MAYBE

Problem:
 U11(tt(),V2) -> U12(isNat(activate(V2)))
 U12(tt()) -> tt()
 U21(tt()) -> tt()
 U31(tt(),N) -> activate(N)
 U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
 U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
 isNat(n__0()) -> tt()
 isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
 isNat(n__s(V1)) -> U21(isNat(activate(V1)))
 plus(N,0()) -> U31(isNat(N),N)
 plus(N,s(M)) -> U41(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(),V2) -> activate#(V2)
   U11#(tt(),V2) -> isNat#(activate(V2))
   U11#(tt(),V2) -> U12#(isNat(activate(V2)))
   U31#(tt(),N) -> activate#(N)
   U41#(tt(),M,N) -> activate#(M)
   U41#(tt(),M,N) -> activate#(N)
   U41#(tt(),M,N) -> isNat#(activate(N))
   U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N))
   U42#(tt(),M,N) -> activate#(M)
   U42#(tt(),M,N) -> activate#(N)
   U42#(tt(),M,N) -> plus#(activate(N),activate(M))
   U42#(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)) -> isNat#(activate(V1))
   isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
   isNat#(n__s(V1)) -> activate#(V1)
   isNat#(n__s(V1)) -> isNat#(activate(V1))
   isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
   plus#(N,0()) -> isNat#(N)
   plus#(N,0()) -> U31#(isNat(N),N)
   plus#(N,s(M)) -> isNat#(M)
   plus#(N,s(M)) -> U41#(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(),V2) -> U12(isNat(activate(V2)))
   U12(tt()) -> tt()
   U21(tt()) -> tt()
   U31(tt(),N) -> activate(N)
   U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
   U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
   isNat(n__0()) -> tt()
   isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
   isNat(n__s(V1)) -> U21(isNat(activate(V1)))
   plus(N,0()) -> U31(isNat(N),N)
   plus(N,s(M)) -> U41(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
  ADG Processor:
   DPs:
    U11#(tt(),V2) -> activate#(V2)
    U11#(tt(),V2) -> isNat#(activate(V2))
    U11#(tt(),V2) -> U12#(isNat(activate(V2)))
    U31#(tt(),N) -> activate#(N)
    U41#(tt(),M,N) -> activate#(M)
    U41#(tt(),M,N) -> activate#(N)
    U41#(tt(),M,N) -> isNat#(activate(N))
    U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N))
    U42#(tt(),M,N) -> activate#(M)
    U42#(tt(),M,N) -> activate#(N)
    U42#(tt(),M,N) -> plus#(activate(N),activate(M))
    U42#(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)) -> isNat#(activate(V1))
    isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
    isNat#(n__s(V1)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    plus#(N,0()) -> isNat#(N)
    plus#(N,0()) -> U31#(isNat(N),N)
    plus#(N,s(M)) -> isNat#(M)
    plus#(N,s(M)) -> U41#(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(),V2) -> U12(isNat(activate(V2)))
    U12(tt()) -> tt()
    U21(tt()) -> tt()
    U31(tt(),N) -> activate(N)
    U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
    U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
    isNat(n__0()) -> tt()
    isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
    isNat(n__s(V1)) -> U21(isNat(activate(V1)))
    plus(N,0()) -> U31(isNat(N),N)
    plus(N,s(M)) -> U41(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()) -> U31#(isNat(N),N) -> U31#(tt(),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)) -> isNat#(activate(V1))
    plus#(N,0()) -> isNat#(N) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
    plus#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> activate#(V1)
    plus#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> isNat#(activate(V1))
    plus#(N,0()) -> isNat#(N) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    plus#(N,s(M)) -> U41#(isNat(M),M,N) ->
    U41#(tt(),M,N) -> activate#(M)
    plus#(N,s(M)) -> U41#(isNat(M),M,N) ->
    U41#(tt(),M,N) -> activate#(N)
    plus#(N,s(M)) -> U41#(isNat(M),M,N) ->
    U41#(tt(),M,N) -> isNat#(activate(N))
    plus#(N,s(M)) -> U41#(isNat(M),M,N) ->
    U41#(tt(),M,N) -> U42#(isNat(activate(N)),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)) -> isNat#(activate(V1))
    plus#(N,s(M)) -> isNat#(M) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNat(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)) -> isNat#(activate(V1))
    plus#(N,s(M)) -> isNat#(M) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    U42#(tt(),M,N) -> plus#(activate(N),activate(M)) ->
    plus#(N,0()) -> isNat#(N)
    U42#(tt(),M,N) -> plus#(activate(N),activate(M)) ->
    plus#(N,0()) -> U31#(isNat(N),N)
    U42#(tt(),M,N) -> plus#(activate(N),activate(M)) ->
    plus#(N,s(M)) -> isNat#(M)
    U42#(tt(),M,N) -> plus#(activate(N),activate(M)) ->
    plus#(N,s(M)) -> U41#(isNat(M),M,N)
    U42#(tt(),M,N) -> activate#(M) -> activate#(n__0()) -> 0#()
    U42#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U42#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U42#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U42#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> activate#(X)
    U42#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> s#(activate(X))
    U42#(tt(),M,N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U42#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U42#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U42#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U42#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> activate#(X)
    U42#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N)) ->
    U42#(tt(),M,N) -> activate#(M)
    U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N)) ->
    U42#(tt(),M,N) -> activate#(N)
    U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N)) ->
    U42#(tt(),M,N) -> plus#(activate(N),activate(M))
    U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N)) ->
    U42#(tt(),M,N) -> s#(plus(activate(N),activate(M)))
    U41#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    U41#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    U41#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1))
    U41#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
    U41#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    U41#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    U41#(tt(),M,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    U41#(tt(),M,N) -> activate#(M) -> activate#(n__0()) -> 0#()
