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

TRS termination of:
[1] U11(tt,V1,V2) -> U12(isNat(activate(V1)),activate(V2))
[2] U12(tt,V2) -> U13(isNat(activate(V2)))
[3] U13(tt) -> tt
[4] U21(tt,V1) -> U22(isNat(activate(V1)))
[5] U22(tt) -> tt
[6] U31(tt,V1,V2) -> U32(isNat(activate(V1)),activate(V2))
[7] U32(tt,V2) -> U33(isNat(activate(V2)))
[8] U33(tt) -> tt
[9] U41(tt,N) -> activate(N)
[10] U51(tt,M,N) -> s(plus(activate(N),activate(M)))
[11] U61(tt) -> 0
[12] U71(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N))
[13] and(tt,X) -> activate(X)
[14] isNat(n__0) -> tt
[15] isNat(n__plus(V1,V2)) ->
 U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),
  activate(V2))
[16] isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
[17] isNat(n__x(V1,V2)) ->
 U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),
  activate(V2))
[18] isNatKind(n__0) -> tt
[19] isNatKind(n__plus(V1,V2)) ->
 and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
[20] isNatKind(n__s(V1)) -> isNatKind(activate(V1))
[21] isNatKind(n__x(V1,V2)) ->
 and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
[22] plus(N,0) -> U41(and(isNat(N),n__isNatKind(N)),N)
[23] plus(N,s(M)) ->
 U51(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),
  M,N)
[24] x(N,0) -> U61(and(isNat(N),n__isNatKind(N)))
[25] x(N,s(M)) ->
 U71(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),
  M,N)
[26] 0 -> n__0
[27] plus(X1,X2) -> n__plus(X1,X2)
[28] isNatKind(X) -> n__isNatKind(X)
[29] s(X) -> n__s(X)
[30] x(X1,X2) -> n__x(X1,X2)
[31] and(X1,X2) -> n__and(X1,X2)
[32] isNat(X) -> n__isNat(X)
[33] activate(n__0) -> 0
[34] activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
[35] activate(n__isNatKind(X)) -> isNatKind(X)
[36] activate(n__s(X)) -> s(activate(X))
[37] activate(n__x(X1,X2)) -> x(activate(X1),activate(X2))
[38] activate(n__and(X1,X2)) -> and(activate(X1),X2)
[39] activate(n__isNat(X)) -> isNat(X)
[40] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_U11(tt,V1,V2) , Marked_U12(isNat(activate(V1)),activate(V2))>
<Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))>
<Marked_U11(tt,V1,V2) , Marked_activate(V1)>
<Marked_U11(tt,V1,V2) , Marked_activate(V2)>
<Marked_U12(tt,V2) , Marked_U13(isNat(activate(V2)))>
<Marked_U12(tt,V2) , Marked_isNat(activate(V2))>
<Marked_U12(tt,V2) , Marked_activate(V2)>
<Marked_U21(tt,V1) , Marked_U22(isNat(activate(V1)))>
<Marked_U21(tt,V1) , Marked_isNat(activate(V1))>
<Marked_U21(tt,V1) , Marked_activate(V1)>
<Marked_U31(tt,V1,V2) , Marked_U32(isNat(activate(V1)),activate(V2))>
<Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))>
<Marked_U31(tt,V1,V2) , Marked_activate(V1)>
<Marked_U31(tt,V1,V2) , Marked_activate(V2)>
<Marked_U32(tt,V2) , Marked_U33(isNat(activate(V2)))>
<Marked_U32(tt,V2) , Marked_isNat(activate(V2))>
<Marked_U32(tt,V2) , Marked_activate(V2)>
<Marked_U41(tt,N) , Marked_activate(N)>
<Marked_U51(tt,M,N) , Marked_s(plus(activate(N),activate(M)))>
<Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U51(tt,M,N) , Marked_activate(N)>
<Marked_U51(tt,M,N) , Marked_activate(M)>
<Marked_U61(tt) , Marked_0>
<Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))>
<Marked_U71(tt,M,N) , Marked_x(activate(N),activate(M))>
<Marked_U71(tt,M,N) , Marked_activate(N)>
<Marked_U71(tt,M,N) , Marked_activate(M)>
<Marked_U71(tt,M,N) , Marked_activate(N)>
<Marked_and(tt,X) , Marked_activate(X)>
<Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                            n__isNatKind(activate(V2))),
                                 activate(V1),activate(V2))>
<Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                 n__isNatKind(activate(V2)))>
<Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
<Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
<Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                         n__isNatKind(activate(V2))),
                              activate(V1),activate(V2))>
<Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                              n__isNatKind(activate(V2)))>
<Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
<Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
<Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
<Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
<Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
<Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                     n__isNatKind(activate(V2)))>
<Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
<Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
<Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
<Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
<Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
<Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                  n__isNatKind(activate(V2)))>
<Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
<Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)>
<Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)>
<Marked_plus(N,0) , Marked_U41(and(isNat(N),n__isNatKind(N)),N)>
<Marked_plus(N,0) , Marked_and(isNat(N),n__isNatKind(N))>
<Marked_plus(N,0) , Marked_isNat(N)>
<Marked_plus(N,s(M)) , Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                   n__and(n__isNat(N),n__isNatKind(N))),
                        M,N)>
<Marked_plus(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                        n__and(n__isNat(N),n__isNatKind(N)))>
<Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))>
<Marked_plus(N,s(M)) , Marked_isNat(M)>
<Marked_x(N,0) , Marked_U61(and(isNat(N),n__isNatKind(N)))>
<Marked_x(N,0) , Marked_and(isNat(N),n__isNatKind(N))>
<Marked_x(N,0) , Marked_isNat(N)>
<Marked_x(N,s(M)) , Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                n__and(n__isNat(N),n__isNatKind(N))),
                     M,N)>
<Marked_x(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                     n__and(n__isNat(N),n__isNatKind(N)))>
<Marked_x(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))>
<Marked_x(N,s(M)) , Marked_isNat(M)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))>
<Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
<Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
<Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
<Marked_activate(n__s(X)) , Marked_s(activate(X))>
<Marked_activate(n__s(X)) , Marked_activate(X)>
<Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
<Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
<Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
<Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
<Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
<Marked_activate(n__isNat(X)) , Marked_isNat(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
      --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_activate(n__isNat(X)) , Marked_isNat(X)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))> 
     --> <Marked_x(N,s(M)) , Marked_isNat(M)>
  <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))> 
     --> <Marked_x(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))>
  <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))> 
     --> <Marked_x(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                              n__and(n__isNat(N),n__isNatKind(N)))>
  <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))> 
     --> <Marked_x(N,s(M)) , Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                         n__and(n__isNat(N),n__isNatKind(N))),
                              M,N)>
  <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))> 
     --> <Marked_x(N,0) , Marked_isNat(N)>
  <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))> 
