EQUATIONS: 
p(x,0()) = x
p(x,s(y)) = s(p(x,y))
f(0()) = 0()
f(s(0())) = s(0())
f(s(s(z))) = p(f(s(z)),f(z))
g(0()) = b(s(0()),0())
g(s(z)) = n(g(z))
n(b(x,y)) = b(p(x,y),x)
u(b(x,y)) = p(x,y)
g(x) = b(f(s(x)),f(x))

COMPLETE TRS:
RULES:
f(0()) -> 0()
f(s(0())) -> s(0())
g(0()) -> b(s(0()),0())
g(s(z)) -> n(g(z))
f(s(s(x))) -> u(g(x))
n(b(x,y)) -> b(u(b(x,y)),x)
b(u(g(x)),f(s(x))) -> n(g(x))
n(n(g(x))) -> b(u(n(g(x))),u(g(x)))
p(x,y) -> u(b(x,y))
b(f(s(x)),f(x)) -> g(x)
u(b(x,0())) -> x
u(b(x,s(y))) -> s(u(b(x,y)))

SUCCESS
MaxTRS: 12 
Search time: 100.32 seconds