(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< 0, s(X) >)
(SIGNATURES
    plus :: [A x A] -> A
    times :: [A x A] -> A
    exp :: [A x A] -> A
    p :: [A] -> A
    tower :: [A x A] -> A
    towerIter :: [A x A x A] -> A)
(RULES
    plus(0(),x) -> x
    plus(s(x),y) -> s(plus(p(s(x))
                          ,y))
    times(0(),y) -> 0()
    times(s(x),y) -> plus(y
                         ,times(p(s(x)),y))
    exp(x,0()) -> s(0())
    exp(x,s(y)) -> times(x,exp(x,y))
    p(s(0())) -> 0()
    p(s(s(x))) -> s(p(s(x)))
    tower(x,y) -> towerIter(x
                           ,y
                           ,s(0()))
    towerIter(0(),y,z) -> z
    towerIter(s(x),y,z) ->
      towerIter(p(s(x)),y,exp(y,z)))