(STRATEGY
    INNERMOST)

(VAR
    M N V1 V2 X X1 X2)
(DATATYPES
    A = µX.< tt, n__0, n__plus(X, X), n__s(X) >)
(SIGNATURES
    U11 :: [A x A x A] -> A
    U12 :: [A x A x A] -> A
    U13 :: [A x A x A] -> A
    U14 :: [A x A x A] -> A
    U15 :: [A x A] -> A
    U16 :: [A] -> A
    U21 :: [A x A] -> A
    U22 :: [A x A] -> A
    U23 :: [A] -> A
    U31 :: [A x A] -> A
    U32 :: [A] -> A
    U41 :: [A] -> A
    U51 :: [A x A] -> A
    U52 :: [A x A] -> A
    U61 :: [A x A x A] -> A
    U62 :: [A x A x A] -> A
    U63 :: [A x A x A] -> A
    U64 :: [A x A x A] -> A
    isNat :: [A] -> A
    isNatKind :: [A] -> A
    plus :: [A x A] -> A
    0 :: [] -> A
    s :: [A] -> A
    activate :: [A] -> A)
(RULES
    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(X1,X2)
    activate(n__s(X)) -> s(X)
    activate(X) -> X)