3.79/1.79 MAYBE 3.79/1.79 3.79/1.79 Proof: 3.79/1.79 ConCon could not decide confluence of the system. 3.79/1.79 \cite{ALS94}, Theorem 4.1 does not apply. 3.79/1.79 This system is of type 3 or smaller. 3.79/1.79 This system is strongly deterministic. 3.79/1.79 This system is quasi-decreasing. 3.79/1.79 By \cite{A14}, Theorem 11.5.9. 3.79/1.79 This system is of type 3 or smaller. 3.79/1.79 This system is deterministic. 3.79/1.79 System R transformed to V(R) + Emb. 3.79/1.79 This system is terminating. 3.79/1.79 Call external tool: 3.79/1.79 ./ttt2.sh 3.79/1.79 Input: 3.79/1.79 (VAR x) 3.79/1.79 (RULES 3.79/1.79 f(x) -> x 3.79/1.79 f(x) -> s(x) 3.79/1.79 s(a) -> t(b) 3.79/1.79 a -> b 3.79/1.79 s(x) -> x 3.79/1.79 t(x) -> x 3.79/1.79 f(x) -> x 3.79/1.79 ) 3.79/1.79 3.79/1.79 Polynomial Interpretation Processor: 3.79/1.79 dimension: 1 3.79/1.79 interpretation: 3.79/1.79 [t](x0) = x0 + 4, 3.79/1.79 3.79/1.79 [b] = 4, 3.79/1.79 3.79/1.79 [a] = 7, 3.79/1.79 3.79/1.80 [s](x0) = x0 + 2, 3.79/1.80 3.79/1.80 [f](x0) = x0 + 4 3.79/1.80 orientation: 3.79/1.80 f(x) = x + 4 >= x = x 3.79/1.80 3.79/1.80 f(x) = x + 4 >= x + 2 = s(x) 3.79/1.80 3.79/1.80 s(a()) = 9 >= 8 = t(b()) 3.79/1.80 3.79/1.80 a() = 7 >= 4 = b() 3.79/1.80 3.79/1.80 s(x) = x + 2 >= x = x 3.79/1.80 3.79/1.80 t(x) = x + 4 >= x = x 3.79/1.80 problem: 3.79/1.80 3.79/1.80 Qed 3.79/1.80 ConCon could not decide whether all 1 critical pairs are joinable or not. 3.79/1.80 Overlap: (rule1: s(a) -> t(b), rule2: a -> b, pos: 1, mgu: {}) 3.79/1.80 CP: s(b) = t(b) 3.79/1.80 ConCon could not decide context-joinability of this critical pair. 3.79/1.80 3.79/1.82 EOF