- : 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,N) -> activate(N)
[7] U41(tt,M,N) -> s(plus(activate(N),activate(M)))
[8] and(tt,X) -> activate(X)
[9] isNat(n__0) -> tt
[10] isNat(n__plus(V1,V2)) ->
 U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),
  activate(V2))
[11] isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
[12] isNatKind(n__0) -> tt
[13] isNatKind(n__plus(V1,V2)) ->
 and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
[14] isNatKind(n__s(V1)) -> isNatKind(activate(V1))
[15] plus(N,0) -> U31(and(isNat(N),n__isNatKind(N)),N)
[16] plus(N,s(M)) ->
 U41(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),
  M,N)
[17] 0 -> n__0
[18] plus(X1,X2) -> n__plus(X1,X2)
[19] isNatKind(X) -> n__isNatKind(X)
[20] s(X) -> n__s(X)
[21] and(X1,X2) -> n__and(X1,X2)
[22] isNat(X) -> n__isNat(X)
[23] activate(n__0) -> 0
[24] activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
[25] activate(n__isNatKind(X)) -> isNatKind(X)
[26] activate(n__s(X)) -> s(activate(X))
[27] activate(n__and(X1,X2)) -> and(activate(X1),X2)
[28] activate(n__isNat(X)) -> isNat(X)
[29] 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,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_s(plus(activate(N),activate(M)))>
<Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_activate(M)>
<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_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_plus(N,0) , Marked_U31(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_U41(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_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__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__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__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__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__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__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__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__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_U41(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_U31(and(isNat(N),n__isNatKind(N)),N)>
  <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_U41(and(and(isNat(M),n__isNatKind(M)),
                                     n__and(n__isNat(N),n__isNatKind(N))),
                          M,N)> --> <Marked_U41(tt,M,N) , Marked_activate(M)>
  <Marked_plus(N,s(M)) , Marked_U41(and(and(isNat(M),n__isNatKind(M)),
                                     n__and(n__isNat(N),n__isNatKind(N))),
                          M,N)> --> <Marked_U41(tt,M,N) , Marked_activate(N)>
  <Marked_plus(N,s(M)) , Marked_U41(and(and(isNat(M),n__isNatKind(M)),
                                     n__and(n__isNat(N),n__isNatKind(N))),
                          M,N)> 
     --> <Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))>
  <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_U31(and(isNat(N),n__isNatKind(N)),N)> 
     --> <Marked_U31(tt,N) , Marked_activate(N)>
  <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__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__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__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__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__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__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__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__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__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__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__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__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__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__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__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_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,M,N) , Marked_activate(M)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U41(tt,M,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_isNat(M)>
  <Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_and(isNat(M),n__isNatKind(M))>
  <Marked_U41(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_U41(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,s(M)) , Marked_U41(and(and(isNat(M),n__isNatKind(M)),
                                            n__and(n__isNat(N),n__isNatKind(N))),
                                 M,N)>
  <Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_isNat(N)>
