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

TRS termination of:
[1] a__U11(tt,V2) -> a__U12(a__isNat(V2))
[2] a__U12(tt) -> tt
[3] a__U21(tt) -> tt
[4] a__U31(tt,N) -> mark(N)
[5] a__U41(tt,M,N) -> a__U42(a__isNat(N),M,N)
[6] a__U42(tt,M,N) -> s(a__plus(mark(N),mark(M)))
[7] a__isNat(0) -> tt
[8] a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2)
[9] a__isNat(s(V1)) -> a__U21(a__isNat(V1))
[10] a__plus(N,0) -> a__U31(a__isNat(N),N)
[11] a__plus(N,s(M)) -> a__U41(a__isNat(M),M,N)
[12] mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
[13] mark(U12(X)) -> a__U12(mark(X))
[14] mark(isNat(X)) -> a__isNat(X)
[15] mark(U21(X)) -> a__U21(mark(X))
[16] mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
[17] mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
[18] mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3)
[19] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[20] mark(tt) -> tt
[21] mark(s(X)) -> s(mark(X))
[22] mark(0) -> 0
[23] a__U11(X1,X2) -> U11(X1,X2)
[24] a__U12(X) -> U12(X)
[25] a__isNat(X) -> isNat(X)
[26] a__U21(X) -> U21(X)
[27] a__U31(X1,X2) -> U31(X1,X2)
[28] a__U41(X1,X2,X3) -> U41(X1,X2,X3)
[29] a__U42(X1,X2,X3) -> U42(X1,X2,X3)
[30] a__plus(X1,X2) -> plus(X1,X2)


Sub problem: 
guided: 

DP termination of:
<Marked_a__U11(tt,V2) , Marked_a__U12(a__isNat(V2))>
<Marked_a__U11(tt,V2) , Marked_a__isNat(V2)>
<Marked_a__U31(tt,N) , Marked_mark(N)>
<Marked_a__U41(tt,M,N) , Marked_a__U42(a__isNat(N),M,N)>
<Marked_a__U41(tt,M,N) , Marked_a__isNat(N)>
<Marked_a__U42(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__U42(tt,M,N) , Marked_mark(N)>
<Marked_a__U42(tt,M,N) , Marked_mark(M)>
<Marked_a__isNat(plus(V1,V2)) , Marked_a__U11(a__isNat(V1),V2)>
<Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
<Marked_a__isNat(s(V1)) , Marked_a__U21(a__isNat(V1))>
<Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
<Marked_a__plus(N,0) , Marked_a__U31(a__isNat(N),N)>
<Marked_a__plus(N,0) , Marked_a__isNat(N)>
<Marked_a__plus(N,s(M)) , Marked_a__U41(a__isNat(M),M,N)>
<Marked_a__plus(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(U12(X)) , Marked_a__U12(mark(X))>
<Marked_mark(U12(X)) , Marked_mark(X)>
<Marked_mark(isNat(X)) , Marked_a__isNat(X)>
<Marked_mark(U21(X)) , Marked_a__U21(mark(X))>
<Marked_mark(U21(X)) , Marked_mark(X)>
<Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
<Marked_mark(U31(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(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
<Marked_mark(U42(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(s(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_mark(s(X)) , Marked_mark(X)> 
      --> <Marked_mark(s(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(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <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(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <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(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(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <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(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <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(s(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(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <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(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <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_a__plus(N,s(M)) , Marked_a__U41(a__isNat(M),M,N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_a__U31(a__isNat(N),N)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)> 
     --> <Marked_a__U42(tt,M,N) , Marked_mark(M)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)> 
     --> <Marked_a__U42(tt,M,N) , Marked_mark(N)>
  <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)> 
     --> <Marked_a__U42(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
  <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(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(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <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(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <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_a__U41(tt,M,N) , Marked_a__U42(a__isNat(N),M,N)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U31(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)> 
