(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< 0, s(X), false, true >)
(SIGNATURES
    minus :: [A x A] -> A
    plus :: [A x A] -> A
    zero :: [A] -> A
    p :: [A] -> A
    div :: [A x A] -> A
    quot :: [A x A x A] -> A
    if :: [A x A x A x A] -> A)
(RULES
    minus(0(),y) -> 0()
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    plus(0(),y) -> y
    plus(s(x),y) -> plus(x,s(y))
    zero(s(x)) -> false()
    zero(0()) -> true()
    p(s(x)) -> x
    div(x,y) -> quot(x,y,0())
    quot(x,y,z) -> if(zero(x)
                     ,x
                     ,y
                     ,plus(z,s(0())))
    if(true(),x,y,z) -> p(z)
    if(false(),x,s(y),z) ->
      quot(minus(x,s(y)),s(y),z))