  <Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_and(isNat(N),n__isNatKind(N))>
  <Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))> 
     --> <Marked_plus(N,0) , Marked_U31(and(isNat(N),n__isNatKind(N)),N)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNat(X)) , Marked_isNat(X)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__isNatKind(X)) , Marked_isNatKind(X)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X2)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_activate(X1)>
  <Marked_U31(tt,N) , Marked_activate(N)> 
     --> <Marked_activate(n__plus(X1,X2)) , Marked_plus(activate(X1),
                                             activate(X2))>
  <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__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__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__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__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__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__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__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(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__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))) ;
  U31(tt,N) >= activate(N) ;
  s(X) >= n__s(X) ;
  plus(N,s(M)) >= U41(and(and(isNat(M),n__isNatKind(M)),
                       n__and(n__isNat(N),n__isNatKind(N))),M,N) ;
  plus(N,0) >= U31(and(isNat(N),n__isNatKind(N)),N) ;
  plus(X1,X2) >= n__plus(X1,X2) ;
  U41(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  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(X) >= n__isNatKind(X) ;
  0 >= n__0 ;
  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__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_and(tt,X) >= Marked_activate(X) ;
  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_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_U41(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_U31(and(isNat(N),n__isNatKind(N)),N) ;
  Marked_U41(tt,M,N) >= Marked_activate(N) ;
  Marked_U41(tt,M,N) >= Marked_activate(M) ;
  Marked_U41(tt,M,N) >= Marked_plus(activate(N),activate(M)) ;
  Marked_U31(tt,N) >= Marked_activate(N) ;
  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_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__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_and(tt,X) > Marked_activate(X) ;
 }
{
  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_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_U41(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_U31(and(isNat(N),n__isNatKind(N)),N) ;
 }
{
  Marked_U41(tt,M,N) > Marked_activate(N) ;
 }
{
  Marked_U41(tt,M,N) > Marked_activate(M) ;
 }
{
  Marked_U41(tt,M,N) > Marked_plus(activate(N),activate(M)) ;
 }
{
  Marked_U31(tt,N) > Marked_activate(N) ;
 }
{
  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_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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: U12(tt,V2) >= U13(isNat(activate(V2)))
constraint: isNat(n__0) >= tt
constraint: isNat(n__plus(V1,V2)) >= U11(and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2))),
                                      activate(V1),activate(V2))
constraint: isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1))
constraint: isNat(X) >= n__isNat(X)
constraint: activate(n__0) >= 0
constraint: activate(n__isNatKind(X)) >= isNatKind(X)
constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2))
constraint: activate(n__s(X)) >= s(activate(X))
constraint: activate(n__and(X1,X2)) >= and(activate(X1),X2)
constraint: activate(n__isNat(X)) >= isNat(X)
constraint: activate(X) >= X
constraint: U11(tt,V1,V2) >= U12(isNat(activate(V1)),activate(V2))
constraint: U13(tt) >= tt
constraint: U22(tt) >= tt
constraint: U21(tt,V1) >= U22(isNat(activate(V1)))
constraint: U31(tt,N) >= activate(N)
constraint: s(X) >= n__s(X)
constraint: plus(N,s(M)) >= U41(and(and(isNat(M),n__isNatKind(M)),
                                 n__and(n__isNat(N),n__isNatKind(N))),
                             M,N)
constraint: plus(N,0) >= U31(and(isNat(N),n__isNatKind(N)),N)
constraint: plus(X1,X2) >= n__plus(X1,X2)
constraint: U41(tt,M,N) >= s(plus(activate(N),activate(M)))
constraint: and(tt,X) >= activate(X)
constraint: and(X1,X2) >= n__and(X1,X2)
constraint: isNatKind(n__0) >= tt
constraint: isNatKind(n__plus(V1,V2)) >= and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))
constraint: isNatKind(n__s(V1)) >= isNatKind(activate(V1))