     --> <Marked_a__U31(tt,N) , Marked_mark(N)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <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(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(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <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(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_a__U41(a__isNat(M),M,N)> 
     --> <Marked_a__U41(tt,M,N) , Marked_a__U42(a__isNat(N),M,N)>
  <Marked_a__plus(N,0) , Marked_a__U31(a__isNat(N),N)> 
     --> <Marked_a__U31(tt,N) , Marked_mark(N)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_a__U42(tt,M,N) , Marked_mark(M)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_a__U42(tt,M,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U42(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__U41(a__isNat(M),M,N)>
  <Marked_a__U42(tt,M,N) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,0) , Marked_a__U31(a__isNat(N),N)>
  <Marked_a__U41(tt,M,N) , Marked_a__U42(a__isNat(N),M,N)> 
     --> <Marked_a__U42(tt,M,N) , Marked_mark(M)>
  <Marked_a__U41(tt,M,N) , Marked_a__U42(a__isNat(N),M,N)> 
     --> <Marked_a__U42(tt,M,N) , Marked_mark(N)>
  <Marked_a__U41(tt,M,N) , Marked_a__U42(a__isNat(N),M,N)> 
     --> <Marked_a__U42(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U41(X1,X2,X3)) , Marked_a__U41(mark(X1),X2,X3)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_mark(X1)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_a__U31(tt,N) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
}

{  <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__U11(a__isNat(V1),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__U11(a__isNat(V1),V2)>
  <Marked_a__isNat(plus(V1,V2)) , Marked_a__U11(a__isNat(V1),V2)> 
     --> <Marked_a__U11(tt,V2) , Marked_a__isNat(V2)>
  <Marked_a__U11(tt,V2) , Marked_a__isNat(V2)> 
     --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
  <Marked_a__U11(tt,V2) , Marked_a__isNat(V2)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
  <Marked_a__U11(tt,V2) , Marked_a__isNat(V2)> 
     --> <Marked_a__isNat(plus(V1,V2)) , Marked_a__U11(a__isNat(V1),V2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__U12(tt) >= tt ;
  a__U12(X) >= U12(X) ;
  a__isNat(s(V1)) >= a__U21(a__isNat(V1)) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2) ;
  a__isNat(X) >= isNat(X) ;
  a__U11(tt,V2) >= a__U12(a__isNat(V2)) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__U21(tt) >= tt ;
  a__U21(X) >= U21(X) ;
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U12(X)) >= a__U12(mark(X)) ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(U21(X)) >= a__U21(mark(X)) ;
  mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3) ;
  a__U31(tt,N) >= mark(N) ;
  a__U31(X1,X2) >= U31(X1,X2) ;
  a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U42(X1,X2,X3) >= U42(X1,X2,X3) ;
  a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N) ;
  a__plus(N,0) >= a__U31(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  Marked_a__plus(N,s(M)) >= Marked_a__U41(a__isNat(M),M,N) ;
  Marked_a__plus(N,0) >= Marked_a__U31(a__isNat(N),N) ;
  Marked_a__U42(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ;
  Marked_a__U42(tt,M,N) >= Marked_mark(N) ;
  Marked_a__U42(tt,M,N) >= Marked_mark(M) ;
  Marked_a__U41(tt,M,N) >= Marked_a__U42(a__isNat(N),M,N) ;
  Marked_a__U31(tt,N) >= Marked_mark(N) ;
  Marked_mark(s(X)) >= Marked_mark(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(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U12(X)) >= Marked_mark(X) ;
  Marked_mark(U21(X)) >= Marked_mark(X) ;
  Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2) ;
  Marked_mark(U31(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(U42(X1,X2,X3)) >= Marked_a__U42(mark(X1),X2,X3) ;
  Marked_mark(U42(X1,X2,X3)) >= Marked_mark(X1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__plus(N,s(M)) > Marked_a__U41(a__isNat(M),M,N) ;
 }
{
  Marked_a__plus(N,0) > Marked_a__U31(a__isNat(N),N) ;
 }
{
