MAYBE

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

Proof:
 Open