2.52/1.23 MAYBE 2.52/1.23 2.52/1.23 Proof: 2.52/1.23 ConCon could not decide confluence of the system. 2.52/1.23 \cite{ALS94}, Theorem 4.1 does not apply. 2.52/1.23 This system is of type 3 or smaller. 2.52/1.23 This system is strongly deterministic. 2.52/1.23 This system is quasi-decreasing. 2.52/1.23 By \cite{A14}, Theorem 11.5.9. 2.52/1.23 This system is of type 3 or smaller. 2.52/1.23 This system is deterministic. 2.52/1.23 System R transformed to V(R) + Emb. 2.52/1.23 This system is terminating. 2.52/1.23 Call external tool: 2.52/1.23 ./ttt2.sh 2.52/1.23 Input: 2.52/1.23 a -> c 2.52/1.23 a -> d 2.52/1.23 f(x) -> x 2.52/1.23 f(x) -> d 2.52/1.23 f(x) -> x 2.52/1.23 2.52/1.23 Polynomial Interpretation Processor: 2.52/1.23 dimension: 1 2.52/1.23 interpretation: 2.52/1.23 [f](x0) = 2x0 + 4, 2.52/1.23 2.52/1.23 [d] = 0, 2.52/1.23 2.52/1.23 [c] = 0, 2.52/1.23 2.52/1.23 [a] = 4 2.52/1.23 orientation: 2.52/1.23 a() = 4 >= 0 = c() 2.52/1.23 2.52/1.23 a() = 4 >= 0 = d() 2.52/1.23 2.52/1.23 f(x) = 2x + 4 >= x = x 2.52/1.23 2.52/1.23 f(x) = 2x + 4 >= 0 = d() 2.52/1.23 problem: 2.52/1.23 2.52/1.23 Qed 2.52/1.23 This critical pair is not trivial. 2.52/1.23 2.52/1.25 EOF