MAYBE

Problem:
 U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
 U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
 U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
 U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
 U15(tt(),V2) -> U16(isNat(activate(V2)))
 U16(tt()) -> tt()
 U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
 U22(tt(),V1) -> U23(isNat(activate(V1)))
 U23(tt()) -> tt()
 U31(tt(),V2) -> U32(isNatKind(activate(V2)))
 U32(tt()) -> tt()
 U41(tt()) -> tt()
 U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
 U52(tt(),N) -> activate(N)
 U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
 U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
 U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
 U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
 isNat(n__0()) -> tt()
 isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
 isNatKind(n__0()) -> tt()
 isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
 isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
 plus(N,0()) -> U51(isNat(N),N)
 plus(N,s(M)) -> U61(isNat(M),M,N)
 0() -> n__0()
 plus(X1,X2) -> n__plus(X1,X2)
 s(X) -> n__s(X)
 activate(n__0()) -> 0()
 activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   U11#(tt(),V1,V2) -> activate#(V2)
   U11#(tt(),V1,V2) -> activate#(V1)
   U11#(tt(),V1,V2) -> isNatKind#(activate(V1))
   U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2))
   U12#(tt(),V1,V2) -> activate#(V1)
   U12#(tt(),V1,V2) -> activate#(V2)
   U12#(tt(),V1,V2) -> isNatKind#(activate(V2))
   U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2))
   U13#(tt(),V1,V2) -> activate#(V1)
   U13#(tt(),V1,V2) -> activate#(V2)
   U13#(tt(),V1,V2) -> isNatKind#(activate(V2))
   U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2))
   U14#(tt(),V1,V2) -> activate#(V2)
   U14#(tt(),V1,V2) -> activate#(V1)
   U14#(tt(),V1,V2) -> isNat#(activate(V1))
   U14#(tt(),V1,V2) -> U15#(isNat(activate(V1)),activate(V2))
   U15#(tt(),V2) -> activate#(V2)
   U15#(tt(),V2) -> isNat#(activate(V2))
   U15#(tt(),V2) -> U16#(isNat(activate(V2)))
   U21#(tt(),V1) -> activate#(V1)
   U21#(tt(),V1) -> isNatKind#(activate(V1))
   U21#(tt(),V1) -> U22#(isNatKind(activate(V1)),activate(V1))
   U22#(tt(),V1) -> activate#(V1)
   U22#(tt(),V1) -> isNat#(activate(V1))
   U22#(tt(),V1) -> U23#(isNat(activate(V1)))
   U31#(tt(),V2) -> activate#(V2)
   U31#(tt(),V2) -> isNatKind#(activate(V2))
   U31#(tt(),V2) -> U32#(isNatKind(activate(V2)))
   U51#(tt(),N) -> activate#(N)
   U51#(tt(),N) -> isNatKind#(activate(N))
   U51#(tt(),N) -> U52#(isNatKind(activate(N)),activate(N))
   U52#(tt(),N) -> activate#(N)
   U61#(tt(),M,N) -> activate#(N)
   U61#(tt(),M,N) -> activate#(M)
   U61#(tt(),M,N) -> isNatKind#(activate(M))
   U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N))
   U62#(tt(),M,N) -> activate#(M)
   U62#(tt(),M,N) -> activate#(N)
   U62#(tt(),M,N) -> isNat#(activate(N))
   U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N))
   U63#(tt(),M,N) -> activate#(M)
   U63#(tt(),M,N) -> activate#(N)
   U63#(tt(),M,N) -> isNatKind#(activate(N))
   U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N))
   U64#(tt(),M,N) -> activate#(M)
   U64#(tt(),M,N) -> activate#(N)
   U64#(tt(),M,N) -> plus#(activate(N),activate(M))
   U64#(tt(),M,N) -> s#(plus(activate(N),activate(M)))
   isNat#(n__plus(V1,V2)) -> activate#(V2)
   isNat#(n__plus(V1,V2)) -> activate#(V1)
   isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
   isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
   isNat#(n__s(V1)) -> activate#(V1)
   isNat#(n__s(V1)) -> isNatKind#(activate(V1))
   isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
   isNatKind#(n__plus(V1,V2)) -> activate#(V2)
   isNatKind#(n__plus(V1,V2)) -> activate#(V1)
   isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
   isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
   isNatKind#(n__s(V1)) -> activate#(V1)
   isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
   isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
   plus#(N,0()) -> isNat#(N)
   plus#(N,0()) -> U51#(isNat(N),N)
   plus#(N,s(M)) -> isNat#(M)
   plus#(N,s(M)) -> U61#(isNat(M),M,N)
   activate#(n__0()) -> 0#()
   activate#(n__plus(X1,X2)) -> activate#(X2)
   activate#(n__plus(X1,X2)) -> activate#(X1)
   activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
  TRS:
   U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
   U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
   U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
   U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
   U15(tt(),V2) -> U16(isNat(activate(V2)))
   U16(tt()) -> tt()
   U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
   U22(tt(),V1) -> U23(isNat(activate(V1)))
   U23(tt()) -> tt()
   U31(tt(),V2) -> U32(isNatKind(activate(V2)))
   U32(tt()) -> tt()
   U41(tt()) -> tt()
   U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
   U52(tt(),N) -> activate(N)
   U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
   U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
   U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
   U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
   isNat(n__0()) -> tt()
   isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
   isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
   isNatKind(n__0()) -> tt()
   isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
   isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
   plus(N,0()) -> U51(isNat(N),N)
   plus(N,s(M)) -> U61(isNat(M),M,N)
   0() -> n__0()
   plus(X1,X2) -> n__plus(X1,X2)
   s(X) -> n__s(X)
   activate(n__0()) -> 0()
   activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X
  CDG Processor:
   DPs:
    U11#(tt(),V1,V2) -> activate#(V2)
    U11#(tt(),V1,V2) -> activate#(V1)
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1))
    U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2))
    U12#(tt(),V1,V2) -> activate#(V1)
    U12#(tt(),V1,V2) -> activate#(V2)
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2))
    U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2))
    U13#(tt(),V1,V2) -> activate#(V1)
    U13#(tt(),V1,V2) -> activate#(V2)
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2))
    U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2))
    U14#(tt(),V1,V2) -> activate#(V2)
    U14#(tt(),V1,V2) -> activate#(V1)
    U14#(tt(),V1,V2) -> isNat#(activate(V1))
    U14#(tt(),V1,V2) -> U15#(isNat(activate(V1)),activate(V2))
    U15#(tt(),V2) -> activate#(V2)
    U15#(tt(),V2) -> isNat#(activate(V2))
    U15#(tt(),V2) -> U16#(isNat(activate(V2)))
    U21#(tt(),V1) -> activate#(V1)
    U21#(tt(),V1) -> isNatKind#(activate(V1))
    U21#(tt(),V1) -> U22#(isNatKind(activate(V1)),activate(V1))
    U22#(tt(),V1) -> activate#(V1)
    U22#(tt(),V1) -> isNat#(activate(V1))
    U22#(tt(),V1) -> U23#(isNat(activate(V1)))
    U31#(tt(),V2) -> activate#(V2)
    U31#(tt(),V2) -> isNatKind#(activate(V2))
    U31#(tt(),V2) -> U32#(isNatKind(activate(V2)))
    U51#(tt(),N) -> activate#(N)
    U51#(tt(),N) -> isNatKind#(activate(N))
    U51#(tt(),N) -> U52#(isNatKind(activate(N)),activate(N))
    U52#(tt(),N) -> activate#(N)
    U61#(tt(),M,N) -> activate#(N)
    U61#(tt(),M,N) -> activate#(M)
    U61#(tt(),M,N) -> isNatKind#(activate(M))
    U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N))
    U62#(tt(),M,N) -> activate#(M)
    U62#(tt(),M,N) -> activate#(N)
    U62#(tt(),M,N) -> isNat#(activate(N))
    U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N))
    U63#(tt(),M,N) -> activate#(M)
    U63#(tt(),M,N) -> activate#(N)
    U63#(tt(),M,N) -> isNatKind#(activate(N))
    U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N))
    U64#(tt(),M,N) -> activate#(M)
    U64#(tt(),M,N) -> activate#(N)
    U64#(tt(),M,N) -> plus#(activate(N),activate(M))
    U64#(tt(),M,N) -> s#(plus(activate(N),activate(M)))
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
    isNat#(n__s(V1)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNatKind#(activate(V1))
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    isNatKind#(n__s(V1)) -> activate#(V1)
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    plus#(N,0()) -> isNat#(N)
    plus#(N,0()) -> U51#(isNat(N),N)
    plus#(N,s(M)) -> isNat#(M)
    plus#(N,s(M)) -> U61#(isNat(M),M,N)
    activate#(n__0()) -> 0#()
    activate#(n__plus(X1,X2)) -> activate#(X2)
    activate#(n__plus(X1,X2)) -> activate#(X1)
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
   TRS:
    U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
    U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
    U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
    U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
    U15(tt(),V2) -> U16(isNat(activate(V2)))
    U16(tt()) -> tt()
    U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
    U22(tt(),V1) -> U23(isNat(activate(V1)))
    U23(tt()) -> tt()
    U31(tt(),V2) -> U32(isNatKind(activate(V2)))
    U32(tt()) -> tt()
    U41(tt()) -> tt()
    U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
    U52(tt(),N) -> activate(N)
    U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
    U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
    U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
    U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
    isNat(n__0()) -> tt()
    isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
    isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
    isNatKind(n__0()) -> tt()
    isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
    isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
    plus(N,0()) -> U51(isNat(N),N)
    plus(N,s(M)) -> U61(isNat(M),M,N)
    0() -> n__0()
    plus(X1,X2) -> n__plus(X1,X2)
    s(X) -> n__s(X)
    activate(n__0()) -> 0()
    activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
    activate(n__s(X)) -> s(activate(X))
    activate(X) -> X
   graph:
    plus#(N,0()) -> U51#(isNat(N),N) ->
    U51#(tt(),N) -> activate#(N)
    plus#(N,0()) -> U51#(isNat(N),N) ->
    U51#(tt(),N) -> isNatKind#(activate(N))
    plus#(N,0()) -> U51#(isNat(N),N) ->
    U51#(tt(),N) -> U52#(isNatKind(activate(N)),activate(N))
    plus#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V2)
    plus#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V1)
    plus#(N,0()) -> isNat#(N) ->
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    plus#(N,0()) -> isNat#(N) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
    plus#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> activate#(V1)
    plus#(N,0()) -> isNat#(N) ->
    isNat#(n__s(V1)) -> isNatKind#(activate(V1))
    plus#(N,0()) -> isNat#(N) ->
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