constraint: isNatKind(X) >= n__isNatKind(X)
constraint: 0 >= n__0
constraint: Marked_activate(n__isNatKind(X)) >= Marked_isNatKind(X)
constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1)
constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2)
constraint: Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1),
                                                activate(X2))
constraint: Marked_activate(n__s(X)) >= Marked_activate(X)
constraint: Marked_activate(n__and(X1,X2)) >= Marked_activate(X1)
constraint: Marked_activate(n__and(X1,X2)) >= Marked_and(activate(X1),X2)
constraint: Marked_activate(n__isNat(X)) >= Marked_isNat(X)
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1)
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2)
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_and(isNatKind(activate(V1)),
                                             n__isNatKind(activate(V2)))
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1))
constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(and(isNatKind(
                                                            activate(
                                                             V1)),
                                                        n__isNatKind(
                                                         activate(V2))),
                                             activate(V1),activate(V2))
constraint: Marked_isNat(n__s(V1)) >= Marked_activate(V1)
constraint: Marked_isNat(n__s(V1)) >= Marked_isNatKind(activate(V1))
constraint: Marked_isNat(n__s(V1)) >= Marked_U21(isNatKind(activate(V1)),
                                       activate(V1))
constraint: Marked_and(tt,X) >= Marked_activate(X)
constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_activate(V1)
constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_activate(V2)
constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_and(isNatKind(
                                                            activate(
                                                             V1)),
                                                 n__isNatKind(activate(V2)))
constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1))
constraint: Marked_isNatKind(n__s(V1)) >= Marked_activate(V1)
constraint: Marked_isNatKind(n__s(V1)) >= Marked_isNatKind(activate(V1))
constraint: Marked_plus(N,s(M)) >= Marked_isNat(M)
constraint: Marked_plus(N,s(M)) >= Marked_and(isNat(M),n__isNatKind(M))
constraint: Marked_plus(N,s(M)) >= Marked_and(and(isNat(M),n__isNatKind(M)),
                                    n__and(n__isNat(N),n__isNatKind(N)))
constraint: Marked_plus(N,s(M)) >= Marked_U41(and(and(isNat(M),n__isNatKind(M)),
                                               n__and(n__isNat(N),
                                                n__isNatKind(N))),M,N)
constraint: Marked_plus(N,0) >= Marked_isNat(N)
constraint: Marked_plus(N,0) >= Marked_and(isNat(N),n__isNatKind(N))
constraint: Marked_plus(N,0) >= Marked_U31(and(isNat(N),n__isNatKind(N)),N)
constraint: Marked_U41(tt,M,N) >= Marked_activate(N)
constraint: Marked_U41(tt,M,N) >= Marked_activate(M)
constraint: Marked_U41(tt,M,N) >= Marked_plus(activate(N),activate(M))
constraint: Marked_U31(tt,N) >= Marked_activate(N)
constraint: Marked_U21(tt,V1) >= Marked_activate(V1)
constraint: Marked_U21(tt,V1) >= Marked_isNat(activate(V1))
constraint: Marked_U11(tt,V1,V2) >= Marked_activate(V1)
constraint: Marked_U11(tt,V1,V2) >= Marked_activate(V2)
constraint: Marked_U11(tt,V1,V2) >= Marked_isNat(activate(V1))
constraint: Marked_U11(tt,V1,V2) >= Marked_U12(isNat(activate(V1)),
                                     activate(V2))
constraint: Marked_U12(tt,V2) >= Marked_activate(V2)
constraint: Marked_U12(tt,V2) >= Marked_isNat(activate(V2))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <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_and(activate(X1),X2)> 
     --> <Marked_and(tt,X) , Marked_activate(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)>
}
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(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__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))) ;
  U31(tt,N) >= activate(N) ;
  s(X) >= n__s(X) ;
  plus(N,s(M)) >= U41(and(and(isNat(M),n__isNatKind(M)),
                       n__and(n__isNat(N),n__isNatKind(N))),M,N) ;
  plus(N,0) >= U31(and(isNat(N),n__isNatKind(N)),N) ;
  plus(X1,X2) >= n__plus(X1,X2) ;
  U41(tt,M,N) >= s(plus(activate(N),activate(M))) ;
  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(X) >= n__isNatKind(X) ;