     --> <Marked_x(N,0) , Marked_and(isNat(N),n__isNatKind(N))>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2)))>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2)))>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,s(M)) , Marked_isNat(M)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                                 n__and(n__isNat(N),n__isNatKind(N)))>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,s(M)) , Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                            n__and(n__isNat(N),n__isNatKind(N))),
                                 M,N)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,0) , Marked_isNat(N)>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,0) , Marked_and(isNat(N),n__isNatKind(N))>
  <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),activate(X2))> 
     --> <Marked_plus(N,0) , Marked_U41(and(isNat(N),n__isNatKind(N)),N)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_x(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_x(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_x(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                       n__and(n__isNat(N),n__isNatKind(N)))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_x(N,s(M)) , Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                  n__and(n__isNat(N),n__isNatKind(N))),
                       M,N)> --> <Marked_U71(tt,M,N) , Marked_activate(N)>
  <Marked_x(N,s(M)) , Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                  n__and(n__isNat(N),n__isNatKind(N))),
                       M,N)> --> <Marked_U71(tt,M,N) , Marked_activate(M)>
  <Marked_x(N,s(M)) , Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                  n__and(n__isNat(N),n__isNatKind(N))),
                       M,N)> --> <Marked_U71(tt,M,N) , Marked_activate(N)>
  <Marked_x(N,s(M)) , Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                  n__and(n__isNat(N),n__isNatKind(N))),
                       M,N)> 
     --> <Marked_U71(tt,M,N) , Marked_x(activate(N),activate(M))>
  <Marked_x(N,s(M)) , Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                  n__and(n__isNat(N),n__isNatKind(N))),
                       M,N)> 
     --> <Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),
                                activate(N))>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_x(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_x(N,0) , Marked_and(isNat(N),n__isNatKind(N))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_plus(N,s(M)) , Marked_isNat(M)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_plus(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                          n__and(n__isNat(N),n__isNatKind(N)))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_plus(N,s(M)) , Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                     n__and(n__isNat(N),n__isNatKind(N))),
                          M,N)> --> <Marked_U51(tt,M,N) , Marked_activate(M)>
  <Marked_plus(N,s(M)) , Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                     n__and(n__isNat(N),n__isNatKind(N))),
                          M,N)> --> <Marked_U51(tt,M,N) , Marked_activate(N)>
  <Marked_plus(N,s(M)) , Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                     n__and(n__isNat(N),n__isNatKind(N))),
                          M,N)> 
     --> <Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_plus(N,0) , Marked_isNat(N)> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_plus(N,0) , Marked_and(isNat(N),n__isNatKind(N))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_plus(N,0) , Marked_U41(and(isNat(N),n__isNatKind(N)),N)> 
     --> <Marked_U41(tt,N) , Marked_activate(N)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2)))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2)))>
  <Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                    n__isNatKind(activate(V2)))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2)))>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2)))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2)))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2)))>
