MAYBE

Problem:
 thrice(0(x1)) -> p(s(p(p(p(s(s(s(0(p(s(p(s(x1)))))))))))))
 thrice(s(x1)) -> p(p(s(s(half(p(p(s(s(p(s(sixtimes(p(s(p(p(s(s(x1))))))))))))))))))
 half(0(x1)) -> p(p(s(s(p(s(0(p(s(s(s(s(x1))))))))))))
 half(s(x1)) -> p(s(p(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x1)))))))))))))))))
 half(s(s(x1))) -> p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x1))))))))))))))))
 sixtimes(0(x1)) -> p(s(p(s(0(s(s(s(s(s(p(s(p(s(x1))))))))))))))
 sixtimes(s(x1)) ->
 p(p(s(s(s(s(s(s(s(p(p(s(p(s(s(s(sixtimes(p(s(p(p(p(s(s(s(x1)))))))))))))))))))))))))
 p(p(s(x1))) -> p(x1)
 p(s(x1)) -> x1
 p(0(x1)) -> 0(s(s(s(s(x1)))))
 0(x1) -> x1

Proof:
 Open