(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, true, s(X), false >)
(SIGNATURES
    even :: [A] -> A
    half :: [A] -> A
    plus :: [A x A] -> A
    times :: [A x A] -> A
    if_times :: [A x A x A] -> A)
(RULES
    even(0()) -> true()
    even(s(0())) -> false()
    even(s(s(x))) -> even(x)
    half(0()) -> 0()
    half(s(s(x))) -> s(half(x))
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    times(0(),y) -> 0()
    times(s(x),y) ->
      if_times(even(s(x)),s(x),y)
    if_times(true(),s(x),y) ->
      plus(times(half(s(x)),y)
          ,times(half(s(x)),y))
    if_times(false(),s(x),y) ->
      plus(y,times(x,y)))