MAYBE

Problem:
 s(s(0())) -> f(0())
 f(0()) -> 0()
 s(s(s(0()))) -> f(s(0()))
 f(s(0())) -> s(0())
 s(s(s(s(s(s(s(s(0())))))))) -> f(s(s(0())))
 f(s(s(0()))) -> s(s(s(s(s(s(0()))))))
 g(x) -> h(x,x)
 s(x) -> h(x,0())
 s(x) -> h(0(),x)
 f(g(x)) -> g(g(f(x)))
 g(s(x)) -> s(s(g(x)))
 h(f(x),g(x)) -> f(s(x))

Proof:
 Open