) -> x(X1,X2)
[31] a__and(X1,X2) -> and(X1,X2)
[32] a__isNat(X) -> isNat(X)


Sub problem: 
guided: 

DP termination of:
<Marked_a__U11(tt,N) , Marked_mark(N)>
<Marked_a__U21(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__U21(tt,M,N) , Marked_mark(N)>
<Marked_a__U21(tt,M,N) , Marked_mark(M)>
<Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
<Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))>
<Marked_a__U41(tt,M,N) , Marked_mark(N)>
<Marked_a__U41(tt,M,N) , Marked_mark(M)>
<Marked_a__U41(tt,M,N) , Marked_mark(N)>
<Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
<Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
<Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
<Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
<Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
<Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
<Marked_a__plus(N,0) , Marked_a__isNat(N)>
<Marked_a__plus(N,s(M)) , Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N)>
<Marked_a__plus(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))>
<Marked_a__plus(N,s(M)) , Marked_a__isNat(M)>
<Marked_a__x(N,0) , Marked_a__U31(a__isNat(N))>
<Marked_a__x(N,0) , Marked_a__isNat(N)>
<Marked_a__x(N,s(M)) , Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N)>
<Marked_a__x(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))>
<Marked_a__x(N,s(M)) , Marked_a__isNat(M)>
<Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
<Marked_mark(U21(X1,X2,X3)) , 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(U31(X)) , Marked_a__U31(mark(X))>
<Marked_mark(U31(X)) , Marked_mark(X)>
<Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
<Marked_mark(U41(X1,X2,X3)) , 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(x(X1,X2)) , Marked_mark(X2)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_a__isNat(X)>
<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(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <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(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,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(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(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(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__isNat(M)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,0) , Marked_a__isNat(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(M)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <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(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(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(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__isNat(M)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__U21(a__and(a__isNat(M),isNat(N)),
                                    M,N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)> 
     --> <Marked_a__U21(tt,M,N) , Marked_mark(M)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)> 
     --> <Marked_a__U21(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)> 
     --> <Marked_a__U21(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__x(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__x(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__x(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__x(N,s(M)) , Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(N)>
  <Marked_a__x(N,s(M)) , Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(M)>
  <Marked_a__x(N,s(M)) , Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(N)>
  <Marked_a__x(N,s(M)) , Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))>
  <Marked_a__x(N,s(M)) , Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,s(M)) , Marked_a__isNat(M)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__plus(N,s(M)) , Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N)> 
     --> <Marked_a__U21(tt,M,N) , Marked_mark(M)>
  <Marked_a__plus(N,s(M)) , Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N)> 
     --> <Marked_a__U21(tt,M,N) , Marked_mark(N)>
  <Marked_a__plus(N,s(M)) , Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N)> 
     --> <Marked_a__U21(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <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(isNat(X)) , Marked_a__isNat(X)>
  <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)>
  <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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__isNat(M)>
  <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))>
  <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,s(M)) , Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N)>
  <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,0) , Marked_a__isNat(N)>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__isNat(M)>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__U21(a__and(a__isNat(M),isNat(N)),
                                    M,N)>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U21(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U21(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__isNat(M)>
  <Marked_a__U21(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__and(a__isNat(M),isNat(N))>
  <Marked_a__U21(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__U21(a__and(a__isNat(M),isNat(N)),
                                    M,N)>
  <Marked_a__U21(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_a__U21(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_a__U21(mark(X1),X2,X3)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_a__x(N,s(M)) >= Marked_a__isNat(M) ;
  Marked_a__x(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N)) ;
  Marked_a__x(N,s(M)) >= Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  Marked_a__x(N,0) >= Marked_a__isNat(N) ;
  Marked_a__U41(tt,M,N) >= Marked_a__x(mark(N),mark(M)) ;
  Marked_a__U41(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  Marked_a__U41(tt,M,N) >= Marked_mark(N) ;
  Marked_a__U41(tt,M,N) >= Marked_mark(M) ;
  Marked_a__plus(N,s(M)) >= Marked_a__isNat(M) ;
  Marked_a__plus(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N)) ;
  Marked_a__plus(N,s(M)) >= Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  Marked_a__plus(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U21(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ;
  Marked_a__U21(tt,M,N) >= Marked_mark(N) ;
  Marked_a__U21(tt,M,N) >= Marked_mark(M) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(isNat(X)) >= Marked_a__isNat(X) ;
  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(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_a__U21(mark(X1),X2,X3) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(U31(X)) >= Marked_mark(X) ;
  Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3) ;
  Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_a__x(N,s(M)) > Marked_a__isNat(M) ;
 }
{
  Marked_a__x(N,s(M)) > Marked_a__and(a__isNat(M),isNat(N)) ;
 }
{
  Marked_a__x(N,s(M)) > Marked_a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
 }
{
  Marked_a__x(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_a__x(mark(N),mark(M)) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_mark(N) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_mark(M) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_a__isNat(M) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_a__and(a__isNat(M),isNat(N)) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U21(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ;
 }
{
  Marked_a__U21(tt,M,N) > Marked_mark(N) ;
 }
{
  Marked_a__U21(tt,M,N) > Marked_mark(M) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(isNat(X)) > Marked_a__isNat(X) ;
 }
{
  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(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ;
 }
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_a__U21(mark(X1),X2,X3) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U31(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(U41(X1,X2,X3)) > Marked_a__U41(mark(X1),X2,X3) ;
 }
{
  Marked_mark(U41(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),
                                             isNat(V2))
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2))
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_a__x(N,s(M)) >= Marked_a__isNat(M)
constraint: Marked_a__x(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N))
constraint: Marked_a__x(N,s(M)) >= Marked_a__U41(a__and(a__isNat(M),isNat(N)),
                                    M,N)
constraint: Marked_a__x(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__U41(tt,M,N) >= Marked_a__x(mark(N),mark(M))
constraint: Marked_a__U41(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),
                                      mark(N))
constraint: Marked_a__U41(tt,M,N) >= Marked_mark(N)