  <Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2)))>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2)))>
  <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                n__isNatKind(activate(V2)))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2))),
                                activate(V1),activate(V2))> 
     --> <Marked_U31(tt,V1,V2) , Marked_activate(V2)>
  <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2))),
                                activate(V1),activate(V2))> 
     --> <Marked_U31(tt,V1,V2) , Marked_activate(V1)>
  <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2))),
                                activate(V1),activate(V2))> 
     --> <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))>
  <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2))),
                                activate(V1),activate(V2))> 
     --> <Marked_U31(tt,V1,V2) , Marked_U32(isNat(activate(V1)),activate(V2))>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2)))>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2)))>
  <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),activate(V1))> 
     --> <Marked_U21(tt,V1) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),activate(V1))> 
     --> <Marked_U21(tt,V1) , Marked_isNat(activate(V1))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2)))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2)))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                   n__isNatKind(activate(V2)))> 
     --> <Marked_and(tt,X) , Marked_activate(X)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2))),
                                   activate(V1),activate(V2))> 
     --> <Marked_U11(tt,V1,V2) , Marked_activate(V2)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2))),
                                   activate(V1),activate(V2))> 
     --> <Marked_U11(tt,V1,V2) , Marked_activate(V1)>
  <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2))),
                                   activate(V1),activate(V2))> 
     --> <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))>
  <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2))),
                                   activate(V1),activate(V2))> 
     --> <Marked_U11(tt,V1,V2) , Marked_U12(isNat(activate(V1)),activate(V2))>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_and(tt,X) , Marked_activate(X)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U71(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U71(tt,M,N) , Marked_x(activate(N),activate(M))> 
     --> <Marked_x(N,s(M)) , Marked_isNat(M)>
  <Marked_U71(tt,M,N) , Marked_x(activate(N),activate(M))> 
     --> <Marked_x(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))>
  <Marked_U71(tt,M,N) , Marked_x(activate(N),activate(M))> 
     --> <Marked_x(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                              n__and(n__isNat(N),n__isNatKind(N)))>
  <Marked_U71(tt,M,N) , Marked_x(activate(N),activate(M))> 
     --> <Marked_x(N,s(M)) , Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                         n__and(n__isNat(N),n__isNatKind(N))),
                              M,N)>
  <Marked_U71(tt,M,N) , Marked_x(activate(N),activate(M))> 
     --> <Marked_x(N,0) , Marked_isNat(N)>
  <Marked_U71(tt,M,N) , Marked_x(activate(N),activate(M))> 
     --> <Marked_x(N,0) , Marked_and(isNat(N),n__isNatKind(N))>
  <Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))> 
     --> <Marked_plus(N,s(M)) , Marked_isNat(M)>
  <Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))> 
     --> <Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))>
  <Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))> 
     --> <Marked_plus(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                                 n__and(n__isNat(N),n__isNatKind(N)))>
  <Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))> 
