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

TRS termination of:
[1] active(U11(tt,N)) -> mark(N)
[2] active(U21(tt,M,N)) -> mark(s(plus(N,M)))
[3] active(and(tt,X)) -> mark(X)
[4] active(isNat(0)) -> mark(tt)
[5] active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2)))
[6] active(isNat(s(V1))) -> mark(isNat(V1))
[7] active(plus(N,0)) -> mark(U11(isNat(N),N))
[8] active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N))
[9] mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
[10] mark(tt) -> active(tt)
[11] mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
[12] mark(s(X)) -> active(s(mark(X)))
[13] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
[14] mark(and(X1,X2)) -> active(and(mark(X1),X2))
[15] mark(isNat(X)) -> active(isNat(X))
[16] mark(0) -> active(0)
[17] U11(mark(X1),X2) -> U11(X1,X2)
[18] U11(X1,mark(X2)) -> U11(X1,X2)
[19] U11(active(X1),X2) -> U11(X1,X2)
[20] U11(X1,active(X2)) -> U11(X1,X2)
[21] U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
[22] U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
[23] U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
[24] U21(active(X1),X2,X3) -> U21(X1,X2,X3)
[25] U21(X1,active(X2),X3) -> U21(X1,X2,X3)
[26] U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
[27] s(mark(X)) -> s(X)
[28] s(active(X)) -> s(X)
[29] plus(mark(X1),X2) -> plus(X1,X2)
[30] plus(X1,mark(X2)) -> plus(X1,X2)
[31] plus(active(X1),X2) -> plus(X1,X2)
[32] plus(X1,active(X2)) -> plus(X1,X2)
[33] and(mark(X1),X2) -> and(X1,X2)
[34] and(X1,mark(X2)) -> and(X1,X2)
[35] and(active(X1),X2) -> and(X1,X2)
[36] and(X1,active(X2)) -> and(X1,X2)
[37] isNat(mark(X)) -> isNat(X)
[38] isNat(active(X)) -> isNat(X)


Sub problem: 
guided: 

DP termination of:
<Marked_active(U11(tt,N)) , Marked_mark(N)>
<Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(U21(tt,M,N)) , Marked_s(plus(N,M))>
<Marked_active(U21(tt,M,N)) , Marked_plus(N,M)>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(0)) , Marked_mark(tt)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(plus(V1,V2))) , Marked_and(isNat(V1),isNat(V2))>
<Marked_active(isNat(plus(V1,V2))) , Marked_isNat(V1)>
<Marked_active(isNat(plus(V1,V2))) , Marked_isNat(V2)>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(isNat(s(V1))) , Marked_isNat(V1)>
<Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
<Marked_active(plus(N,0)) , Marked_U11(isNat(N),N)>
<Marked_active(plus(N,0)) , Marked_isNat(N)>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_active(plus(N,s(M))) , Marked_U21(and(isNat(M),isNat(N)),M,N)>
<Marked_active(plus(N,s(M))) , Marked_and(isNat(M),isNat(N))>
<Marked_active(plus(N,s(M))) , Marked_isNat(M)>
<Marked_active(plus(N,s(M))) , Marked_isNat(N)>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U11(X1,X2)) , Marked_U11(mark(X1),X2)>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(tt) , Marked_active(tt)>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_U21(mark(X1),X2,X3)>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_s(mark(X))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(plus(X1,X2)) , Marked_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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
<Marked_mark(0) , Marked_active(0)>
<Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
<Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)>
<Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
<Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)>
<Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
<Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
<Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
<Marked_isNat(mark(X)) , Marked_isNat(X)>
<Marked_isNat(active(X)) , Marked_isNat(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 7 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(X2)))>
  <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(s(X)) , Marked_active(s(mark(X)))>
  <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_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(s(X)) , Marked_active(s(mark(X)))>
  <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_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(s(X)) , Marked_active(s(mark(X)))>
  <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_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_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_active(plus(mark(X1),mark(X2)))>
  <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(s(X)) , Marked_active(s(mark(X)))>
  <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_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(X2)))>
  <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(s(X)) , Marked_active(s(mark(X)))>
  <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_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
}

