MAYBE

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

Proof:
 Open