     --> <Marked_plus(N,s(M)) , Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                            n__and(n__isNat(N),n__isNatKind(N))),
                                 M,N)>
  <Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))> 
     --> <Marked_plus(N,0) , Marked_isNat(N)>
  <Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))> 
     --> <Marked_plus(N,0) , Marked_and(isNat(N),n__isNatKind(N))>
  <Marked_U71(tt,M,N) , Marked_plus(x(activate(N),activate(M)),activate(N))> 
     --> <Marked_plus(N,0) , Marked_U41(and(isNat(N),n__isNatKind(N)),N)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U51(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U51(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_isNat(M)>
  <Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))>
  <Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_and(and(isNat(M),n__isNatKind(M)),
                                 n__and(n__isNat(N),n__isNatKind(N)))>
  <Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                            n__and(n__isNat(N),n__isNatKind(N))),
                                 M,N)>
  <Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_isNat(N)>
  <Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_and(isNat(N),n__isNatKind(N))>
  <Marked_U51(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_U41(and(isNat(N),n__isNatKind(N)),N)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U32(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_U32(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_U31(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_U31(tt,V1,V2) , Marked_U32(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U32(tt,V2) , Marked_activate(V2)>
  <Marked_U31(tt,V1,V2) , Marked_U32(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U32(tt,V2) , Marked_isNat(activate(V2))>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_U21(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U12(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_U12(tt,V2) , Marked_isNat(activate(V2))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X2)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_activate(X1)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__x(X1,X2)) , Marked_x(activate(X1),activate(X2))>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U11(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V2)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_activate(V1)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2)))>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__x(V1,V2)) , Marked_U31(and(isNatKind(activate(V1)),
                                                  n__isNatKind(activate(V2))),
                                       activate(V1),activate(V2))>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V2)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_activate(V1)>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))>
  <Marked_U11(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__plus(V1,V2)) , Marked_U11(and(isNatKind(activate(V1)),
                                                     n__isNatKind(activate(V2))),
                                          activate(V1),activate(V2))>
  <Marked_U11(tt,V1,V2) , Marked_U12(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U12(tt,V2) , Marked_activate(V2)>
  <Marked_U11(tt,V1,V2) , Marked_U12(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U12(tt,V2) , Marked_isNat(activate(V2))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  U12(tt,V2) >= U13(isNat(activate(V2))) ;
  isNat(n__0) >= tt ;
  isNat(n__plus(V1,V2)) >= U11(and(isNatKind(activate(V1)),
                                n__isNatKind(activate(V2))),activate(V1),
                            activate(V2)) ;
  isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ;
  isNat(n__x(V1,V2)) >= U31(and(isNatKind(activate(V1)),
                             n__isNatKind(activate(V2))),activate(V1),
                         activate(V2)) ;