    plus#(N,s(M)) -> U61#(isNat(M),M,N) ->
    U61#(tt(),M,N) -> activate#(N)
    plus#(N,s(M)) -> U61#(isNat(M),M,N) ->
    U61#(tt(),M,N) -> activate#(M)
    plus#(N,s(M)) -> U61#(isNat(M),M,N) ->
    U61#(tt(),M,N) -> isNatKind#(activate(M))
    plus#(N,s(M)) -> U61#(isNat(M),M,N) ->
    U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N))
    plus#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> activate#(V2)
    plus#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> activate#(V1)
    plus#(N,s(M)) -> isNat#(M) ->
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    plus#(N,s(M)) -> isNat#(M) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
    plus#(N,s(M)) -> isNat#(M) -> isNat#(n__s(V1)) -> activate#(V1)
    plus#(N,s(M)) -> isNat#(M) ->
    isNat#(n__s(V1)) -> isNatKind#(activate(V1))
    plus#(N,s(M)) -> isNat#(M) ->
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
    U64#(tt(),M,N) -> plus#(activate(N),activate(M)) ->
    plus#(N,0()) -> isNat#(N)
    U64#(tt(),M,N) -> plus#(activate(N),activate(M)) ->
    plus#(N,0()) -> U51#(isNat(N),N)
    U64#(tt(),M,N) -> plus#(activate(N),activate(M)) ->
    plus#(N,s(M)) -> isNat#(M)
    U64#(tt(),M,N) -> plus#(activate(N),activate(M)) ->
    plus#(N,s(M)) -> U61#(isNat(M),M,N)
    U64#(tt(),M,N) -> activate#(M) -> activate#(n__0()) -> 0#()
    U64#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U64#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U64#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U64#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> activate#(X)
    U64#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> s#(activate(X))
    U64#(tt(),M,N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U64#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U64#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U64#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U64#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> activate#(X)
    U64#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N)) ->
    U64#(tt(),M,N) -> activate#(M)
    U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N)) ->
    U64#(tt(),M,N) -> activate#(N)
    U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N)) ->
    U64#(tt(),M,N) -> plus#(activate(N),activate(M))
    U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N)) ->
    U64#(tt(),M,N) -> s#(plus(activate(N),activate(M)))
    U63#(tt(),M,N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    U63#(tt(),M,N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    U63#(tt(),M,N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U63#(tt(),M,N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    U63#(tt(),M,N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    U63#(tt(),M,N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    U63#(tt(),M,N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    U63#(tt(),M,N) -> activate#(M) -> activate#(n__0()) -> 0#()
    U63#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U63#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U63#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U63#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> activate#(X)
    U63#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> s#(activate(X))
    U63#(tt(),M,N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U63#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U63#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U63#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U63#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> activate#(X)
    U63#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N)) ->
    U63#(tt(),M,N) -> activate#(M)
    U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N)) ->
    U63#(tt(),M,N) -> activate#(N)
    U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N)) ->
    U63#(tt(),M,N) -> isNatKind#(activate(N))
    U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N)) ->
    U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N))
    U62#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    U62#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    U62#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U62#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
    U62#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    U62#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> isNatKind#(activate(V1))
    U62#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
    U62#(tt(),M,N) -> activate#(M) -> activate#(n__0()) -> 0#()
    U62#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U62#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U62#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U62#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> activate#(X)
    U62#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> s#(activate(X))
    U62#(tt(),M,N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U62#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U62#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U62#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U62#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> activate#(X)
    U62#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N)) ->
    U62#(tt(),M,N) -> activate#(M)
    U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N)) ->
    U62#(tt(),M,N) -> activate#(N)
