5.77/2.32 YES 5.77/2.32 5.77/2.32 Proof: 5.77/2.32 This system is confluent. 5.77/2.32 By \cite{SMI95}, Corollary 4.7 or 5.3. 5.77/2.32 This system is oriented. 5.77/2.32 This system is of type 3 or smaller. 5.77/2.32 This system is right-stable. 5.77/2.33 This system is properly oriented. 5.77/2.33 This is an overlay system. 5.77/2.33 This system is left-linear. 5.77/2.33 All 2 critical pairs are trivial or infeasible. 5.77/2.33 Overlap: (rule1: pos(s(y)) -> true <= pos(y) = true, rule2: pos(s(0)) -> true, pos: ε, mgu: {(y,0)}) 5.77/2.33 CP: true = true <= pos(0) = true 5.77/2.33 This critical pair is trivial. 5.77/2.33 Overlap: (rule1: pos(s(0)) -> true, rule2: pos(s(y)) -> true <= pos(y) = true, pos: ε, mgu: {(y,0)}) 5.77/2.33 CP: true = true <= pos(0) = true 5.77/2.33 This critical pair is infeasible. 5.77/2.33 This critical pair is conditional. 5.77/2.33 This critical pair has some non-trivial conditions. 5.77/2.33 Call external tool: 5.77/2.33 ./waldmeister 5.77/2.33 Input: 5.77/2.33 pos(s(0)) -> true 5.77/2.33 pos(0) -> false 5.77/2.33 pos(s(x)) -> true <= pos(x) = true 5.77/2.33 pos(p(x)) -> false <= pos(x) = false 5.77/2.33 5.77/2.33 By Waldmeister. 5.77/2.33 6.27/2.37 EOF