TRS: { prime(0()) -> false(), prime(s(0())) -> false(), prime(s(s(x))) -> prime1(s(s(x)), s(x)), prime1(x, 0()) -> false(), prime1(x, s(0())) -> true(), prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))), divp(x, y) -> =(rem(x, y), 0())} LMPO: Quasi-Precedence: prime > prime1, prime1 > divp, prime1 > not empty Normal: pi(divp) = [1,2], pi(prime1) = [1,2], pi(prime) = [1] Safe: Predicative System: { prime(0();) -> false(), prime(s(0(););) -> false(), prime(s(s(x;););) -> prime1(s(s(x;);),s(x;);), prime1(x,0();) -> false(), prime1(x,s(0(););) -> true(), prime1(x,s(s(y;););) -> and(not(divp(s(s(y;);),x;);),prime1(x,s(y;););), divp(x,y;) -> =(rem(x,y;),0();)} Qed