    U41#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U41#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U41#(tt(),M,N) -> activate#(M) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U41#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> activate#(X)
    U41#(tt(),M,N) -> activate#(M) ->
    activate#(n__s(X)) -> s#(activate(X))
    U41#(tt(),M,N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U41#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U41#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U41#(tt(),M,N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U41#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> activate#(X)
    U41#(tt(),M,N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    U31#(tt(),N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U31#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U31#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U31#(tt(),N) -> activate#(N) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U31#(tt(),N) -> activate#(N) -> activate#(n__s(X)) -> activate#(X)
    U31#(tt(),N) -> activate#(N) ->
    activate#(n__s(X)) -> s#(activate(X))
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1))
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> U21#(isNat(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)) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1))
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    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)) -> 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)) -> U11#(isNat(activate(V1)),activate(V2)) ->
    U11#(tt(),V2) -> activate#(V2)
    isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2)) ->
    U11#(tt(),V2) -> isNat#(activate(V2))
    isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2)) ->
    U11#(tt(),V2) -> U12#(isNat(activate(V2)))
    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()) -> U31#(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)) -> U41#(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(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V2)
    U11#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__plus(V1,V2)) -> activate#(V1)
    U11#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__plus(V1,V2)) -> isNat#(activate(V1))
    U11#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
    U11#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    U11#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    U11#(tt(),V2) -> isNat#(activate(V2)) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    U11#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U11#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X2)
    U11#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> activate#(X1)
    U11#(tt(),V2) -> activate#(V2) ->
    activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
    U11#(tt(),V2) -> activate#(V2) ->
    activate#(n__s(X)) -> activate#(X)
    U11#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(activate(X))
   Restore Modifier:
    DPs:
     U11#(tt(),V2) -> activate#(V2)
     U11#(tt(),V2) -> isNat#(activate(V2))
     U11#(tt(),V2) -> U12#(isNat(activate(V2)))
     U31#(tt(),N) -> activate#(N)
     U41#(tt(),M,N) -> activate#(M)
     U41#(tt(),M,N) -> activate#(N)
     U41#(tt(),M,N) -> isNat#(activate(N))
     U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N))
     U42#(tt(),M,N) -> activate#(M)
     U42#(tt(),M,N) -> activate#(N)
     U42#(tt(),M,N) -> plus#(activate(N),activate(M))
     U42#(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)) -> isNat#(activate(V1))
     isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
     isNat#(n__s(V1)) -> activate#(V1)
     isNat#(n__s(V1)) -> isNat#(activate(V1))
     isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
     plus#(N,0()) -> isNat#(N)
     plus#(N,0()) -> U31#(isNat(N),N)
     plus#(N,s(M)) -> isNat#(M)
     plus#(N,s(M)) -> U41#(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(),V2) -> U12(isNat(activate(V2)))
     U12(tt()) -> tt()
     U21(tt()) -> tt()
     U31(tt(),N) -> activate(N)
     U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
     U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
     isNat(n__0()) -> tt()
     isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
     isNat(n__s(V1)) -> U21(isNat(activate(V1)))
     plus(N,0()) -> U31(isNat(N),N)
     plus(N,s(M)) -> U41(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: 24
     #arcs: 134/841
     DPs:
      plus#(N,0()) -> U31#(isNat(N),N)
      U31#(tt(),N) -> activate#(N)
      activate#(n__s(X)) -> activate#(X)
      activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
      plus#(N,s(M)) -> U41#(isNat(M),M,N)
      U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N))
      U42#(tt(),M,N) -> plus#(activate(N),activate(M))
      plus#(N,s(M)) -> isNat#(M)
      isNat#(n__s(V1)) -> isNat#(activate(V1))
      isNat#(n__s(V1)) -> activate#(V1)
      activate#(n__plus(X1,X2)) -> activate#(X1)
      activate#(n__plus(X1,X2)) -> activate#(X2)
      isNat#(n__plus(V1,V2)) -> U11#(isNat(activate(V1)),activate(V2))
      U11#(tt(),V2) -> isNat#(activate(V2))
      isNat#(n__plus(V1,V2)) -> isNat#(activate(V1))
      isNat#(n__plus(V1,V2)) -> activate#(V1)
      isNat#(n__plus(V1,V2)) -> activate#(V2)
      U11#(tt(),V2) -> activate#(V2)
      plus#(N,0()) -> isNat#(N)
      U42#(tt(),M,N) -> activate#(N)
      U42#(tt(),M,N) -> activate#(M)
      U41#(tt(),M,N) -> isNat#(activate(N))
      U41#(tt(),M,N) -> activate#(N)
      U41#(tt(),M,N) -> activate#(M)
     TRS:
      U11(tt(),V2) -> U12(isNat(activate(V2)))
      U12(tt()) -> tt()
      U21(tt()) -> tt()
      U31(tt(),N) -> activate(N)
      U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
      U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
      isNat(n__0()) -> tt()
      isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
      isNat(n__s(V1)) -> U21(isNat(activate(V1)))
      plus(N,0()) -> U31(isNat(N),N)
      plus(N,s(M)) -> U41(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