{  <Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)> 
      --> <Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)> 
     --> <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)> 
     --> <Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)> 
     --> <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)> 
     --> <Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)> 
     --> <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)> 
     --> <Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)> 
     --> <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)>
  <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
}

{  <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)> 
      --> <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
}

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

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

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

{  <Marked_isNat(active(X)) , Marked_isNat(X)> 
      --> <Marked_isNat(active(X)) , Marked_isNat(X)>
  <Marked_isNat(active(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(mark(X)) , Marked_isNat(X)>
  <Marked_isNat(mark(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(active(X)) , Marked_isNat(X)>
  <Marked_isNat(mark(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(mark(X)) , Marked_isNat(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(s(X)) >= Marked_active(s(mark(X))) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(U11(tt,N)) >= Marked_mark(N) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(plus(N,0)) >= Marked_mark(U11(isNat(N),N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(and(tt,X)) >= Marked_mark(X) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
  Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),isNat(V2))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U11(X1,X2)) > Marked_active(U11(mark(X1),X2)) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(s(X)) > Marked_active(s(mark(X))) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(U11(tt,N)) > Marked_mark(N) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(plus(N,0)) > Marked_mark(U11(isNat(N),N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(and(tt,X)) > Marked_mark(X) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(isNat(V1)) ;
 }
{
  Marked_active(isNat(plus(V1,V2))) > Marked_mark(and(isNat(V1),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: mark(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2))
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X)))
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(U11(tt,N)) >= Marked_mark(N)
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(plus(N,0)) >= Marked_mark(U11(isNat(N),N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(and(tt,X)) >= Marked_mark(X)
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),
                                                              isNat(V2)))
APPLY CRITERIA (Subterm criterion)

ST: Marked_U11 -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_U21 -> 3

APPLY CRITERIA (Subterm criterion)

