(STRATEGY
    INNERMOST)

(VAR
    u x y z)
(DATATYPES
    A = µX.< 0, true, false, s(X), b, c >)
(SIGNATURES
    lcm :: [A x A] -> A
    lcmIter :: [A x A x A x A] -> A
    if :: [A x A x A x A x A] -> A
    if2 :: [A x A x A x A x A] -> A
    plus :: [A x A] -> A
    times :: [A x A] -> A
    ifTimes :: [A x A x A] -> A
    p :: [A] -> A
    ge :: [A x A] -> A
    or :: [A x A] -> A
    divisible :: [A x A] -> A
    div :: [A x A x A] -> A
    a :: [] -> A)
(RULES
    lcm(x,y) -> lcmIter(x
                       ,y
                       ,0()
                       ,times(x,y))
    lcmIter(x,y,z,u) -> if(or(ge(0()
                                ,x)
                             ,ge(z,u))
                          ,x
                          ,y
                          ,z
                          ,u)
    if(true(),x,y,z,u) -> z
    if(false(),x,y,z,u) ->
      if2(divisible(z,y),x,y,z,u)
    if2(true(),x,y,z,u) -> z
    if2(false(),x,y,z,u) ->
      lcmIter(x,y,plus(x,z),u)
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    times(x,y) -> ifTimes(ge(0(),x)
                         ,x
                         ,y)
    ifTimes(true(),x,y) -> 0()
    ifTimes(false(),x,y) -> plus(y
                                ,times(y,p(x)))
    p(s(x)) -> x
    p(0()) -> s(s(0()))
    ge(x,0()) -> true()
    ge(0(),s(y)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    or(true(),y) -> true()
    or(false(),y) -> y
    divisible(0(),s(y)) -> true()
    divisible(s(x),s(y)) -> div(s(x)
                               ,s(y)
                               ,s(y))
    div(x,y,0()) -> divisible(x,y)
    div(0(),y,s(z)) -> false()
    div(s(x),y,s(z)) -> div(x,y,z)
    a() -> b()
    a() -> c())