constraint: Marked_a__U41(tt,M,N) >= Marked_mark(M)
constraint: Marked_a__plus(N,s(M)) >= Marked_a__isNat(M)
constraint: Marked_a__plus(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N))
constraint: Marked_a__plus(N,s(M)) >= Marked_a__U21(a__and(a__isNat(M),
                                                     isNat(N)),M,N)
constraint: Marked_a__plus(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U21(tt,M,N) >= Marked_a__plus(mark(N),mark(M))
constraint: Marked_a__U21(tt,M,N) >= Marked_mark(N)
constraint: Marked_a__U21(tt,M,N) >= Marked_mark(M)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X)
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)
constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_a__U21(mark(X1),X2,X3)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(U31(X)) >= Marked_mark(X)
constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3)
constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
      --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,0) , Marked_a__isNat(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(M)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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)>
  <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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,0) , Marked_a__isNat(N)>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X)) , Marked_mark(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_a__x(N,0) >= Marked_a__isNat(N) ;
  Marked_a__U41(tt,M,N) >= Marked_a__x(mark(N),mark(M)) ;
  Marked_a__U41(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  Marked_a__U41(tt,M,N) >= Marked_mark(N) ;
  Marked_a__U41(tt,M,N) >= Marked_mark(M) ;
  Marked_a__plus(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  Marked_mark(isNat(X)) >= Marked_a__isNat(X) ;
  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(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U31(X)) >= Marked_mark(X) ;
  Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3) ;
  Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_a__x(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_a__x(mark(N),mark(M)) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_mark(N) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_mark(M) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  Marked_mark(isNat(X)) > Marked_a__isNat(X) ;
 }
{
  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(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ;
 }
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U31(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(U41(X1,X2,X3)) > Marked_a__U41(mark(X1),X2,X3) ;
 }
{
  Marked_mark(U41(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),
                                             isNat(V2))
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2))
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_a__x(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__U41(tt,M,N) >= Marked_a__x(mark(N),mark(M))
constraint: Marked_a__U41(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),
                                      mark(N))
constraint: Marked_a__U41(tt,M,N) >= Marked_mark(N)
constraint: Marked_a__U41(tt,M,N) >= Marked_mark(M)
constraint: Marked_a__plus(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X)
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)
constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U31(X)) >= Marked_mark(X)
constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3)
constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
      --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,0) , Marked_a__isNat(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(M)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))>
  <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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)>
  <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(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U41(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U41(tt,M,N) , Marked_a__x(mark(N),mark(M))> 
     --> <Marked_a__x(N,0) , Marked_a__isNat(N)>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_a__U41(tt,M,N) , Marked_a__plus(a__x(mark(N),mark(M)),mark(N))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_a__x(N,0) >= Marked_a__isNat(N) ;
  Marked_a__U41(tt,M,N) >= Marked_a__x(mark(N),mark(M)) ;
  Marked_a__U41(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  Marked_a__U41(tt,M,N) >= Marked_mark(N) ;
  Marked_a__U41(tt,M,N) >= Marked_mark(M) ;
  Marked_a__plus(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  Marked_mark(isNat(X)) >= Marked_a__isNat(X) ;
  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(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3) ;
  Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_a__x(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_a__x(mark(N),mark(M)) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_mark(N) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_mark(M) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  Marked_mark(isNat(X)) > Marked_a__isNat(X) ;
 }
{
  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(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ;
 }
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U41(X1,X2,X3)) > Marked_a__U41(mark(X1),X2,X3) ;
 }
{
  Marked_mark(U41(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),
                                             isNat(V2))
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2))
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_a__x(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__U41(tt,M,N) >= Marked_a__x(mark(N),mark(M))
constraint: Marked_a__U41(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),
                                      mark(N))
constraint: Marked_a__U41(tt,M,N) >= Marked_mark(N)
constraint: Marked_a__U41(tt,M,N) >= Marked_mark(M)
constraint: Marked_a__plus(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X)
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)
constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_a__U41(mark(X1),X2,X3)
constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
      --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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)>
  <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(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_a__U11(mark(X1),X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_a__x(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  Marked_mark(isNat(X)) >= Marked_a__isNat(X) ;
  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(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_a__x(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  Marked_mark(isNat(X)) > Marked_a__isNat(X) ;
 }
{
  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(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ;
 }
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),
                                             isNat(V2))
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2))
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_a__x(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X)
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)
constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
      --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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_a__x(mark(X1),mark(X2))> 
     --> <Marked_a__x(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__x(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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)>
  <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__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_a__x(mark(X1),mark(X2))>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_a__x(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  Marked_mark(isNat(X)) >= Marked_a__isNat(X) ;
  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(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_a__x(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  Marked_mark(isNat(X)) > Marked_a__isNat(X) ;
 }
{
  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(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),
                                             isNat(V2))
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2))
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_a__x(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X)
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)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