ST: Marked_s -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_and -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_isNat -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) ;
  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_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(U11(tt,N)) >= Marked_mark(N) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(plus(N,0)) >= Marked_mark(U11(isNat(N),N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(and(tt,X)) >= Marked_mark(X) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
  Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),isNat(V2))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U11(X1,X2)) > Marked_active(U11(mark(X1),X2)) ;
 }
{
  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_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(U11(tt,N)) > Marked_mark(N) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(plus(N,0)) > Marked_mark(U11(isNat(N),N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(and(tt,X)) > Marked_mark(X) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(isNat(V1)) ;
 }
{
  Marked_active(isNat(plus(V1,V2))) > Marked_mark(and(isNat(V1),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: mark(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2))
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(U11(tt,N)) >= Marked_mark(N)
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(plus(N,0)) >= Marked_mark(U11(isNat(N),N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(and(tt,X)) >= Marked_mark(X)
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),
                                                              isNat(V2)))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U11(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(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_active(U11(mark(X1),X2))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(U11(tt,N)) , Marked_mark(N)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U11(tt,N)) , Marked_mark(N)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) ;
  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_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(U11(tt,N)) >= Marked_mark(N) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(and(tt,X)) >= Marked_mark(X) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
  Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),isNat(V2))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U11(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U11(X1,X2)) > Marked_active(U11(mark(X1),X2)) ;
 }
{
  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_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(U11(tt,N)) > Marked_mark(N) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(and(tt,X)) > Marked_mark(X) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(isNat(V1)) ;
 }
{
  Marked_active(isNat(plus(V1,V2))) > Marked_mark(and(isNat(V1),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: mark(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2))
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(U11(tt,N)) >= Marked_mark(N)
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(and(tt,X)) >= Marked_mark(X)
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),
                                                              isNat(V2)))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) ;
  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_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(and(tt,X)) >= Marked_mark(X) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
  Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),isNat(V2))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U11(X1,X2)) > Marked_active(U11(mark(X1),X2)) ;
 }
{
  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_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(and(tt,X)) > Marked_mark(X) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(isNat(V1)) ;
 }
{
  Marked_active(isNat(plus(V1,V2))) > Marked_mark(and(isNat(V1),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: mark(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2))
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(and(tt,X)) >= Marked_mark(X)
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),
                                                              isNat(V2)))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_active(plus(mark(X1),mark(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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),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_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_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  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_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(and(tt,X)) >= Marked_mark(X) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
  Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),isNat(V2))) ;
 }
 + Disjunctions:{ 
{
  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_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(and(tt,X)) > Marked_mark(X) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(isNat(V1)) ;
 }
{
  Marked_active(isNat(plus(V1,V2))) > Marked_mark(and(isNat(V1),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: mark(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(and(tt,X)) >= Marked_mark(X)
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),
                                                              isNat(V2)))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(and(tt,X)) >= Marked_mark(X) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
  Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),isNat(V2))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(and(tt,X)) > Marked_mark(X) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(isNat(V1)) ;
 }
{
  Marked_active(isNat(plus(V1,V2))) > Marked_mark(and(isNat(V1),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: mark(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(and(tt,X)) >= Marked_mark(X)
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),
                                                              isNat(V2)))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),
                                                           isNat(V2)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
  Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),isNat(V2))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(isNat(V1)) ;
 }
{
  Marked_active(isNat(plus(V1,V2))) > Marked_mark(and(isNat(V1),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: mark(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(and(isNat(V1),
                                                              isNat(V2)))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(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(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <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(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(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(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(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(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                      M,N))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),
                                                     M,N))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(U21(and(isNat(M),isNat(N)),M,N)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(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(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U21(and(isNat(M),
                                                            isNat(N)),
                                                        M,N))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
  Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1)) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
{
  Marked_active(isNat(s(V1))) > Marked_mark(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(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
constraint: Marked_active(isNat(s(V1))) >= Marked_mark(isNat(V1))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNat(X)) , Marked_active(isNat(X))> 
      --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNat(X)) , Marked_active(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(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(isNat(X)) , Marked_active(isNat(X))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(isNat(X)) > Marked_active(isNat(X)) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
 } 
=== 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(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X))
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
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(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
  <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))> 
     --> <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3)) ;
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(isNat(X)) >= active(isNat(X)) ;
  mark(0) >= active(0) ;
  active(U11(tt,N)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N)) ;
  active(plus(N,0)) >= mark(U11(isNat(N),N)) ;
  active(U21(tt,M,N)) >= mark(s(plus(N,M))) ;
  active(and(tt,X)) >= mark(X) ;
  active(isNat(s(V1))) >= mark(isNat(V1)) ;
  active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2))) ;
  active(isNat(0)) >= mark(tt) ;
  U11(mark(X1),X2) >= U11(X1,X2) ;
  U11(active(X1),X2) >= U11(X1,X2) ;
  U11(X1,mark(X2)) >= U11(X1,X2) ;
  U11(X1,active(X2)) >= U11(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  U21(mark(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(active(X1),X2,X3) >= U21(X1,X2,X3) ;
  U21(X1,mark(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,active(X2),X3) >= U21(X1,X2,X3) ;
  U21(X1,X2,mark(X3)) >= U21(X1,X2,X3) ;
  U21(X1,X2,active(X3)) >= U21(X1,X2,X3) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  isNat(mark(X)) >= isNat(X) ;
  isNat(active(X)) >= isNat(X) ;
  Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3)) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(U21(X1,X2,X3)) > Marked_active(U21(mark(X1),X2,X3)) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_active(U21(tt,M,N)) > Marked_mark(s(plus(N,M))) ;
 }
 } 
=== 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(U11(X1,X2)) >= active(U11(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(U21(X1,X2,X3)) >= active(U21(mark(X1),X2,X3))
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(isNat(X)) >= active(isNat(X))
constraint: mark(0) >= active(0)
constraint: active(U11(tt,N)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(U21(and(isNat(M),isNat(N)),M,N))
constraint: active(plus(N,0)) >= mark(U11(isNat(N),N))
constraint: active(U21(tt,M,N)) >= mark(s(plus(N,M)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(isNat(s(V1))) >= mark(isNat(V1))
constraint: active(isNat(plus(V1,V2))) >= mark(and(isNat(V1),isNat(V2)))
constraint: active(isNat(0)) >= mark(tt)
constraint: U11(mark(X1),X2) >= U11(X1,X2)
constraint: U11(active(X1),X2) >= U11(X1,X2)
constraint: U11(X1,mark(X2)) >= U11(X1,X2)
constraint: U11(X1,active(X2)) >= U11(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: U21(mark(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(active(X1),X2,X3) >= U21(X1,X2,X3)
constraint: U21(X1,mark(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,active(X2),X3) >= U21(X1,X2,X3)
constraint: U21(X1,X2,mark(X3)) >= U21(X1,X2,X3)
constraint: U21(X1,X2,active(X3)) >= U21(X1,X2,X3)
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: isNat(mark(X)) >= isNat(X)
constraint: isNat(active(X)) >= isNat(X)
constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_active(U21(mark(X1),X2,X3))
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_active(U21(tt,M,N)) >= Marked_mark(s(plus(N,M)))
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 (Subterm criterion)

