(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< a, b, false, c, true, 0, s(X) >)
(SIGNATURES
    double :: [A] -> A
    permute :: [A x A x A] -> A
    p :: [A] -> A
    ack :: [A x A] -> A
    plus :: [A x A] -> A
    isZero :: [A] -> A)
(RULES
    double(x) -> permute(x,x,a())
    permute(x,y,a()) ->
      permute(isZero(x),x,b())
    permute(false(),x,b()) ->
      permute(ack(x,x),p(x),c())
    permute(true(),x,b()) -> 0()
    permute(y,x,c()) ->
      s(s(permute(x,y,a())))
    p(0()) -> 0()
    p(s(x)) -> x
    ack(0(),x) -> plus(x,s(0()))
    ack(s(x),0()) -> ack(x,s(0()))
    ack(s(x),s(y)) -> ack(x
                         ,ack(s(x),y))
    plus(0(),y) -> y
    plus(s(x),y) -> plus(x,s(y))
    plus(x,s(s(y))) -> s(plus(s(x)
                             ,y))
    plus(x,s(0())) -> s(x)
    plus(x,0()) -> x
    isZero(0()) -> true()
    isZero(s(x)) -> false())