  Marked_a__U42(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ;
 }
{
  Marked_a__U42(tt,M,N) > Marked_mark(N) ;
 }
{
  Marked_a__U42(tt,M,N) > Marked_mark(M) ;
 }
{
  Marked_a__U41(tt,M,N) > Marked_a__U42(a__isNat(N),M,N) ;
 }
{
  Marked_a__U31(tt,N) > Marked_mark(N) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(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(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U12(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(U21(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(U31(X1,X2)) > Marked_a__U31(mark(X1),X2) ;
 }
{
  Marked_mark(U31(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(U42(X1,X2,X3)) > Marked_a__U42(mark(X1),X2,X3) ;
 }
{
  Marked_mark(U42(X1,X2,X3)) > Marked_mark(X1) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__U12(tt) >= tt
constraint: a__U12(X) >= U12(X)
constraint: a__isNat(s(V1)) >= a__U21(a__isNat(V1))
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2)
constraint: a__isNat(X) >= isNat(X)
constraint: a__U11(tt,V2) >= a__U12(a__isNat(V2))
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__U21(tt) >= tt
constraint: a__U21(X) >= U21(X)
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U12(X)) >= a__U12(mark(X))
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(U21(X)) >= a__U21(mark(X))
constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2)
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3)
constraint: a__U31(tt,N) >= mark(N)
constraint: a__U31(X1,X2) >= U31(X1,X2)
constraint: a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U42(X1,X2,X3) >= U42(X1,X2,X3)
constraint: a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N)
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N)
constraint: a__plus(N,0) >= a__U31(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: Marked_a__plus(N,s(M)) >= Marked_a__U41(a__isNat(M),M,N)
constraint: Marked_a__plus(N,0) >= Marked_a__U31(a__isNat(N),N)
constraint: Marked_a__U42(tt,M,N) >= Marked_a__plus(mark(N),mark(M))
constraint: Marked_a__U42(tt,M,N) >= Marked_mark(N)
constraint: Marked_a__U42(tt,M,N) >= Marked_mark(M)
constraint: Marked_a__U41(tt,M,N) >= Marked_a__U42(a__isNat(N),M,N)
constraint: Marked_a__U31(tt,N) >= Marked_mark(N)
constraint: Marked_mark(s(X)) >= Marked_mark(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(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U12(X)) >= Marked_mark(X)
constraint: Marked_mark(U21(X)) >= Marked_mark(X)
constraint: Marked_mark(U31(X1,X2)) >= Marked_a__U31(mark(X1),X2)
constraint: Marked_mark(U31(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(U42(X1,X2,X3)) >= Marked_a__U42(mark(X1),X2,X3)
constraint: Marked_mark(U42(X1,X2,X3)) >= Marked_mark(X1)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__U12(tt) >= tt ;
  a__U12(X) >= U12(X) ;
  a__isNat(s(V1)) >= a__U21(a__isNat(V1)) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2) ;
  a__isNat(X) >= isNat(X) ;
  a__U11(tt,V2) >= a__U12(a__isNat(V2)) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__U21(tt) >= tt ;
  a__U21(X) >= U21(X) ;
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U12(X)) >= a__U12(mark(X)) ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(U21(X)) >= a__U21(mark(X)) ;
  mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3) ;
  a__U31(tt,N) >= mark(N) ;
  a__U31(X1,X2) >= U31(X1,X2) ;
  a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U42(X1,X2,X3) >= U42(X1,X2,X3) ;
  a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N) ;
  a__plus(N,0) >= a__U31(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  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__U11(a__isNat(V1),V2) ;
  Marked_a__U11(tt,V2) >= Marked_a__isNat(V2) ;
 }
 + 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__U11(a__isNat(V1),V2) ;
 }
{
  Marked_a__U11(tt,V2) > Marked_a__isNat(V2) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__U12(tt) >= tt
constraint: a__U12(X) >= U12(X)
constraint: a__isNat(s(V1)) >= a__U21(a__isNat(V1))
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2)
constraint: a__isNat(X) >= isNat(X)
constraint: a__U11(tt,V2) >= a__U12(a__isNat(V2))
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__U21(tt) >= tt