    U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N)) ->
    U62#(tt(),M,N) -> isNat#(activate(N))
    U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N)) ->
    U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N))
    U61#(tt(),M,N) -> isNatKind#(activate(M)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    U61#(tt(),M,N) -> isNatKind#(activate(M)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    U61#(tt(),M,N) -> isNatKind#(activate(M)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U61#(tt(),M,N) -> isNatKind#(activate(M)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    U61#(tt(),M,N) -> isNatKind#(activate(M)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    U61#(tt(),M,N) -> isNatKind#(activate(M)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    U61#(tt(),M,N) -> isNatKind#(activate(M)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    U61#(tt(),M,N) -> activate#(M) -> activate#(n__0()) -> 0#()
    U61#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U61#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U61#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U61#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> activate#(X)
    U61#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> s#(activate(X))
    U61#(tt(),M,N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U61#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U61#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U61#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U61#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> activate#(X)
    U61#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    U52#(tt(),N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U52#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U52#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U52#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U52#(tt(),N) -> activate#(N) -> activate#(n__s(X)) -> activate#(X)
    U52#(tt(),N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    U51#(tt(),N) -> U52#(isNatKind(activate(N)),activate(N)) ->
    U52#(tt(),N) -> activate#(N)
    U51#(tt(),N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    U51#(tt(),N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    U51#(tt(),N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U51#(tt(),N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    U51#(tt(),N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    U51#(tt(),N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    U51#(tt(),N) -> isNatKind#(activate(N)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    U51#(tt(),N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U51#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U51#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U51#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U51#(tt(),N) -> activate#(N) -> activate#(n__s(X)) -> activate#(X)
    U51#(tt(),N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    U31#(tt(),V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    U31#(tt(),V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    U31#(tt(),V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U31#(tt(),V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    U31#(tt(),V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    U31#(tt(),V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    U31#(tt(),V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    U31#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U31#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U31#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U31#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U31#(tt(),V2) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    U31#(tt(),V2) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(activate(X))
    U22#(tt(),V1) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    U22#(tt(),V1) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    U22#(tt(),V1) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U22#(tt(),V1) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
    U22#(tt(),V1) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    U22#(tt(),V1) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> isNatKind#(activate(V1))
    U22#(tt(),V1) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
    U22#(tt(),V1) -> activate#(V1) -> activate#(n__0()) -> 0#()
    U22#(tt(),V1) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U22#(tt(),V1) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U22#(tt(),V1) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U22#(tt(),V1) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    U22#(tt(),V1) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    U21#(tt(),V1) -> U22#(isNatKind(activate(V1)),activate(V1)) ->
    U22#(tt(),V1) -> activate#(V1)
    U21#(tt(),V1) -> U22#(isNatKind(activate(V1)),activate(V1)) ->
    U22#(tt(),V1) -> isNat#(activate(V1))
    U21#(tt(),V1) -> U22#(isNatKind(activate(V1)),activate(V1)) ->
    U22#(tt(),V1) -> U23#(isNat(activate(V1)))
    U21#(tt(),V1) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    U21#(tt(),V1) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    U21#(tt(),V1) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U21#(tt(),V1) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    U21#(tt(),V1) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    U21#(tt(),V1) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    U21#(tt(),V1) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    U21#(tt(),V1) -> activate#(V1) -> activate#(n__0()) -> 0#()