ST: Marked_mark -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)> 
      --> <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
  <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)> 
     --> <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_U11 -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
      --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_U21 -> 2

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
      --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
  <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)> 
     --> <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_U21 -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
      --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
      --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(active(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(active(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_and -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] active(U11(tt,N)) -> mark(N)
[2] active(U21(tt,M,N)) -> mark(s(plus(N,M)))
[3] active(and(tt,X)) -> mark(X)
[4] active(isNat(0)) -> mark(tt)
[5] active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2)))
[6] active(isNat(s(V1))) -> mark(isNat(V1))
[7] active(plus(N,0)) -> mark(U11(isNat(N),N))
[8] active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N))
[9] mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
[10] mark(tt) -> active(tt)
[11] mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
[12] mark(s(X)) -> active(s(mark(X)))
[13] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
[14] mark(and(X1,X2)) -> active(and(mark(X1),X2))
[15] mark(isNat(X)) -> active(isNat(X))
[16] mark(0) -> active(0)
[17] U11(mark(X1),X2) -> U11(X1,X2)
[18] U11(X1,mark(X2)) -> U11(X1,X2)
[19] U11(active(X1),X2) -> U11(X1,X2)
[20] U11(X1,active(X2)) -> U11(X1,X2)
[21] U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
[22] U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
[23] U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
[24] U21(active(X1),X2,X3) -> U21(X1,X2,X3)
[25] U21(X1,active(X2),X3) -> U21(X1,X2,X3)
[26] U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
[27] s(mark(X)) -> s(X)
[28] s(active(X)) -> s(X)
[29] plus(mark(X1),X2) -> plus(X1,X2)
[30] plus(X1,mark(X2)) -> plus(X1,X2)
[31] plus(active(X1),X2) -> plus(X1,X2)
[32] plus(X1,active(X2)) -> plus(X1,X2)
[33] and(mark(X1),X2) -> and(X1,X2)
[34] and(X1,mark(X2)) -> and(X1,X2)
[35] and(active(X1),X2) -> and(X1,X2)
[36] and(X1,active(X2)) -> and(X1,X2)
[37] isNat(mark(X)) -> isNat(X)
[38] isNat(active(X)) -> isNat(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(U11(tt,N)) , Marked_mark(N)>
<Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(U21(tt,M,N)) , Marked_s(plus(N,M))>
<Marked_active(U21(tt,M,N)) , Marked_plus(N,M)>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(0)) , Marked_mark(tt)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(plus(V1,V2))) , Marked_and(isNat(V1),isNat(V2))>
<Marked_active(isNat(plus(V1,V2))) , Marked_isNat(V1)>
<Marked_active(isNat(plus(V1,V2))) , Marked_isNat(V2)>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(isNat(s(V1))) , Marked_isNat(V1)>
<Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
<Marked_active(plus(N,0)) , Marked_U11(isNat(N),N)>
<Marked_active(plus(N,0)) , Marked_isNat(N)>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_active(plus(N,s(M))) , Marked_U21(and(isNat(M),isNat(N)),M,N)>
<Marked_active(plus(N,s(M))) , Marked_and(isNat(M),isNat(N))>
<Marked_active(plus(N,s(M))) , Marked_isNat(M)>
<Marked_active(plus(N,s(M))) , Marked_isNat(N)>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U11(X1,X2)) , Marked_U11(mark(X1),X2)>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(tt) , Marked_active(tt)>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_U21(mark(X1),X2,X3)>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_s(mark(X))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(plus(X1,X2)) , Marked_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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
<Marked_mark(0) , Marked_active(0)>
<Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
<Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)>
<Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
<Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)>
<Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
<Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
<Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
<Marked_isNat(mark(X)) , Marked_isNat(X)>
<Marked_isNat(active(X)) , Marked_isNat(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U11(tt,N)) , Marked_mark(N)>
<Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ Marked_mark ] (X0) = 2; 
 [ isNat ] (X0) = 1; 
 [ s ] (X0) = 0; 
 [ U11 ] (X0,X1) = 1; 
 [ U21 ] (X0,X1,X2) = 1; 
 [ active ] (X0) = 0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 1; 
 removing <Marked_mark(s(X)),Marked_active(s(mark(X)))>
 [ {
      
