(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, s(X), true, false >)
(SIGNATURES
    + :: [A x A] -> A
    * :: [A x A] -> A
    ge :: [A x A] -> A
    - :: [A x A] -> A
    fact :: [A] -> A
    iffact :: [A x A] -> A)
(RULES
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    *(x,0()) -> 0()
    *(x,s(y)) -> +(*(x,y),x)
    ge(x,0()) -> true()
    ge(0(),s(y)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
    fact(x) -> iffact(x
                     ,ge(x,s(s(0()))))
    iffact(x,true()) -> *(x
                         ,fact(-(x,s(0()))))
    iffact(x,false()) -> s(0()))