(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< 0, s(X), true, false, divByZeroError >)
(SIGNATURES
    minus :: [A x A] -> A
    le :: [A x A] -> A
    quot :: [A x A] -> A
    if_quot :: [A x A x A x A] -> A)
(RULES
    minus(x,x) -> 0()
    minus(0(),x) -> 0()
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    quot(x,y) -> if_quot(minus(x,y)
                        ,y
                        ,le(y,0())
                        ,le(y,x))
    if_quot(x,y,true(),z) ->
      divByZeroError()
    if_quot(x,y,false(),true()) ->
      s(quot(x,y))
    if_quot(x,y,false(),false()) ->
      0())