constraint: a__U21(X) >= U21(X)
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U12(X)) >= a__U12(mark(X))
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(U21(X)) >= a__U21(mark(X))
constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2)
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3)
constraint: a__U31(tt,N) >= mark(N)
constraint: a__U31(X1,X2) >= U31(X1,X2)
constraint: a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U42(X1,X2,X3) >= U42(X1,X2,X3)
constraint: a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N)
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N)
constraint: a__plus(N,0) >= a__U31(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
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__U11(a__isNat(V1),V2)
constraint: Marked_a__U11(tt,V2) >= Marked_a__isNat(V2)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <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(U21(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <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(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(U21(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <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(U21(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__U12(tt) >= tt ;
  a__U12(X) >= U12(X) ;
  a__isNat(s(V1)) >= a__U21(a__isNat(V1)) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2) ;
  a__isNat(X) >= isNat(X) ;
  a__U11(tt,V2) >= a__U12(a__isNat(V2)) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__U21(tt) >= tt ;
  a__U21(X) >= U21(X) ;
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U12(X)) >= a__U12(mark(X)) ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(U21(X)) >= a__U21(mark(X)) ;
  mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3) ;
  a__U31(tt,N) >= mark(N) ;
  a__U31(X1,X2) >= U31(X1,X2) ;
  a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U42(X1,X2,X3) >= U42(X1,X2,X3) ;
  a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N) ;
  a__plus(N,0) >= a__U31(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U12(X)) >= Marked_mark(X) ;
  Marked_mark(U21(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U12(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(U21(X)) > Marked_mark(X) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__U12(tt) >= tt
constraint: a__U12(X) >= U12(X)
constraint: a__isNat(s(V1)) >= a__U21(a__isNat(V1))
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2)
constraint: a__isNat(X) >= isNat(X)
constraint: a__U11(tt,V2) >= a__U12(a__isNat(V2))
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__U21(tt) >= tt
constraint: a__U21(X) >= U21(X)
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U12(X)) >= a__U12(mark(X))
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(U21(X)) >= a__U21(mark(X))
constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2)
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3)
constraint: a__U31(tt,N) >= mark(N)
constraint: a__U31(X1,X2) >= U31(X1,X2)
constraint: a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U42(X1,X2,X3) >= U42(X1,X2,X3)
constraint: a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N)
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N)
constraint: a__plus(N,0) >= a__U31(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U12(X)) >= Marked_mark(X)
constraint: Marked_mark(U21(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(U21(X)) , Marked_mark(X)> 
      --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U21(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U12(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U12(X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__U12(tt) >= tt ;
  a__U12(X) >= U12(X) ;
  a__isNat(s(V1)) >= a__U21(a__isNat(V1)) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2) ;
  a__isNat(X) >= isNat(X) ;
  a__U11(tt,V2) >= a__U12(a__isNat(V2)) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__U21(tt) >= tt ;
  a__U21(X) >= U21(X) ;
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U12(X)) >= a__U12(mark(X)) ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(U21(X)) >= a__U21(mark(X)) ;
  mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3) ;
  a__U31(tt,N) >= mark(N) ;
