(STRATEGY
    INNERMOST)

(VAR
    c x y z)
(DATATYPES
    A = µX.< 0, s(X), true, false >)
(SIGNATURES
    plus :: [A x A] -> A
    times :: [A x A] -> A
    exp :: [A x A] -> A
    ge :: [A x A] -> A
    tower :: [A x A] -> A
    towerIter :: [A x A x A x A] -> A
    help :: [A x A x A x A x 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))
    exp(x,0()) -> s(0())
    exp(x,s(y)) -> times(x,exp(x,y))
    ge(x,0()) -> true()
    ge(0(),s(x)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    tower(x,y) -> towerIter(0()
                           ,x
                           ,y
                           ,s(0()))
    towerIter(c,x,y,z) -> help(ge(c
                                 ,x)
                              ,c
                              ,x
                              ,y
                              ,z)
    help(true(),c,x,y,z) -> z
    help(false(),c,x,y,z) ->
      towerIter(s(c),x,y,exp(y,z)))