    U21#(tt(),V1) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U21#(tt(),V1) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U21#(tt(),V1) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U21#(tt(),V1) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    U21#(tt(),V1) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    U15#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    U15#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    U15#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U15#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
    U15#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    U15#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__s(V1)) -> isNatKind#(activate(V1))
    U15#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
    U15#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U15#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U15#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U15#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U15#(tt(),V2) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    U15#(tt(),V2) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(activate(X))
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) ->
    U21#(tt(),V1) -> activate#(V1)
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) ->
    U21#(tt(),V1) -> isNatKind#(activate(V1))
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) ->
    U21#(tt(),V1) -> U22#(isNatKind(activate(V1)),activate(V1))
    isNat#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    isNat#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    isNat#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    isNat#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    isNat#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__0()) -> 0#()
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    isNat#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__0()) -> 0#()
    isNat#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    isNat#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    isNat#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    isNat#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    isNat#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(activate(X))
    isNat#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__0()) -> 0#()
    isNat#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    isNat#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    isNat#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    isNat#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    isNat#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2)) ->
    U11#(tt(),V1,V2) -> activate#(V2)
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2)) ->
    U11#(tt(),V1,V2) -> activate#(V1)
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2)) ->
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1))
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2)) ->
    U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2))
    U14#(tt(),V1,V2) -> U15#(isNat(activate(V1)),activate(V2)) ->
    U15#(tt(),V2) -> activate#(V2)
    U14#(tt(),V1,V2) -> U15#(isNat(activate(V1)),activate(V2)) ->
    U15#(tt(),V2) -> isNat#(activate(V2))
    U14#(tt(),V1,V2) -> U15#(isNat(activate(V1)),activate(V2)) ->
    U15#(tt(),V2) -> U16#(isNat(activate(V2)))
    U14#(tt(),V1,V2) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    U14#(tt(),V1,V2) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    U14#(tt(),V1,V2) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U14#(tt(),V1,V2) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
    U14#(tt(),V1,V2) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    U14#(tt(),V1,V2) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> isNatKind#(activate(V1))
    U14#(tt(),V1,V2) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
    U14#(tt(),V1,V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U14#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U14#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U14#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U14#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    U14#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(activate(X))
    U14#(tt(),V1,V2) -> activate#(V1) -> activate#(n__0()) -> 0#()
    U14#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U14#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U14#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U14#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    U14#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2)) ->
    U14#(tt(),V1,V2) -> activate#(V2)
    U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2)) ->
    U14#(tt(),V1,V2) -> activate#(V1)
    U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2)) ->
    U14#(tt(),V1,V2) -> isNat#(activate(V1))
    U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2)) ->
    U14#(tt(),V1,V2) -> U15#(isNat(activate(V1)),activate(V2))
