(STRATEGY
    INNERMOST)

(VAR
    M N V1 V2 X X1 X2 X3)
(DATATYPES
    A = µX.< tt, s(X), 0, plus(X, X), isNat(X), U11(X, X), U21(X, X, X), and(X, X) >)
(SIGNATURES
    a__U11 :: [A x A] -> A
    a__U21 :: [A x A x A] -> A
    a__and :: [A x A] -> A
    a__isNat :: [A] -> A
    a__plus :: [A x A] -> A
    mark :: [A] -> A)
(RULES
    a__U11(tt(),N) -> mark(N)
    a__U21(tt(),M,N) ->
      s(a__plus(mark(N),mark(M)))
    a__and(tt(),X) -> mark(X)
    a__isNat(0()) -> tt()
    a__isNat(plus(V1,V2)) ->
      a__and(a__isNat(V1),isNat(V2))
    a__isNat(s(V1)) -> a__isNat(V1)
    a__plus(N,0()) ->
      a__U11(a__isNat(N),N)
    a__plus(N,s(M)) ->
      a__U21(a__and(a__isNat(M)
                   ,isNat(N))
            ,M
            ,N)
    mark(U11(X1,X2)) ->
      a__U11(mark(X1),X2)
    mark(U21(X1,X2,X3)) ->
      a__U21(mark(X1),X2,X3)
    mark(plus(X1,X2)) ->
      a__plus(mark(X1),mark(X2))
    mark(and(X1,X2)) ->
      a__and(mark(X1),X2)
    mark(isNat(X)) -> a__isNat(X)
    mark(tt()) -> tt()
    mark(s(X)) -> s(mark(X))
    mark(0()) -> 0()
    a__U11(X1,X2) -> U11(X1,X2)
    a__U21(X1,X2,X3) -> U21(X1
                           ,X2
                           ,X3)
    a__plus(X1,X2) -> plus(X1,X2)
    a__and(X1,X2) -> and(X1,X2)
    a__isNat(X) -> isNat(X))