  isNat(X) >= n__isNat(X) ;
  activate(n__0) >= 0 ;
  activate(n__isNatKind(X)) >= isNatKind(X) ;
  activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) ;
  activate(n__s(X)) >= s(activate(X)) ;
  activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) ;
  activate(n__and(X1,X2)) >= and(activate(X1),X2) ;
  activate(n__isNat(X)) >= isNat(X) ;
  activate(X) >= X ;
  U11(tt,V1,V2) >= U12(isNat(activate(V1)),activate(V2)) ;
  U13(tt) >= tt ;
  U22(tt) >= tt ;
  U21(tt,V1) >= U22(isNat(activate(V1))) ;
  U32(tt,V2) >= U33(isNat(activate(V2))) ;
  U31(tt,V1,V2) >= U32(isNat(activate(V1)),activate(V2)) ;
  U33(tt) >= tt ;
  U41(tt,N) >= activate(N) ;
  s(X) >= n__s(X) ;
  plus(N,s(M)) >= U51(and(and(isNat(M),n__isNatKind(M)),
                       n__and(n__isNat(N),n__isNatKind(N))),M,N) ;
  plus(N,0) >= U41(and(isNat(N),n__isNatKind(N)),N) ;
  plus(X1,X2) >= n__plus(X1,X2) ;
  U51(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  0 >= n__0 ;
  U61(tt) >= 0 ;
  x(N,s(M)) >= U71(and(and(isNat(M),n__isNatKind(M)),
                    n__and(n__isNat(N),n__isNatKind(N))),M,N) ;
  x(N,0) >= U61(and(isNat(N),n__isNatKind(N))) ;
  x(X1,X2) >= n__x(X1,X2) ;
  U71(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ;
  and(tt,X) >= activate(X) ;
  and(X1,X2) >= n__and(X1,X2) ;
  isNatKind(n__0) >= tt ;
  isNatKind(n__plus(V1,V2)) >= and(isNatKind(activate(V1)),
                                n__isNatKind(activate(V2))) ;
  isNatKind(n__s(V1)) >= isNatKind(activate(V1)) ;
  isNatKind(n__x(V1,V2)) >= and(isNatKind(activate(V1)),
                             n__isNatKind(activate(V2))) ;
  isNatKind(X) >= n__isNatKind(X) ;
  Marked_activate(n__isNatKind(X)) >= Marked_isNatKind(X) ;
  Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1) ;
  Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2) ;
  Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1),activate(X2)) ;
  Marked_activate(n__s(X)) >= Marked_activate(X) ;
  Marked_activate(n__x(X1,X2)) >= Marked_activate(X1) ;
  Marked_activate(n__x(X1,X2)) >= Marked_activate(X2) ;
  Marked_activate(n__x(X1,X2)) >= Marked_x(activate(X1),activate(X2)) ;
  Marked_activate(n__and(X1,X2)) >= Marked_activate(X1) ;
  Marked_activate(n__and(X1,X2)) >= Marked_and(activate(X1),X2) ;
  Marked_activate(n__isNat(X)) >= Marked_isNat(X) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_and(isNatKind(activate(V1)),
                                   n__isNatKind(activate(V2))) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) ;
  Marked_isNat(n__plus(V1,V2)) >= Marked_U11(and(isNatKind(activate(V1)),
                                              n__isNatKind(activate(V2))),
                                   activate(V1),activate(V2)) ;
  Marked_isNat(n__s(V1)) >= Marked_activate(V1) ;
  Marked_isNat(n__s(V1)) >= Marked_isNatKind(activate(V1)) ;
  Marked_isNat(n__s(V1)) >= Marked_U21(isNatKind(activate(V1)),activate(V1)) ;
  Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) ;
  Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) ;
  Marked_isNat(n__x(V1,V2)) >= Marked_and(isNatKind(activate(V1)),
                                n__isNatKind(activate(V2))) ;
  Marked_isNat(n__x(V1,V2)) >= Marked_isNatKind(activate(V1)) ;
  Marked_isNat(n__x(V1,V2)) >= Marked_U31(and(isNatKind(activate(V1)),
                                           n__isNatKind(activate(V2))),
                                activate(V1),activate(V2)) ;
  Marked_and(tt,X) >= Marked_activate(X) ;
  Marked_x(N,s(M)) >= Marked_isNat(M) ;
  Marked_x(N,s(M)) >= Marked_and(isNat(M),n__isNatKind(M)) ;
  Marked_x(N,s(M)) >= Marked_and(and(isNat(M),n__isNatKind(M)),
                       n__and(n__isNat(N),n__isNatKind(N))) ;
  Marked_x(N,s(M)) >= Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                  n__and(n__isNat(N),n__isNatKind(N))),
                       M,N) ;
  Marked_x(N,0) >= Marked_isNat(N) ;
  Marked_x(N,0) >= Marked_and(isNat(N),n__isNatKind(N)) ;