  a__U31(X1,X2) >= U31(X1,X2) ;
  a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U42(X1,X2,X3) >= U42(X1,X2,X3) ;
  a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N) ;
  a__plus(N,0) >= a__U31(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U12(X)) >= Marked_mark(X) ;
  Marked_mark(U21(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U12(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(U21(X)) > Marked_mark(X) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__U12(tt) >= tt
constraint: a__U12(X) >= U12(X)
constraint: a__isNat(s(V1)) >= a__U21(a__isNat(V1))
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2)
constraint: a__isNat(X) >= isNat(X)
constraint: a__U11(tt,V2) >= a__U12(a__isNat(V2))
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__U21(tt) >= tt
constraint: a__U21(X) >= U21(X)
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U12(X)) >= a__U12(mark(X))
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(U21(X)) >= a__U21(mark(X))
constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2)
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3)
constraint: a__U31(tt,N) >= mark(N)
constraint: a__U31(X1,X2) >= U31(X1,X2)
constraint: a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U42(X1,X2,X3) >= U42(X1,X2,X3)
constraint: a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N)
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N)
constraint: a__plus(N,0) >= a__U31(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U12(X)) >= Marked_mark(X)
constraint: Marked_mark(U21(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(U21(X)) , Marked_mark(X)> 
      --> <Marked_mark(U21(X)) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__U12(tt) >= tt ;
  a__U12(X) >= U12(X) ;
  a__isNat(s(V1)) >= a__U21(a__isNat(V1)) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2) ;
  a__isNat(X) >= isNat(X) ;
  a__U11(tt,V2) >= a__U12(a__isNat(V2)) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__U21(tt) >= tt ;
  a__U21(X) >= U21(X) ;
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U12(X)) >= a__U12(mark(X)) ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(U21(X)) >= a__U21(mark(X)) ;
  mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3) ;
  a__U31(tt,N) >= mark(N) ;
  a__U31(X1,X2) >= U31(X1,X2) ;
  a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U42(X1,X2,X3) >= U42(X1,X2,X3) ;
  a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N) ;
  a__plus(N,0) >= a__U31(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  Marked_mark(U21(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U21(X)) > Marked_mark(X) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__U12(tt) >= tt
constraint: a__U12(X) >= U12(X)
constraint: a__isNat(s(V1)) >= a__U21(a__isNat(V1))
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2)
constraint: a__isNat(X) >= isNat(X)
constraint: a__U11(tt,V2) >= a__U12(a__isNat(V2))
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__U21(tt) >= tt
constraint: a__U21(X) >= U21(X)
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U12(X)) >= a__U12(mark(X))
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(U21(X)) >= a__U21(mark(X))
constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2)
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3)
constraint: a__U31(tt,N) >= mark(N)
constraint: a__U31(X1,X2) >= U31(X1,X2)
constraint: a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U42(X1,X2,X3) >= U42(X1,X2,X3)
constraint: a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N)
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N)
constraint: a__plus(N,0) >= a__U31(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: Marked_mark(U21(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)> 
      --> <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__U12(tt) >= tt ;
  a__U12(X) >= U12(X) ;
  a__isNat(s(V1)) >= a__U21(a__isNat(V1)) ;
  a__isNat(0) >= tt ;
  a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2) ;
  a__isNat(X) >= isNat(X) ;
  a__U11(tt,V2) >= a__U12(a__isNat(V2)) ;
  a__U11(X1,X2) >= U11(X1,X2) ;
  a__U21(tt) >= tt ;
  a__U21(X) >= U21(X) ;
  mark(tt) >= tt ;
  mark(s(X)) >= s(mark(X)) ;