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    U13#(tt(),V1,V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U13#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U13#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U13#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U13#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    U13#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(activate(X))
    U13#(tt(),V1,V2) -> activate#(V1) -> activate#(n__0()) -> 0#()
    U13#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U13#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U13#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U13#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    U13#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2)) ->
    U13#(tt(),V1,V2) -> activate#(V1)
    U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2)) ->
    U13#(tt(),V1,V2) -> activate#(V2)
    U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2)) ->
    U13#(tt(),V1,V2) -> isNatKind#(activate(V2))
    U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2)) ->
    U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2))
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    U12#(tt(),V1,V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U12#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U12#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U12#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U12#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    U12#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(activate(X))
    U12#(tt(),V1,V2) -> activate#(V1) -> activate#(n__0()) -> 0#()
    U12#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U12#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U12#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U12#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    U12#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    isNatKind#(n__s(V1)) -> activate#(V1) ->
    activate#(n__0()) -> 0#()
    isNatKind#(n__s(V1)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    isNatKind#(n__s(V1)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    isNatKind#(n__s(V1)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    isNatKind#(n__s(V1)) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    isNatKind#(n__s(V1)) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2)) ->
    U31#(tt(),V2) -> activate#(V2)
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2)) ->
    U31#(tt(),V2) -> isNatKind#(activate(V2))
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2)) ->
    U31#(tt(),V2) -> U32#(isNatKind(activate(V2)))
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    isNatKind#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__0()) -> 0#()
    isNatKind#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    isNatKind#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    isNatKind#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    isNatKind#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    isNatKind#(n__plus(V1,V2)) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(activate(X))
    isNatKind#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__0()) -> 0#()
    isNatKind#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    isNatKind#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    isNatKind#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    isNatKind#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    isNatKind#(n__plus(V1,V2)) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__0()) -> 0#()
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2)) ->
    plus#(N,0()) -> isNat#(N)
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2)) ->
    plus#(N,0()) -> U51#(isNat(N),N)
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2)) ->
    plus#(N,s(M)) -> isNat#(M)
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2)) ->
    plus#(N,s(M)) -> U61#(isNat(M),M,N)
    activate#(n__plus(X1,X2)) -> activate#(X2) ->
    activate#(n__0()) -> 0#()
    activate#(n__plus(X1,X2)) -> activate#(X2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    activate#(n__plus(X1,X2)) -> activate#(X2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    activate#(n__plus(X1,X2)) -> activate#(X2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    activate#(n__plus(X1,X2)) -> activate#(X2) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__plus(X1,X2)) -> activate#(X2) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__plus(X1,X2)) -> activate#(X1) ->
    activate#(n__0()) -> 0#()
    activate#(n__plus(X1,X2)) -> activate#(X1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    activate#(n__plus(X1,X2)) -> activate#(X1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    activate#(n__plus(X1,X2)) -> activate#(X1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    activate#(n__plus(X1,X2)) -> activate#(X1) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__plus(X1,X2)) -> activate#(X1) ->
    activate#(n__s(X)) -> s#(activate(X))
    U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2)) ->
    U12#(tt(),V1,V2) -> activate#(V1)
    U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2)) ->
    U12#(tt(),V1,V2) -> activate#(V2)
    U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2)) ->
    U12#(tt(),V1,V2) -> isNatKind#(activate(V2))
    U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2)) ->