  0 >= n__0 ;
  Marked_activate(n__and(X1,X2)) >= Marked_activate(X1) ;
  Marked_activate(n__and(X1,X2)) >= Marked_and(activate(X1),X2) ;
  Marked_and(tt,X) >= Marked_activate(X) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__and(X1,X2)) > Marked_activate(X1) ;
 }
{
  Marked_activate(n__and(X1,X2)) > Marked_and(activate(X1),X2) ;
 }
{
  Marked_and(tt,X) > Marked_activate(X) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: U12(tt,V2) >= U13(isNat(activate(V2)))
constraint: isNat(n__0) >= tt
constraint: isNat(n__plus(V1,V2)) >= U11(and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2))),
                                      activate(V1),activate(V2))
constraint: isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1))
constraint: isNat(X) >= n__isNat(X)
constraint: activate(n__0) >= 0
constraint: activate(n__isNatKind(X)) >= isNatKind(X)
constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2))
constraint: activate(n__s(X)) >= s(activate(X))
constraint: activate(n__and(X1,X2)) >= and(activate(X1),X2)
constraint: activate(n__isNat(X)) >= isNat(X)
constraint: activate(X) >= X
constraint: U11(tt,V1,V2) >= U12(isNat(activate(V1)),activate(V2))
constraint: U13(tt) >= tt
constraint: U22(tt) >= tt
constraint: U21(tt,V1) >= U22(isNat(activate(V1)))
constraint: U31(tt,N) >= activate(N)
constraint: s(X) >= n__s(X)
constraint: plus(N,s(M)) >= U41(and(and(isNat(M),n__isNatKind(M)),
                                 n__and(n__isNat(N),n__isNatKind(N))),
                             M,N)
constraint: plus(N,0) >= U31(and(isNat(N),n__isNatKind(N)),N)
constraint: plus(X1,X2) >= n__plus(X1,X2)
constraint: U41(tt,M,N) >= s(plus(activate(N),activate(M)))
constraint: and(tt,X) >= activate(X)
constraint: and(X1,X2) >= n__and(X1,X2)
constraint: isNatKind(n__0) >= tt
constraint: isNatKind(n__plus(V1,V2)) >= and(isNatKind(activate(V1)),
                                          n__isNatKind(activate(V2)))
constraint: isNatKind(n__s(V1)) >= isNatKind(activate(V1))
constraint: isNatKind(X) >= n__isNatKind(X)
constraint: 0 >= n__0
constraint: Marked_activate(n__and(X1,X2)) >= Marked_activate(X1)
constraint: Marked_activate(n__and(X1,X2)) >= Marked_and(activate(X1),X2)
constraint: Marked_and(tt,X) >= Marked_activate(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
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,N) -> activate(N)
[7] U41(tt,M,N) -> s(plus(activate(N),activate(M)))
[8] and(tt,X) -> activate(X)
[9] isNat(n__0) -> tt
[10] isNat(n__plus(V1,V2)) ->
 U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),
  activate(V2))
[11] isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
[12] isNatKind(n__0) -> tt
[13] isNatKind(n__plus(V1,V2)) ->
 and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
[14] isNatKind(n__s(V1)) -> isNatKind(activate(V1))
[15] plus(N,0) -> U31(and(isNat(N),n__isNatKind(N)),N)
[16] plus(N,s(M)) ->
 U41(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),
  M,N)
[17] 0 -> n__0
[18] plus(X1,X2) -> n__plus(X1,X2)
[19] isNatKind(X) -> n__isNatKind(X)
[20] s(X) -> n__s(X)
[21] and(X1,X2) -> n__and(X1,X2)
[22] isNat(X) -> n__isNat(X)
[23] activate(n__0) -> 0
[24] activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
[25] activate(n__isNatKind(X)) -> isNatKind(X)
[26] activate(n__s(X)) -> s(activate(X))
[27] activate(n__and(X1,X2)) -> and(activate(X1),X2)
[28] activate(n__isNat(X)) -> isNat(X)
[29] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     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,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_s(plus(activate(N),activate(M)))>
<Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_activate(M)>
<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_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_plus(N,0) , Marked_U31(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_U41(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_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__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)>
 ,
 CRITERION: SG
 [ {
      
     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_isNat(activate(V2))>
<Marked_U12(tt,V2) , Marked_activate(V2)>
<Marked_U21(tt,V1) , Marked_isNat(activate(V1))>
<Marked_U21(tt,V1) , Marked_activate(V1)>
<Marked_U31(tt,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_plus(activate(N),activate(M))>
<Marked_U41(tt,M,N) , Marked_activate(N)>
<Marked_U41(tt,M,N) , Marked_activate(M)>