  mark(0) >= 0 ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ;
  mark(U12(X)) >= a__U12(mark(X)) ;
  mark(isNat(X)) >= a__isNat(X) ;
  mark(U21(X)) >= a__U21(mark(X)) ;
  mark(U31(X1,X2)) >= a__U31(mark(X1),X2) ;
  mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3) ;
  mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3) ;
  a__U31(tt,N) >= mark(N) ;
  a__U31(X1,X2) >= U31(X1,X2) ;
  a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M))) ;
  a__U42(X1,X2,X3) >= U42(X1,X2,X3) ;
  a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N) ;
  a__U41(X1,X2,X3) >= U41(X1,X2,X3) ;
  a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N) ;
  a__plus(N,0) >= a__U31(a__isNat(N),N) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ;
 }
 + Disjunctions:{ 
{
  Marked_a__isNat(s(V1)) > 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: a__U12(tt) >= tt
constraint: a__U12(X) >= U12(X)
constraint: a__isNat(s(V1)) >= a__U21(a__isNat(V1))
constraint: a__isNat(0) >= tt
constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNat(V1),V2)
constraint: a__isNat(X) >= isNat(X)
constraint: a__U11(tt,V2) >= a__U12(a__isNat(V2))
constraint: a__U11(X1,X2) >= U11(X1,X2)
constraint: a__U21(tt) >= tt
constraint: a__U21(X) >= U21(X)
constraint: mark(tt) >= tt
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(0) >= 0
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2)
constraint: mark(U12(X)) >= a__U12(mark(X))
constraint: mark(isNat(X)) >= a__isNat(X)
constraint: mark(U21(X)) >= a__U21(mark(X))
constraint: mark(U31(X1,X2)) >= a__U31(mark(X1),X2)
constraint: mark(U41(X1,X2,X3)) >= a__U41(mark(X1),X2,X3)
constraint: mark(U42(X1,X2,X3)) >= a__U42(mark(X1),X2,X3)
constraint: a__U31(tt,N) >= mark(N)
constraint: a__U31(X1,X2) >= U31(X1,X2)
constraint: a__U42(tt,M,N) >= s(a__plus(mark(N),mark(M)))
constraint: a__U42(X1,X2,X3) >= U42(X1,X2,X3)
constraint: a__U41(tt,M,N) >= a__U42(a__isNat(N),M,N)
constraint: a__U41(X1,X2,X3) >= U41(X1,X2,X3)
constraint: a__plus(N,s(M)) >= a__U41(a__isNat(M),M,N)
constraint: a__plus(N,0) >= a__U31(a__isNat(N),N)
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__U11(tt,V2) -> a__U12(a__isNat(V2))
[2] a__U12(tt) -> tt
[3] a__U21(tt) -> tt
[4] a__U31(tt,N) -> mark(N)
[5] a__U41(tt,M,N) -> a__U42(a__isNat(N),M,N)
[6] a__U42(tt,M,N) -> s(a__plus(mark(N),mark(M)))
[7] a__isNat(0) -> tt
[8] a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2)
[9] a__isNat(s(V1)) -> a__U21(a__isNat(V1))
[10] a__plus(N,0) -> a__U31(a__isNat(N),N)
[11] a__plus(N,s(M)) -> a__U41(a__isNat(M),M,N)
[12] mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
[13] mark(U12(X)) -> a__U12(mark(X))
[14] mark(isNat(X)) -> a__isNat(X)
[15] mark(U21(X)) -> a__U21(mark(X))
[16] mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
[17] mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
[18] mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3)
[19] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[20] mark(tt) -> tt
[21] mark(s(X)) -> s(mark(X))
[22] mark(0) -> 0
[23] a__U11(X1,X2) -> U11(X1,X2)
[24] a__U12(X) -> U12(X)
[25] a__isNat(X) -> isNat(X)
[26] a__U21(X) -> U21(X)
[27] a__U31(X1,X2) -> U31(X1,X2)
[28] a__U41(X1,X2,X3) -> U41(X1,X2,X3)
[29] a__U42(X1,X2,X3) -> U42(X1,X2,X3)
[30] a__plus(X1,X2) -> plus(X1,X2)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__U11(tt,V2) , Marked_a__U12(a__isNat(V2))>
<Marked_a__U11(tt,V2) , Marked_a__isNat(V2)>
<Marked_a__U31(tt,N) , Marked_mark(N)>
<Marked_a__U41(tt,M,N) , Marked_a__U42(a__isNat(N),M,N)>
<Marked_a__U41(tt,M,N) , Marked_a__isNat(N)>
<Marked_a__U42(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__U42(tt,M,N) , Marked_mark(N)>
<Marked_a__U42(tt,M,N) , Marked_mark(M)>
<Marked_a__isNat(plus(V1,V2)) , Marked_a__U11(a__isNat(V1),V2)>
<Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
<Marked_a__isNat(s(V1)) , Marked_a__U21(a__isNat(V1))>
<Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
<Marked_a__plus(N,0) , Marked_a__U31(a__isNat(N),N)>
<Marked_a__plus(N,0) , Marked_a__isNat(N)>
<Marked_a__plus(N,s(M)) , Marked_a__U41(a__isNat(M),M,N)>
<Marked_a__plus(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(U12(X)) , Marked_a__U12(mark(X))>
<Marked_mark(U12(X)) , Marked_mark(X)>
<Marked_mark(isNat(X)) , Marked_a__isNat(X)>