    U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2))
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V2)
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> activate#(V1)
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> activate#(V1)
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
    U11#(tt(),V1,V2) -> isNatKind#(activate(V1)) ->
    isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
    U11#(tt(),V1,V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U11#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U11#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U11#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U11#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    U11#(tt(),V1,V2) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(activate(X))
    U11#(tt(),V1,V2) -> activate#(V1) -> activate#(n__0()) -> 0#()
    U11#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U11#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U11#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U11#(tt(),V1,V2) -> activate#(V1) ->
    activate#(n__s(X)) -> activate#(X)
    U11#(tt(),V1,V2) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X))
   Restore Modifier:
    DPs:
     U11#(tt(),V1,V2) -> activate#(V2)
     U11#(tt(),V1,V2) -> activate#(V1)
     U11#(tt(),V1,V2) -> isNatKind#(activate(V1))
     U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2))
     U12#(tt(),V1,V2) -> activate#(V1)
     U12#(tt(),V1,V2) -> activate#(V2)
     U12#(tt(),V1,V2) -> isNatKind#(activate(V2))
     U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2))
     U13#(tt(),V1,V2) -> activate#(V1)
     U13#(tt(),V1,V2) -> activate#(V2)
     U13#(tt(),V1,V2) -> isNatKind#(activate(V2))
     U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2))
     U14#(tt(),V1,V2) -> activate#(V2)
     U14#(tt(),V1,V2) -> activate#(V1)
     U14#(tt(),V1,V2) -> isNat#(activate(V1))
     U14#(tt(),V1,V2) -> U15#(isNat(activate(V1)),activate(V2))
     U15#(tt(),V2) -> activate#(V2)
     U15#(tt(),V2) -> isNat#(activate(V2))
     U15#(tt(),V2) -> U16#(isNat(activate(V2)))
     U21#(tt(),V1) -> activate#(V1)
     U21#(tt(),V1) -> isNatKind#(activate(V1))
     U21#(tt(),V1) -> U22#(isNatKind(activate(V1)),activate(V1))
     U22#(tt(),V1) -> activate#(V1)
     U22#(tt(),V1) -> isNat#(activate(V1))
     U22#(tt(),V1) -> U23#(isNat(activate(V1)))
     U31#(tt(),V2) -> activate#(V2)
     U31#(tt(),V2) -> isNatKind#(activate(V2))
     U31#(tt(),V2) -> U32#(isNatKind(activate(V2)))
     U51#(tt(),N) -> activate#(N)
     U51#(tt(),N) -> isNatKind#(activate(N))
     U51#(tt(),N) -> U52#(isNatKind(activate(N)),activate(N))
     U52#(tt(),N) -> activate#(N)
     U61#(tt(),M,N) -> activate#(N)
     U61#(tt(),M,N) -> activate#(M)
     U61#(tt(),M,N) -> isNatKind#(activate(M))
     U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N))
     U62#(tt(),M,N) -> activate#(M)
     U62#(tt(),M,N) -> activate#(N)
     U62#(tt(),M,N) -> isNat#(activate(N))
     U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N))
     U63#(tt(),M,N) -> activate#(M)
     U63#(tt(),M,N) -> activate#(N)
     U63#(tt(),M,N) -> isNatKind#(activate(N))
     U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N))
     U64#(tt(),M,N) -> activate#(M)
     U64#(tt(),M,N) -> activate#(N)
     U64#(tt(),M,N) -> plus#(activate(N),activate(M))
     U64#(tt(),M,N) -> s#(plus(activate(N),activate(M)))
     isNat#(n__plus(V1,V2)) -> activate#(V2)
     isNat#(n__plus(V1,V2)) -> activate#(V1)
     isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
     isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
     isNat#(n__s(V1)) -> activate#(V1)
     isNat#(n__s(V1)) -> isNatKind#(activate(V1))
     isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
     isNatKind#(n__plus(V1,V2)) -> activate#(V2)
     isNatKind#(n__plus(V1,V2)) -> activate#(V1)
     isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
     isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
     isNatKind#(n__s(V1)) -> activate#(V1)
     isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
     isNatKind#(n__s(V1)) -> U41#(isNatKind(activate(V1)))
     plus#(N,0()) -> isNat#(N)
     plus#(N,0()) -> U51#(isNat(N),N)
     plus#(N,s(M)) -> isNat#(M)
     plus#(N,s(M)) -> U61#(isNat(M),M,N)
     activate#(n__0()) -> 0#()
     activate#(n__plus(X1,X2)) -> activate#(X2)
     activate#(n__plus(X1,X2)) -> activate#(X1)
     activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
     activate#(n__s(X)) -> activate#(X)
     activate#(n__s(X)) -> s#(activate(X))
    TRS:
     U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
     U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
     U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
     U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
     U15(tt(),V2) -> U16(isNat(activate(V2)))
     U16(tt()) -> tt()
     U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
     U22(tt(),V1) -> U23(isNat(activate(V1)))
     U23(tt()) -> tt()
     U31(tt(),V2) -> U32(isNatKind(activate(V2)))
     U32(tt()) -> tt()
     U41(tt()) -> tt()
     U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
     U52(tt(),N) -> activate(N)
     U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
     U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
     U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
