MAYBE

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

Proof:
 Open