     DP termination of:
     <Marked_active(U11(tt,N)) , Marked_mark(N)>
<Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U11(tt,N)) , Marked_mark(N)>
<Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,0)) , Marked_mark(U11(isNat(N),N))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ isNat ] (X0) = 0; 
 [ s ] (X0) = 1*X0; 
 [ U11 ] (X0,X1) = 2*X1 + 2*X0; 
 [ U21 ] (X0,X1,X2) = 2*X2 + 1*X1 + 2*X0; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 1; 
 [ plus ] (X0,X1) = 1*X1 + 2*X0; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 1*X1 + 2*X0; 
 removing <Marked_active(plus(N,0)),Marked_mark(U11(isNat(N),N))>
 [ {
      
     DP termination of:
     <Marked_active(U11(tt,N)) , Marked_mark(N)>
<Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U11(tt,N)) , Marked_mark(N)>
<Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U11(X1,X2)) , Marked_mark(X1)>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ isNat ] (X0) = 0; 
 [ s ] (X0) = 1*X0; 
 [ U11 ] (X0,X1) = 1*X1 + 2*X0 + 1; 
 [ U21 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 2; 
 [ plus ] (X0,X1) = 2*X1 + 1*X0; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 2*X1 + 2*X0; 
 removing <Marked_active(U11(tt,N)),Marked_mark(N)><Marked_mark(U11(X1,X2)),
Marked_mark(X1)>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U11(X1,X2)) , Marked_active(U11(mark(X1),X2))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ Marked_mark ] (X0) = 2; 
 [ isNat ] (X0) = 1; 
 [ s ] (X0) = 0; 
 [ U11 ] (X0,X1) = 0; 
 [ U21 ] (X0,X1,X2) = 1; 
 [ active ] (X0) = 0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 1; 
 removing <Marked_mark(U11(X1,X2)),Marked_active(U11(mark(X1),X2))>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(U21(X1,X2,X3)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(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_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ isNat ] (X0) = 0; 
 [ s ] (X0) = 1*X0; 
 [ U11 ] (X0,X1) = 1*X1 + 2; 
 [ U21 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0 + 2; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 2*X1 + 1*X0; 
 removing <Marked_mark(U21(X1,X2,X3)),Marked_mark(X1)><Marked_mark(plus(X1,X2)),
Marked_mark(X1)><Marked_mark(plus(X1,X2)),Marked_mark(X2)>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ isNat ] (X0) = 2*X0; 
 [ s ] (X0) = 1*X0; 
 [ U11 ] (X0,X1) = 1*X1; 
 [ U21 ] (X0,X1,X2) = 2*X2 + 2*X1; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 2; 
 [ plus ] (X0,X1) = 2*X1 + 2*X0; 
 [ tt ] () = 1; 
 [ and ] (X0,X1) = 2*X1 + 2*X0; 
 removing <Marked_active(and(tt,X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(plus(V1,V2))) , Marked_mark(and(isNat(V1),isNat(V2)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ isNat ] (X0) = 2*X0; 
 [ s ] (X0) = 1*X0; 
 [ U11 ] (X0,X1) = 1*X1 + 1; 
 [ U21 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 2*X1 + 1*X0 + 1; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 2*X1 + 1*X0; 
 removing <Marked_active(isNat(plus(V1,V2))),Marked_mark(and(isNat(V1),
                                                          isNat(V2)))>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ Marked_mark ] (X0) = 2; 
 [ isNat ] (X0) = 2; 
 [ s ] (X0) = 0; 
 [ U11 ] (X0,X1) = 0; 
 [ U21 ] (X0,X1,X2) = 2; 
 [ active ] (X0) = 0; 
 [ Marked_active ] (X0) = 1*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 2; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 0; 
 removing <Marked_mark(and(X1,X2)),Marked_active(and(mark(X1),X2))>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ isNat ] (X0) = 0; 
 [ s ] (X0) = 1*X0 + 1; 
 [ U11 ] (X0,X1) = 2*X1; 
 [ U21 ] (X0,X1,X2) = 2*X2 + 1*X1 + 1; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1*X1 + 2*X0; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 2*X1 + 2*X0; 
