(STRATEGY
    INNERMOST)

(VAR
    x y)
(DATATYPES
    A = µX.< 0, true, 1, false, s(X), c(X) >)
(SIGNATURES
    f :: [A] -> A
    if :: [A x A x A] -> A
    g :: [A x A] -> A)
(RULES
    f(0()) -> true()
    f(1()) -> false()
    f(s(x)) -> f(x)
    if(true(),s(x),s(y)) -> s(x)
    if(false(),s(x),s(y)) -> s(y)
    g(x,c(y)) -> c(g(x,y))
    g(x,c(y)) -> g(x
                  ,if(f(x),c(g(s(x),y)),c(y))))