(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< 0, s(X) >)
(SIGNATURES
    minus :: [A x A] -> A
    p :: [A] -> A
    div :: [A x A] -> A
    plus :: [A x A] -> A)
(RULES
    minus(x,0()) -> x
    minus(0(),y) -> 0()
    minus(s(x),s(y)) ->
      minus(p(s(x)),p(s(y)))
    minus(x,plus(y,z)) ->
      minus(minus(x,y),z)
    p(s(s(x))) -> s(p(s(x)))
    p(0()) -> s(s(0()))
    div(s(x),s(y)) -> s(div(minus(x
                                 ,y)
                           ,s(y)))
    div(plus(x,y),z) -> plus(div(x
                                ,z)
                            ,div(y,z))
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(y
                          ,minus(s(x),s(0())))))