(STRATEGY
    INNERMOST)

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