     U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
     isNat(n__0()) -> tt()
     isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
     isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
     isNatKind(n__0()) -> tt()
     isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
     isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
     plus(N,0()) -> U51(isNat(N),N)
     plus(N,s(M)) -> U61(isNat(M),M,N)
     0() -> n__0()
     plus(X1,X2) -> n__plus(X1,X2)
     s(X) -> n__s(X)
     activate(n__0()) -> 0()
     activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
    SCC Processor:
     #sccs: 1
     #rules: 65
     #arcs: 368/5184
     DPs:
      plus#(N,0()) -> U51#(isNat(N),N)
      U51#(tt(),N) -> U52#(isNatKind(activate(N)),activate(N))
      U52#(tt(),N) -> activate#(N)
      activate#(n__s(X)) -> activate#(X)
      activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
      plus#(N,s(M)) -> U61#(isNat(M),M,N)
      U61#(tt(),M,N) -> U62#(isNatKind(activate(M)),activate(M),activate(N))
      U62#(tt(),M,N) -> U63#(isNat(activate(N)),activate(M),activate(N))
      U63#(tt(),M,N) -> U64#(isNatKind(activate(N)),activate(M),activate(N))
      U64#(tt(),M,N) -> plus#(activate(N),activate(M))
      plus#(N,s(M)) -> isNat#(M)
      isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1))
      U21#(tt(),V1) -> U22#(isNatKind(activate(V1)),activate(V1))
      U22#(tt(),V1) -> isNat#(activate(V1))
      isNat#(n__s(V1)) -> isNatKind#(activate(V1))
      isNatKind#(n__s(V1)) -> isNatKind#(activate(V1))
      isNatKind#(n__s(V1)) -> activate#(V1)
      activate#(n__plus(X1,X2)) -> activate#(X1)
      activate#(n__plus(X1,X2)) -> activate#(X2)
      isNatKind#(n__plus(V1,V2)) -> U31#(isNatKind(activate(V1)),activate(V2))
      U31#(tt(),V2) -> isNatKind#(activate(V2))
      isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
      isNatKind#(n__plus(V1,V2)) -> activate#(V1)
      isNatKind#(n__plus(V1,V2)) -> activate#(V2)
      U31#(tt(),V2) -> activate#(V2)
      isNat#(n__s(V1)) -> activate#(V1)
      isNat#(n__plus(V1,V2)) -> U11#(isNatKind(activate(V1)),activate(V1),activate(V2))
      U11#(tt(),V1,V2) -> U12#(isNatKind(activate(V1)),activate(V1),activate(V2))
      U12#(tt(),V1,V2) -> U13#(isNatKind(activate(V2)),activate(V1),activate(V2))
      U13#(tt(),V1,V2) -> U14#(isNatKind(activate(V2)),activate(V1),activate(V2))
      U14#(tt(),V1,V2) -> U15#(isNat(activate(V1)),activate(V2))
      U15#(tt(),V2) -> isNat#(activate(V2))
      isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1))
      isNat#(n__plus(V1,V2)) -> activate#(V1)
      isNat#(n__plus(V1,V2)) -> activate#(V2)
      U15#(tt(),V2) -> activate#(V2)
      U14#(tt(),V1,V2) -> isNat#(activate(V1))
      U14#(tt(),V1,V2) -> activate#(V1)
      U14#(tt(),V1,V2) -> activate#(V2)
      U13#(tt(),V1,V2) -> isNatKind#(activate(V2))
      U13#(tt(),V1,V2) -> activate#(V2)
      U13#(tt(),V1,V2) -> activate#(V1)
      U12#(tt(),V1,V2) -> isNatKind#(activate(V2))
      U12#(tt(),V1,V2) -> activate#(V2)
      U12#(tt(),V1,V2) -> activate#(V1)
      U11#(tt(),V1,V2) -> isNatKind#(activate(V1))
      U11#(tt(),V1,V2) -> activate#(V1)
      U11#(tt(),V1,V2) -> activate#(V2)
      U22#(tt(),V1) -> activate#(V1)
      U21#(tt(),V1) -> isNatKind#(activate(V1))
      U21#(tt(),V1) -> activate#(V1)
      plus#(N,0()) -> isNat#(N)
      U64#(tt(),M,N) -> activate#(N)
      U64#(tt(),M,N) -> activate#(M)
      U63#(tt(),M,N) -> isNatKind#(activate(N))
      U63#(tt(),M,N) -> activate#(N)
      U63#(tt(),M,N) -> activate#(M)
      U62#(tt(),M,N) -> isNat#(activate(N))
      U62#(tt(),M,N) -> activate#(N)
      U62#(tt(),M,N) -> activate#(M)
      U61#(tt(),M,N) -> isNatKind#(activate(M))
      U61#(tt(),M,N) -> activate#(M)
      U61#(tt(),M,N) -> activate#(N)
      U51#(tt(),N) -> isNatKind#(activate(N))
      U51#(tt(),N) -> activate#(N)
     TRS:
      U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
      U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
      U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
      U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
      U15(tt(),V2) -> U16(isNat(activate(V2)))
      U16(tt()) -> tt()
      U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
      U22(tt(),V1) -> U23(isNat(activate(V1)))
      U23(tt()) -> tt()
      U31(tt(),V2) -> U32(isNatKind(activate(V2)))
      U32(tt()) -> tt()
      U41(tt()) -> tt()
      U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
      U52(tt(),N) -> activate(N)
      U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
      U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
      U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
      U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
      isNat(n__0()) -> tt()
      isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
      isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
      isNatKind(n__0()) -> tt()
      isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
      isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
      plus(N,0()) -> U51(isNat(N),N)
      plus(N,s(M)) -> U61(isNat(M),M,N)
      0() -> n__0()
      plus(X1,X2) -> n__plus(X1,X2)
      s(X) -> n__s(X)
      activate(n__0()) -> 0()
      activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
      activate(n__s(X)) -> s(activate(X))
      activate(X) -> X
     Open