<Marked_mark(U21(X)) , Marked_a__U21(mark(X))>
<Marked_mark(U21(X)) , Marked_mark(X)>
<Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
<Marked_mark(U31(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(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
<Marked_mark(U42(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(s(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__U31(tt,N) , Marked_mark(N)>
<Marked_a__U41(tt,M,N) , Marked_a__U42(a__isNat(N),M,N)>
<Marked_a__U42(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__U42(tt,M,N) , Marked_mark(N)>
<Marked_a__U42(tt,M,N) , Marked_mark(M)>
<Marked_a__plus(N,0) , Marked_a__U31(a__isNat(N),N)>
<Marked_a__plus(N,s(M)) , Marked_a__U41(a__isNat(M),M,N)>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U12(X)) , Marked_mark(X)>
<Marked_mark(U21(X)) , Marked_mark(X)>
<Marked_mark(U31(X1,X2)) , Marked_a__U31(mark(X1),X2)>
<Marked_mark(U31(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(U42(X1,X2,X3)) , Marked_a__U42(mark(X1),X2,X3)>
<Marked_mark(U42(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(s(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a__U12 ] (X0) = 1*X0; 
 [ U21 ] (X0) = 1*X0; 
 [ a__U41 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0 + 3; 
 [ a__U21 ] (X0) = 1*X0; 
 [ Marked_a__plus ] (X0,X1) = 2*X1 + 2*X0 + 2; 
 [ plus ] (X0,X1) = 2*X1 + 1*X0; 
 [ Marked_mark ] (X0) = 2*X0 + 2; 
 [ a__U11 ] (X0,X1) = 1*X0; 
 [ U41 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0 + 3; 
 [ a__plus ] (X0,X1) = 2*X1 + 1*X0; 
 [ a__U31 ] (X0,X1) = 1*X1 + 2*X0 + 1; 
 [ Marked_a__U41 ] (X0,X1,X2) = 2*X2 + 2*X1 + 3; 
 [ U12 ] (X0) = 1*X0; 
 [ a__isNat ] (X0) = 0; 
 [ U31 ] (X0,X1) = 1*X1 + 2*X0 + 1; 
 [ s ] (X0) = 1*X0 + 2; 
 [ mark ] (X0) = 1*X0; 
 [ Marked_a__U42 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; 
 [ U11 ] (X0,X1) = 1*X0; 
 [ tt ] () = 0; 
 [ U42 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0 + 3; 
 [ 0 ] () = 3; 
 [ a__U42 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0 + 3; 
 [ Marked_a__U31 ] (X0,X1) = 2*X1 + 2*X0 + 2; 
 [ isNat ] (X0) = 0; 
 removing <Marked_a__U41(tt,M,N),Marked_a__U42(a__isNat(N),M,N)><Marked_a__plus(
                                                                  N,0),
Marked_a__U31(a__isNat(N),N)><Marked_a__plus(N,s(M)),Marked_a__U41(a__isNat(M),
                                                      M,N)><Marked_mark(
                                                             U31(X1,X2)),
Marked_a__U31(mark(X1),X2)><Marked_mark(U31(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(U42(X1,X2,X3)),Marked_a__U42(mark(X1),X2,X3)><Marked_mark(
                                                           U42(X1,X2,
                                                            X3)),Marked_mark(
                                                                  X1)><
Marked_mark(s(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_a__U31(tt,N) , Marked_mark(N)>
<Marked_a__U42(tt,M,N) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__U42(tt,M,N) , Marked_mark(N)>
<Marked_a__U42(tt,M,N) , Marked_mark(M)>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U12(X)) , Marked_mark(X)>
<Marked_mark(U21(X)) , Marked_mark(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)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U12(X)) , Marked_mark(X)>
<Marked_mark(U21(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a__U12 ] (X0) = 1*X0; 
 [ U21 ] (X0) = 1*X0; 
 [ a__U41 ] (X0,X1,X2) = 2; 
 [ a__U21 ] (X0) = 1*X0; 
 [ plus ] (X0,X1) = 2*X1 + 1*X0 + 2; 
 [ Marked_mark ] (X0) = 3*X0; 
 [ a__U11 ] (X0,X1) = 1*X0; 
 [ U41 ] (X0,X1,X2) = 2; 
 [ a__plus ] (X0,X1) = 2*X1 + 1*X0 + 2; 
 [ a__U31 ] (X0,X1) = 1*X1; 
 [ U12 ] (X0) = 1*X0; 
 [ a__isNat ] (X0) = 0; 
 [ U31 ] (X0,X1) = 1*X1; 
 [ s ] (X0) = 2; 
 [ mark ] (X0) = 1*X0; 
 [ U11 ] (X0,X1) = 1*X0; 
 [ tt ] () = 0; 
 [ U42 ] (X0,X1,X2) = 2; 
 [ 0 ] () = 0; 
 [ a__U42 ] (X0,X1,X2) = 2; 
 [ isNat ] (X0) = 0; 
 removing <Marked_mark(plus(X1,X2)),Marked_mark(X1)><Marked_mark(plus(X1,X2)),
Marked_mark(X2)>
 [ {
      
     DP termination of:
     <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U12(X)) , Marked_mark(X)>
