(STRATEGY
    INNERMOST)

(VAR
    c x y)
(DATATYPES
    A = µX.< 0, s(X), true, false >)
(SIGNATURES
    lt :: [A x A] -> A
    times :: [A x A] -> A
    plus :: [A x A] -> A
    fac :: [A] -> A
    loop :: [A x A x A] -> A
    if :: [A x A x A x A] -> A)
(RULES
    lt(0(),s(x)) -> true()
    lt(x,0()) -> false()
    lt(s(x),s(y)) -> lt(x,y)
    times(0(),y) -> 0()
    times(s(x),y) -> plus(y
                         ,times(x,y))
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    fac(x) -> loop(x,s(0()),s(0()))
    loop(x,c,y) -> if(lt(x,c),x,c,y)
    if(false(),x,c,y) -> loop(x
                             ,s(c)
                             ,times(y,s(c)))
    if(true(),x,c,y) -> y)