2.74/1.26 MAYBE 2.74/1.26 2.74/1.26 Proof: 2.74/1.26 ConCon could not decide confluence of the system. 2.74/1.26 \cite{ALS94}, Theorem 4.1 does not apply. 2.74/1.26 This system is of type 3 or smaller. 2.74/1.26 This system is strongly deterministic. 2.74/1.26 This system is quasi-decreasing. 2.74/1.26 By \cite{A14}, Theorem 11.5.9. 2.74/1.26 This system is of type 3 or smaller. 2.74/1.26 This system is deterministic. 2.74/1.26 System R transformed to V(R) + Emb. 2.74/1.26 This system is terminating. 2.74/1.26 Call external tool: 2.74/1.26 ./ttt2.sh 2.74/1.26 Input: 2.74/1.26 f(x) -> x 2.74/1.26 f(x) -> s(x) 2.74/1.26 s(a) -> t(b) 2.74/1.26 a -> b 2.74/1.26 s(x) -> x 2.74/1.26 t(x) -> x 2.74/1.26 f(x) -> x 2.74/1.26 2.74/1.26 Polynomial Interpretation Processor: 2.74/1.26 dimension: 1 2.74/1.26 interpretation: 2.74/1.26 [t](x0) = x0 + 4, 2.74/1.26 2.74/1.26 [b] = 4, 2.74/1.26 2.74/1.26 [a] = 7, 2.74/1.26 2.74/1.26 [s](x0) = x0 + 2, 2.74/1.26 2.74/1.26 [f](x0) = x0 + 4 2.74/1.26 orientation: 2.74/1.26 f(x) = x + 4 >= x = x 2.74/1.26 2.74/1.26 f(x) = x + 4 >= x + 2 = s(x) 2.74/1.26 2.74/1.26 s(a()) = 9 >= 8 = t(b()) 2.74/1.26 2.74/1.26 a() = 7 >= 4 = b() 2.74/1.26 2.74/1.26 s(x) = x + 2 >= x = x 2.74/1.26 2.74/1.26 t(x) = x + 4 >= x = x 2.74/1.26 problem: 2.74/1.26 2.74/1.26 Qed 2.74/1.26 This critical pair is not unfeasible. 2.74/1.26 ConCon could not decide whether all 1 critical pairs are joinable or not. 2.74/1.26 Overlap: (rule1: s(a) -> t(b), rule2: a -> b, pos: 1, mgu: {}) 2.74/1.26 CP: s(b) = t(b) 2.74/1.26 This critical pair is not unfeasible. 2.74/1.26 2.74/1.28 EOF