(STRATEGY
    INNERMOST)

(VAR
    b x y z)
(DATATYPES
    A = µX.< s(X), 0, false, true, baseError, logZeroError >)
(SIGNATURES
    le :: [A x A] -> A
    plus :: [A x A] -> A
    times :: [A x A] -> A
    log :: [A x A] -> A
    loop :: [A x A x A x A] -> A
    if :: [A x A x A x A x A] -> A)
(RULES
    le(s(x),0()) -> false()
    le(0(),y) -> true()
    le(s(x),s(y)) -> le(x,y)
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    times(0(),y) -> 0()
    times(s(x),y) -> plus(y
                         ,times(x,y))
    log(x,0()) -> baseError()
    log(x,s(0())) -> baseError()
    log(0(),s(s(b))) ->
      logZeroError()
    log(s(x),s(s(b))) -> loop(s(x)
                             ,s(s(b))
                             ,s(0())
                             ,0())
    loop(x,s(s(b)),s(y),z) ->
      if(le(x,s(y)),x,s(s(b)),s(y),z)
    if(true(),x,b,y,z) -> z
    if(false(),x,b,y,z) -> loop(x
                               ,b
                               ,times(b,y)
                               ,s(z)))