(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< 0, s(X), true, minus(X, X), false, ge(X, X), div(X, X), if(X, X, X) >)
(SIGNATURES
    minus_active :: [A x A] -> A
    mark :: [A] -> A
    ge_active :: [A x A] -> A
    div_active :: [A x A] -> A
    if_active :: [A x A x A] -> A)
(RULES
    minus_active(0(),y) -> 0()
    mark(0()) -> 0()
    minus_active(s(x),s(y)) ->
      minus_active(x,y)
    mark(s(x)) -> s(mark(x))
    ge_active(x,0()) -> true()
    mark(minus(x,y)) ->
      minus_active(x,y)
    ge_active(0(),s(y)) -> false()
    mark(ge(x,y)) -> ge_active(x,y)
    ge_active(s(x),s(y)) ->
      ge_active(x,y)
    mark(div(x,y)) ->
      div_active(mark(x),y)
    div_active(0(),s(y)) -> 0()
    mark(if(x,y,z)) ->
      if_active(mark(x),y,z)
    div_active(s(x),s(y)) ->
      if_active(ge_active(x,y)
               ,s(div(minus(x,y),s(y)))
               ,0())
    if_active(true(),x,y) -> mark(x)
    minus_active(x,y) -> minus(x,y)
    if_active(false(),x,y) ->
      mark(y)
    ge_active(x,y) -> ge(x,y)
    if_active(x,y,z) -> if(x,y,z)
    div_active(x,y) -> div(x,y))