(STRATEGY
    INNERMOST)

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