<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_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_plus(N,0) , Marked_U31(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_U41(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_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_activate(X)>
<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)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ U12 ] (X0,X1) = 0; 
 [ n__plus ] (X0,X1) = 2*X1 + 3*X0 + 1; 
 [ U31 ] (X0,X1) = 1*X1; 
 [ tt ] () = 0; 
 [ n__isNat ] (X0) = 1*X0; 
 [ and ] (X0,X1) = 1*X1 + 2*X0; 
 [ Marked_U41 ] (X0,X1,X2) = 3*X2 + 2*X1 + 3; 
 [ activate ] (X0) = 1*X0; 
 [ Marked_U12 ] (X0,X1) = 1*X1 + 1; 
 [ 0 ] () = 1; 
 [ plus ] (X0,X1) = 2*X1 + 3*X0 + 1; 
 [ Marked_plus ] (X0,X1) = 2*X1 + 3*X0; 
 [ U22 ] (X0) = 0; 
 [ Marked_isNat ] (X0) = 1*X0; 
 [ isNatKind ] (X0) = 1*X0; 
 [ Marked_U21 ] (X0,X1) = 1*X1 + 1; 
 [ isNat ] (X0) = 1*X0; 
 [ n__s ] (X0) = 1*X0 + 2; 
 [ s ] (X0) = 1*X0 + 2; 
 [ Marked_isNatKind ] (X0) = 1*X0; 
 [ U13 ] (X0) = 0; 
 [ Marked_activate ] (X0) = 1*X0 + 1; 
 [ n__0 ] () = 1; 
 [ Marked_U31 ] (X0,X1) = 2*X1 + 2; 
 [ U11 ] (X0,X1,X2) = 0; 
 [ n__and ] (X0,X1) = 1*X1 + 2*X0; 
 [ U41 ] (X0,X1,X2) = 3*X2 + 2*X1 + 3; 
 [ U21 ] (X0,X1) = 0; 
 [ Marked_and ] (X0,X1) = 1*X1 + 1; 
 [ n__isNatKind ] (X0) = 1*X0; 
 [ Marked_U11 ] (X0,X1,X2) = 2*X2 + 1*X1 + 1; 
 removing <Marked_U11(tt,V1,V2),Marked_isNat(activate(V1))><Marked_U12(tt,V2),
Marked_isNat(activate(V2))><Marked_U21(tt,V1),Marked_isNat(activate(V1))><
Marked_U31(tt,N),Marked_activate(N)><Marked_U41(tt,M,N),Marked_plus(activate(N),
                                                         activate(M))><
Marked_U41(tt,M,N),Marked_activate(N)><Marked_U41(tt,M,N),Marked_activate(M)><
Marked_isNat(n__plus(V1,V2)),Marked_isNatKind(activate(V1))><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_isNatKind(n__plus(V1,V2)),
Marked_isNatKind(activate(V1))><Marked_isNatKind(n__s(V1)),Marked_isNatKind(
                                                            activate(
                                                             V1))><Marked_isNatKind(
                                                                    n__s(
                                                                    V1)),
Marked_activate(V1)><Marked_plus(N,0),Marked_and(isNat(N),n__isNatKind(N))><
Marked_plus(N,0),Marked_isNat(N)><Marked_plus(N,s(M)),Marked_U41(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_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_activate(X)><Marked_activate(n__isNat(X)),Marked_isNat(X)>
 [ {
      
     DP termination of:
     <Marked_U11(tt,V1,V2) , Marked_U12(isNat(activate(V1)),activate(V2))>
<Marked_U11(tt,V1,V2) , Marked_activate(V1)>
<Marked_U11(tt,V1,V2) , Marked_activate(V2)>
<Marked_U12(tt,V2) , Marked_activate(V2)>
<Marked_U21(tt,V1) , Marked_activate(V1)>
<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_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_isNatKind(n__plus(V1,V2)) , Marked_and(isNatKind(activate(V1)),
                                     n__isNatKind(activate(V2)))>
<Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V1)>
<Marked_isNatKind(n__plus(V1,V2)) , Marked_activate(V2)>
<Marked_plus(N,0) , Marked_U31(and(isNat(N),n__isNatKind(N)),N)>
<Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
<Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_and(tt,X) , Marked_activate(X)>
<Marked_activate(n__and(X1,X2)) , Marked_and(activate(X1),X2)>
<Marked_activate(n__and(X1,X2)) , Marked_activate(X1)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ U12 ] (X0,X1) = 1*X0; 
 [ n__plus ] (X0,X1) = 2*X1 + 2*X0 + 1; 
 [ U31 ] (X0,X1) = 2*X1 + 1; 
 [ tt ] () = 0; 
 [ n__isNat ] (X0) = 1; 
 [ and ] (X0,X1) = 1*X1 + 2*X0 + 1; 
 [ activate ] (X0) = 1*X0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 2*X1 + 2*X0 + 1; 
 [ U22 ] (X0) = 0; 
 [ isNatKind ] (X0) = 2*X0; 
 [ isNat ] (X0) = 1; 
 [ n__s ] (X0) = 1*X0; 
 [ s ] (X0) = 1*X0; 
 [ U13 ] (X0) = 0; 
 [ Marked_activate ] (X0) = 1*X0; 
 [ n__0 ] () = 0; 
 [ U11 ] (X0,X1,X2) = 1; 
 [ n__and ] (X0,X1) = 1*X1 + 2*X0 + 1; 
 [ U41 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1; 
 [ U21 ] (X0,X1) = 0; 
 [ Marked_and ] (X0,X1) = 1*X1; 
 [ n__isNatKind ] (X0) = 2*X0; 
 removing <Marked_activate(n__and(X1,X2)),Marked_and(activate(X1),X2)><
Marked_activate(n__and(X1,X2)),Marked_activate(X1)>
 [ {
      
     DP termination of:
     <Marked_and(tt,X) , Marked_activate(X)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.739728 seconds (real time)
Cime Exit Status: 0