(STRATEGY
    INNERMOST)

(VAR
    b1 b2 x y)
(DATATYPES
    A = µX.< 0, true, s(X), false >)
(SIGNATURES
    le :: [A x A] -> A
    zero :: [A] -> A
    id :: [A] -> A
    minus :: [A x A] -> A
    mod :: [A x A] -> A
    if_mod :: [A x A x A x A x A] -> A
    if2 :: [A x A x A x A] -> A
    if3 :: [A x A x A] -> A)
(RULES
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    zero(0()) -> true()
    zero(s(x)) -> false()
    id(0()) -> 0()
    id(s(x)) -> s(id(x))
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    mod(x,y) -> if_mod(zero(x)
                      ,zero(y)
                      ,le(y,x)
                      ,id(x)
                      ,id(y))
    if_mod(true(),b1,b2,x,y) -> 0()
    if_mod(false(),b1,b2,x,y) ->
      if2(b1,b2,x,y)
    if2(true(),b2,x,y) -> 0()
    if2(false(),b2,x,y) -> if3(b2
                              ,x
                              ,y)
    if3(true(),x,y) -> mod(minus(x
                                ,y)
                          ,s(y))
    if3(false(),x,y) -> x)