<Marked_mark(U21(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U12(X)) , Marked_mark(X)>
<Marked_mark(U21(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a__U12 ] (X0) = 1*X0 + 1; 
 [ U21 ] (X0) = 1*X0; 
 [ a__U41 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; 
 [ a__U21 ] (X0) = 1*X0; 
 [ plus ] (X0,X1) = 2*X1 + 1*X0 + 2; 
 [ Marked_mark ] (X0) = 3*X0; 
 [ a__U11 ] (X0,X1) = 2*X1 + 1*X0 + 1; 
 [ U41 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; 
 [ a__plus ] (X0,X1) = 2*X1 + 1*X0 + 2; 
 [ a__U31 ] (X0,X1) = 1*X1; 
 [ U12 ] (X0) = 1*X0 + 1; 
 [ a__isNat ] (X0) = 2*X0; 
 [ U31 ] (X0,X1) = 1*X1; 
 [ s ] (X0) = 1*X0; 
 [ mark ] (X0) = 1*X0; 
 [ U11 ] (X0,X1) = 2*X1 + 1*X0 + 1; 
 [ tt ] () = 0; 
 [ U42 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; 
 [ 0 ] () = 2; 
 [ a__U42 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; 
 [ isNat ] (X0) = 2*X0; 
 removing <Marked_mark(U11(X1,X2)),Marked_mark(X1)><Marked_mark(U12(X)),
Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_mark(U21(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(U21(X)) , Marked_mark(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ a__U12 ] (X0) = 0; 
 [ U21 ] (X0) = 2 + 1*X0 + 0; 
 [ a__U41 ] (X0,X1,X2) = 1 + 1*X1 + 1*X2 + 0; 
 [ a__U21 ] (X0) = 2 + 1*X0 + 0; 
 [ plus ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ Marked_mark ] (X0) = 3*X0 + 0; 
 [ a__U11 ] (X0,X1) = 0; 
 [ U41 ] (X0,X1,X2) = 1 + 1*X1 + 1*X2 + 0; 
 [ a__plus ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ a__U31 ] (X0,X1) = 1*X1 + 0; 
 [ U12 ] (X0) = 0; 
 [ a__isNat ] (X0) = 2*X0 + 0; 
 [ U31 ] (X0,X1) = 1*X1 + 0; 
 [ s ] (X0) = 1 + 1*X0 + 0; 
 [ mark ] (X0) = 1*X0 + 0; 
 [ U11 ] (X0,X1) = 0; 
 [ tt ] () = 0; 
 [ U42 ] (X0,X1,X2) = 1 + 1*X1 + 1*X2 + 0; 
 [ 0 ] () = 0; 
 [ a__U42 ] (X0,X1,X2) = 1 + 1*X1 + 1*X2 + 0; 
 [ isNat ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_a__U11(tt,V2) , Marked_a__isNat(V2)>
<Marked_a__isNat(plus(V1,V2)) , Marked_a__U11(a__isNat(V1),V2)>
<Marked_a__isNat(plus(V1,V2)) , Marked_a__isNat(V1)>
<Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a__U12 ] (X0) = 2; 
 [ U21 ] (X0) = 1*X0; 
 [ a__U41 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; 
 [ a__U21 ] (X0) = 1*X0; 
 [ plus ] (X0,X1) = 2*X1 + 2*X0 + 2; 
 [ a__U11 ] (X0,X1) = 1*X0; 
 [ U41 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; 
 [ a__plus ] (X0,X1) = 2*X1 + 2*X0 + 2; 
 [ a__U31 ] (X0,X1) = 1*X1; 
 [ U12 ] (X0) = 2; 
 [ a__isNat ] (X0) = 2; 
 [ U31 ] (X0,X1) = 1*X1; 
 [ s ] (X0) = 1*X0; 
 [ Marked_a__isNat ] (X0) = 3*X0 + 2; 
 [ mark ] (X0) = 1*X0; 
 [ U11 ] (X0,X1) = 1*X0; 
 [ tt ] () = 2; 
 [ U42 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; 
 [ 0 ] () = 0; 
 [ Marked_a__U11 ] (X0,X1) = 3*X1 + 2*X0 + 1; 
 [ a__U42 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; 
 [ isNat ] (X0) = 2; 
 removing <Marked_a__U11(tt,V2),Marked_a__isNat(V2)><Marked_a__isNat(
                                                      plus(V1,V2)),Marked_a__U11(
                                                                    a__isNat(
                                                                    V1),
                                                                    V2)><
Marked_a__isNat(plus(V1,V2)),Marked_a__isNat(V1)>
 [ {
      
     DP termination of:
     <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__isNat(s(V1)) , Marked_a__isNat(V1)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ a__U12 ] (X0) = 0; 
 [ U21 ] (X0) = 0; 
 [ a__U41 ] (X0,X1,X2) = 2 + 2*X1 + 1*X2 + 0; 
 [ a__U21 ] (X0) = 0; 
 [ plus ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ a__U11 ] (X0,X1) = 0; 
 [ U41 ] (X0,X1,X2) = 2 + 2*X1 + 1*X2 + 0; 
 [ a__plus ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ a__U31 ] (X0,X1) = 1*X1 + 0; 
 [ U12 ] (X0) = 0; 
 [ a__isNat ] (X0) = 0; 
 [ U31 ] (X0,X1) = 1*X1 + 0; 
 [ s ] (X0) = 1 + 1*X0 + 0; 
 [ Marked_a__isNat ] (X0) = 3*X0 + 0; 
 [ mark ] (X0) = 1*X0 + 0; 
 [ U11 ] (X0,X1) = 0; 
 [ tt ] () = 0; 
 [ U42 ] (X0,X1,X2) = 1 + 2*X1 + 1*X2 + 0; 
 [ 0 ] () = 2 + 0; 
 [ a__U42 ] (X0,X1,X2) = 1 + 2*X1 + 1*X2 + 0; 
 [ isNat ] (X0) = 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.779255 seconds (real time)
Cime Exit Status: 0