(STRATEGY
    INNERMOST)

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