(STRATEGY
    INNERMOST)

(VAR
    u x y z)
(DATATYPES
    A = µX.< 0, false, s(X), true, minus(X, X), if(X, X, X), le(X, X) >)
(SIGNATURES
    perfectp :: [A] -> A
    f :: [A x A x A x A] -> A)
(RULES
    perfectp(0()) -> false()
    perfectp(s(x)) -> f(x
                       ,s(0())
                       ,s(x)
                       ,s(x))
    f(0(),y,0(),u) -> true()
    f(0(),y,s(z),u) -> false()
    f(s(x),0(),z,u) -> f(x
                        ,u
                        ,minus(z,s(x))
                        ,u)
    f(s(x),s(y),z,u) -> if(le(x,y)
                          ,f(s(x),minus(y,x),z,u)
                          ,f(x,u,z,u)))