(STRATEGY
    INNERMOST)

(VAR
    M N V1 V2 X X1 X2)
(DATATYPES
    A = µX.< tt, n__0, n__plus(X, X), n__isNat(X), n__s(X) >)
(SIGNATURES
    U11 :: [A x A] -> A
    U21 :: [A x A x A] -> A
    and :: [A x A] -> A
    isNat :: [A] -> A
    plus :: [A x A] -> A
    0 :: [] -> A
    s :: [A] -> A
    activate :: [A] -> A)
(RULES
    U11(tt(),N) -> activate(N)
    U21(tt(),M,N) ->
      s(plus(activate(N),activate(M)))
    and(tt(),X) -> activate(X)
    isNat(n__0()) -> tt()
    isNat(n__plus(V1,V2)) ->
      and(isNat(activate(V1))
         ,n__isNat(activate(V2)))
    isNat(n__s(V1)) ->
      isNat(activate(V1))
    plus(N,0()) -> U11(isNat(N),N)
    plus(N,s(M)) -> U21(and(isNat(M)
                           ,n__isNat(N))
                       ,M
                       ,N)
    0() -> n__0()
    plus(X1,X2) -> n__plus(X1,X2)
    isNat(X) -> n__isNat(X)
    s(X) -> n__s(X)
    activate(n__0()) -> 0()
    activate(n__plus(X1,X2)) ->
      plus(X1,X2)
    activate(n__isNat(X)) ->
      isNat(X)
    activate(n__s(X)) -> s(X)
    activate(X) -> X)