  Marked_isNatKind(n__plus(V1,V2)) >= Marked_activate(V1) ;
  Marked_isNatKind(n__plus(V1,V2)) >= Marked_activate(V2) ;
  Marked_isNatKind(n__plus(V1,V2)) >= Marked_and(isNatKind(activate(V1)),
                                       n__isNatKind(activate(V2))) ;
  Marked_isNatKind(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) ;
  Marked_isNatKind(n__s(V1)) >= Marked_activate(V1) ;
  Marked_isNatKind(n__s(V1)) >= Marked_isNatKind(activate(V1)) ;
  Marked_isNatKind(n__x(V1,V2)) >= Marked_activate(V1) ;
  Marked_isNatKind(n__x(V1,V2)) >= Marked_activate(V2) ;
  Marked_isNatKind(n__x(V1,V2)) >= Marked_and(isNatKind(activate(V1)),
                                    n__isNatKind(activate(V2))) ;
  Marked_isNatKind(n__x(V1,V2)) >= Marked_isNatKind(activate(V1)) ;
  Marked_plus(N,s(M)) >= Marked_isNat(M) ;
  Marked_plus(N,s(M)) >= Marked_and(isNat(M),n__isNatKind(M)) ;
  Marked_plus(N,s(M)) >= Marked_and(and(isNat(M),n__isNatKind(M)),
                          n__and(n__isNat(N),n__isNatKind(N))) ;
  Marked_plus(N,s(M)) >= Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                     n__and(n__isNat(N),n__isNatKind(N))),
                          M,N) ;
  Marked_plus(N,0) >= Marked_isNat(N) ;
  Marked_plus(N,0) >= Marked_and(isNat(N),n__isNatKind(N)) ;
  Marked_plus(N,0) >= Marked_U41(and(isNat(N),n__isNatKind(N)),N) ;
  Marked_U71(tt,M,N) >= Marked_activate(N) ;
  Marked_U71(tt,M,N) >= Marked_activate(M) ;
  Marked_U71(tt,M,N) >= Marked_x(activate(N),activate(M)) ;
  Marked_U71(tt,M,N) >= Marked_plus(x(activate(N),activate(M)),activate(N)) ;
  Marked_U51(tt,M,N) >= Marked_activate(N) ;
  Marked_U51(tt,M,N) >= Marked_activate(M) ;
  Marked_U51(tt,M,N) >= Marked_plus(activate(N),activate(M)) ;
  Marked_U41(tt,N) >= Marked_activate(N) ;
  Marked_U31(tt,V1,V2) >= Marked_activate(V1) ;
  Marked_U31(tt,V1,V2) >= Marked_activate(V2) ;
  Marked_U31(tt,V1,V2) >= Marked_isNat(activate(V1)) ;
  Marked_U31(tt,V1,V2) >= Marked_U32(isNat(activate(V1)),activate(V2)) ;
  Marked_U21(tt,V1) >= Marked_activate(V1) ;
  Marked_U21(tt,V1) >= Marked_isNat(activate(V1)) ;
  Marked_U11(tt,V1,V2) >= Marked_activate(V1) ;
  Marked_U11(tt,V1,V2) >= Marked_activate(V2) ;
  Marked_U11(tt,V1,V2) >= Marked_isNat(activate(V1)) ;
  Marked_U11(tt,V1,V2) >= Marked_U12(isNat(activate(V1)),activate(V2)) ;
  Marked_U32(tt,V2) >= Marked_activate(V2) ;
  Marked_U32(tt,V2) >= Marked_isNat(activate(V2)) ;
  Marked_U12(tt,V2) >= Marked_activate(V2) ;
  Marked_U12(tt,V2) >= Marked_isNat(activate(V2)) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__isNatKind(X)) > Marked_isNatKind(X) ;
 }
{
  Marked_activate(n__plus(X1,X2)) > Marked_activate(X1) ;
 }
{
  Marked_activate(n__plus(X1,X2)) > Marked_activate(X2) ;
 }
{
  Marked_activate(n__plus(X1,X2)) > Marked_plus(activate(X1),activate(X2)) ;
 }
{
  Marked_activate(n__s(X)) > Marked_activate(X) ;
 }
{
  Marked_activate(n__x(X1,X2)) > Marked_activate(X1) ;
 }
{
  Marked_activate(n__x(X1,X2)) > Marked_activate(X2) ;
 }
{
  Marked_activate(n__x(X1,X2)) > Marked_x(activate(X1),activate(X2)) ;
 }
{
  Marked_activate(n__and(X1,X2)) > Marked_activate(X1) ;
 }
{
  Marked_activate(n__and(X1,X2)) > Marked_and(activate(X1),X2) ;
 }
{
  Marked_activate(n__isNat(X)) > Marked_isNat(X) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_activate(V1) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_activate(V2) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_and(isNatKind(activate(V1)),
                                  n__isNatKind(activate(V2))) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_isNatKind(activate(V1)) ;
 }
{
  Marked_isNat(n__plus(V1,V2)) > Marked_U11(and(isNatKind(activate(V1)),
                                             n__isNatKind(activate(V2))),
                                  activate(V1),activate(V2)) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_activate(V1) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_isNatKind(activate(V1)) ;
