2.91/1.24 YES 2.91/1.24 2.91/1.24 Proof: 2.91/1.24 This system is confluent. 2.91/1.24 By \cite{SMI95}, Corollary 4.7 or 5.3. 2.91/1.24 This system is oriented. 2.91/1.24 This system is of type 3 or smaller. 2.91/1.24 This system is right-stable. 2.91/1.24 This system is properly oriented. 2.91/1.24 This is an overlay system. 2.91/1.24 This system is left-linear. 2.91/1.24 All 2 critical pairs are trivial or infeasible. 2.91/1.24 Overlap: (rule1: f(z, x') -> h(s(z)) <= c(h(z)) = c(a), rule2: f(y', z') -> g(s(y')) <= c(g(y')) = c(a), pos: ε, mgu: {(y',z), (z',x')}) 2.91/1.24 CP: g(s(z)) = h(s(z)) <= c(h(z)) = c(a), c(g(z)) = c(a) 2.91/1.24 This critical pair is infeasible. 2.91/1.24 This critical pair is conditional. 2.91/1.24 This critical pair has some non-trivial conditions. 2.91/1.24 Call external tool: 2.91/1.24 ./waldmeister 2.91/1.25 Input: 2.91/1.25 f(x, y) -> g(s(x)) <= c(g(x)) = c(a) 2.91/1.25 f(x, y) -> h(s(x)) <= c(h(x)) = c(a) 2.91/1.25 g(s(x)) -> x 2.91/1.25 h(s(x)) -> x 2.91/1.25 b -> b 2.91/1.25 2.91/1.25 By Waldmeister. 2.91/1.25 Overlap: (rule1: f(z, x') -> g(s(z)) <= c(g(z)) = c(a), rule2: f(y', z') -> h(s(y')) <= c(h(y')) = c(a), pos: ε, mgu: {(y',z), (z',x')}) 2.91/1.25 CP: h(s(z)) = g(s(z)) <= c(g(z)) = c(a), c(h(z)) = c(a) 2.91/1.25 This critical pair is infeasible. 2.91/1.25 This critical pair is conditional. 2.91/1.25 This critical pair has some non-trivial conditions. 2.91/1.25 Call external tool: 2.91/1.25 ./waldmeister 2.91/1.25 Input: 2.91/1.25 f(x, y) -> g(s(x)) <= c(g(x)) = c(a) 2.91/1.25 f(x, y) -> h(s(x)) <= c(h(x)) = c(a) 2.91/1.25 g(s(x)) -> x 2.91/1.25 h(s(x)) -> x 2.91/1.25 b -> b 2.91/1.25 2.91/1.25 By Waldmeister. 2.91/1.25 3.11/1.61 EOF