      --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(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_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(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(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(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(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(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(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(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_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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)>
  <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(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__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_a__plus(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  Marked_mark(isNat(X)) >= Marked_a__isNat(X) ;
  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(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  Marked_mark(isNat(X)) > Marked_a__isNat(X) ;
 }
{
  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(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),
                                             isNat(V2))
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2))
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_a__plus(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X)
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_mark(X1)
constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
      --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_mark(isNat(X)) , Marked_a__isNat(X)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(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_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_mark(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(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(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(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(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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(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(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(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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_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(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_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__isNat(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__plus(N,0) , Marked_a__isNat(N)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__and(a__isNat(V1),isNat(V2))> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <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)>
  <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(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__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_a__isNat(X)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_a__plus(N,0) >= Marked_a__isNat(N) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  Marked_mark(isNat(X)) >= Marked_a__isNat(X) ;
  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(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__isNat(N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  Marked_mark(isNat(X)) > Marked_a__isNat(X) ;
 }
{
  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(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),
                                             isNat(V2))
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2))
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_a__plus(N,0) >= Marked_a__isNat(N)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X)
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_mark(X1)
constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <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(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(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(x(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <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(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(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <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(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(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <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(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(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <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(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_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(x(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
}

{  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
      --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(x(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  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(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  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(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
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_mark(X1)
constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
  Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
{
  Marked_a__isNat(x(V1,V2)) > Marked_a__isNat(V1) ;
 }
 } 
=== 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(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1)
constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__isNat(V1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <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(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(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <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(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <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_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)>
  <Marked_a__plus(N,0) , Marked_a__U11(a__isNat(N),N)> 
     --> <Marked_a__U11(tt,N) , Marked_mark(N)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U11(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ;
  Marked_a__U11(tt,N) >= Marked_mark(N) ;
  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(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ;
 }
{
  Marked_a__U11(tt,N) > Marked_mark(N) ;
 }
{
  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(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N)
constraint: Marked_a__U11(tt,N) >= Marked_mark(N)
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(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <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(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(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(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(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <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)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
      --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(and(X1,X2)) > 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
=== 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 ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3)
constraint: mark(U31(X)) >= a__U31(mark(X))
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: a__U11(tt,N) >= mark(N)
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__plus(N,0) >= a__U11(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3)
constraint: a__U31(tt) >= 0
constraint: a__U31(X) >= U31(X)
constraint: a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N)
constraint: a__x(N,0) >= a__U31(a__isNat(N))
constraint: a__x(X1,X2) >= x(X1,X2)
constraint: a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N))
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNat(s(V1)) >= a__isNat(V1)
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2))
constraint: a__isNat(X) >= isNat(X)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)> 
      --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ;
  mark(U31(X)) >= a__U31(mark(X)) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  a__U11(tt,N) >= mark(N) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__plus(N,0) >= a__U11(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U21(X1,X2,X3) >= U21(X1,X2,X3) ;
  a__U31(tt) >= 0 ;
  a__U31(X) >= U31(X) ;
  a__x(N,s(M)) >= a__U41(a__and(a__isNat(M),isNat(N)),M,N) ;
  a__x(N,0) >= a__U31(a__isNat(N)) ;
  a__x(X1,X2) >= x(X1,X2) ;
  a__U41(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNat(s(V1)) >= a__isNat(V1) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(x(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ;
  a__isNat(X) >= isNat(X) ;
  Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ;
 }
 } 
=== 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.. 

Global timeout: 300.000000