 removing <Marked_mark(s(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ isNat ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ U11 ] (X0,X1) = 2*X1; 
 [ U21 ] (X0,X1,X2) = 0; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 2*X0 + 1; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 2*X1 + 2*X0; 
 removing <Marked_mark(plus(X1,X2)),Marked_active(plus(mark(X1),mark(X2)))>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_active(plus(N,s(M))) , Marked_mark(U21(and(isNat(M),isNat(N)),M,N))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ Marked_mark ] (X0) = 0; 
 [ isNat ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ U11 ] (X0,X1) = 0; 
 [ U21 ] (X0,X1,X2) = 0; 
 [ active ] (X0) = 0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 0; 
 removing <Marked_active(plus(N,s(M))),Marked_mark(U21(and(isNat(M),isNat(N)),
                                                    M,N))>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_active(isNat(s(V1))) , Marked_mark(isNat(V1))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0 + 3; 
 [ isNat ] (X0) = 2*X0 + 1; 
 [ s ] (X0) = 1*X0 + 1; 
 [ U11 ] (X0,X1) = 1*X1; 
 [ U21 ] (X0,X1,X2) = 2*X2 + 1*X1 + 3; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 2*X0 + 3; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1*X1 + 2*X0 + 2; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 1*X1 + 2*X0; 
 removing <Marked_active(isNat(s(V1))),Marked_mark(isNat(V1))>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNat(X)) , Marked_active(isNat(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ Marked_mark ] (X0) = 2; 
 [ isNat ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ U11 ] (X0,X1) = 0; 
 [ U21 ] (X0,X1,X2) = 1; 
 [ active ] (X0) = 0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 0; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 0; 
 removing <Marked_mark(isNat(X)),Marked_active(isNat(X))>
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(U21(tt,M,N)) , Marked_mark(s(plus(N,M)))>
<Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 1*X0; 
 [ isNat ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ U11 ] (X0,X1) = 1*X1 + 2; 
 [ U21 ] (X0,X1,X2) = 1*X2 + 1; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 1; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1*X0 + 2; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 2*X1 + 2*X0; 
 removing <Marked_active(U21(tt,M,N)),Marked_mark(s(plus(N,M)))>
 [ {
      
     DP termination of:
     <Marked_mark(U21(X1,X2,X3)) , Marked_active(U21(mark(X1),X2,X3))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
<Marked_U11(X1,mark(X2)) , Marked_U11(X1,X2)>
<Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
<Marked_U11(X1,active(X2)) , Marked_U11(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
<Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_U11(active(X1),X2) , Marked_U11(X1,X2)>
<Marked_U11(mark(X1),X2) , Marked_U11(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,X2,mark(X3)) , Marked_U21(X1,X2,X3)>
<Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,X2,active(X3)) , Marked_U21(X1,X2,X3)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_U21(X1,active(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(X1,mark(X2),X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_U21(mark(X1),X2,X3) , Marked_U21(X1,X2,X3)>
<Marked_U21(active(X1),X2,X3) , Marked_U21(X1,X2,X3)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
<Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_isNat(mark(X)) , Marked_isNat(X)>
<Marked_isNat(active(X)) , Marked_isNat(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 4.047693 seconds (real time)
Cime Exit Status: 0