 }
{
  Marked_isNat(n__s(V1)) > Marked_U21(isNatKind(activate(V1)),activate(V1)) ;
 }
{
  Marked_isNat(n__x(V1,V2)) > Marked_activate(V1) ;
 }
{
  Marked_isNat(n__x(V1,V2)) > Marked_activate(V2) ;
 }
{
  Marked_isNat(n__x(V1,V2)) > Marked_and(isNatKind(activate(V1)),
                               n__isNatKind(activate(V2))) ;
 }
{
  Marked_isNat(n__x(V1,V2)) > Marked_isNatKind(activate(V1)) ;
 }
{
  Marked_isNat(n__x(V1,V2)) > Marked_U31(and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2))),
                               activate(V1),activate(V2)) ;
 }
{
  Marked_and(tt,X) > Marked_activate(X) ;
 }
{
  Marked_x(N,s(M)) > Marked_isNat(M) ;
 }
{
  Marked_x(N,s(M)) > Marked_and(isNat(M),n__isNatKind(M)) ;
 }
{
  Marked_x(N,s(M)) > Marked_and(and(isNat(M),n__isNatKind(M)),
                      n__and(n__isNat(N),n__isNatKind(N))) ;
 }
{
  Marked_x(N,s(M)) > Marked_U71(and(and(isNat(M),n__isNatKind(M)),
                                 n__and(n__isNat(N),n__isNatKind(N))),
                      M,N) ;
 }
{
  Marked_x(N,0) > Marked_isNat(N) ;
 }
{
  Marked_x(N,0) > Marked_and(isNat(N),n__isNatKind(N)) ;
 }
{
  Marked_isNatKind(n__plus(V1,V2)) > Marked_activate(V1) ;
 }
{
  Marked_isNatKind(n__plus(V1,V2)) > Marked_activate(V2) ;
 }
{
  Marked_isNatKind(n__plus(V1,V2)) > Marked_and(isNatKind(activate(V1)),
                                      n__isNatKind(activate(V2))) ;
 }
{
  Marked_isNatKind(n__plus(V1,V2)) > Marked_isNatKind(activate(V1)) ;
 }
{
  Marked_isNatKind(n__s(V1)) > Marked_activate(V1) ;
 }
{
  Marked_isNatKind(n__s(V1)) > Marked_isNatKind(activate(V1)) ;
 }
{
  Marked_isNatKind(n__x(V1,V2)) > Marked_activate(V1) ;
 }
{
  Marked_isNatKind(n__x(V1,V2)) > Marked_activate(V2) ;
 }
{
  Marked_isNatKind(n__x(V1,V2)) > Marked_and(isNatKind(activate(V1)),
                                   n__isNatKind(activate(V2))) ;
 }
{
  Marked_isNatKind(n__x(V1,V2)) > Marked_isNatKind(activate(V1)) ;
 }
{
  Marked_plus(N,s(M)) > Marked_isNat(M) ;
 }
{
  Marked_plus(N,s(M)) > Marked_and(isNat(M),n__isNatKind(M)) ;
 }
{
  Marked_plus(N,s(M)) > Marked_and(and(isNat(M),n__isNatKind(M)),
                         n__and(n__isNat(N),n__isNatKind(N))) ;
 }
{
  Marked_plus(N,s(M)) > Marked_U51(and(and(isNat(M),n__isNatKind(M)),
                                    n__and(n__isNat(N),n__isNatKind(N))),
                         M,N) ;
 }
{
  Marked_plus(N,0) > Marked_isNat(N) ;
 }
{
  Marked_plus(N,0) > Marked_and(isNat(N),n__isNatKind(N)) ;
 }
{
  Marked_plus(N,0) > Marked_U41(and(isNat(N),n__isNatKind(N)),N) ;
 }
{
  Marked_U71(tt,M,N) > Marked_activate(N) ;
 }
{
  Marked_U71(tt,M,N) > Marked_activate(M) ;
 }
{
  Marked_U71(tt,M,N) > Marked_x(activate(N),activate(M)) ;
 }
{
  Marked_U71(tt,M,N) > Marked_plus(x(activate(N),activate(M)),activate(N)) ;
 }
{
  Marked_U51(tt,M,N) > Marked_activate(N) ;
 }
{
  Marked_U51(tt,M,N) > Marked_activate(M) ;
 }
{
  Marked_U51(tt,M,N) > Marked_plus(activate(N),activate(M)) ;
 }
{
  Marked_U41(tt,N) > Marked_activate(N) ;
 }
{
  Marked_U31(tt,V1,V2) > Marked_activate(V1) ;
 }
{
  Marked_U31(tt,V1,V2) > Marked_activate(V2) ;
 }
{
  Marked_U31(tt,V1,V2) > Marked_isNat(activate(V1)) ;
 }
{
  Marked_U31(tt,V1,V2) > Marked_U32(isNat(activate(V1)),activate(V2)) ;
 }
{
  Marked_U21(tt,V1) > Marked_activate(V1) ;
 }
{
  Marked_U21(tt,V1) > Marked_isNat(activate(V1)) ;
 }
{
  Marked_U11(tt,V1,V2) > Marked_activate(V1) ;
 }
{
  Marked_U11(tt,V1,V2) > Marked_activate(V2) ;
 }
{
  Marked_U11(tt,V1,V2) > Marked_isNat(activate(V1)) ;
 }
{
  Marked_U11(tt,V1,V2) > Marked_U12(isNat(activate(V1)),activate(V2)) ;
 }
{
  Marked_U32(tt,V2) > Marked_activate(V2) ;
 }
{
  Marked_U32(tt,V2) > Marked_isNat(activate(V2)) ;
 }
{
  Marked_U12(tt,V2) > Marked_activate(V2) ;
 }
{
  Marked_U12(tt,V2) > Marked_isNat(activate(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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 117.064947 seconds (real time)
Cime Exit Status: 0