3.65/1.84 MAYBE 3.65/1.84 3.65/1.84 Proof: 3.65/1.85 ConCon could not decide confluence of the system. 3.65/1.85 \cite{ALS94}, Theorem 4.1 does not apply. 3.65/1.85 This system is of type 3 or smaller. 3.65/1.85 This system is strongly deterministic. 3.65/1.85 This system is quasi-decreasing. 3.65/1.85 By \cite{A14}, Theorem 11.5.9. 3.65/1.85 This system is of type 3 or smaller. 3.65/1.85 This system is deterministic. 3.65/1.85 System R transformed to V(R) + Emb. 3.65/1.85 This system is terminating. 3.65/1.85 Call external tool: 3.65/1.85 ./ttt2.sh 3.65/1.85 Input: 3.65/1.85 (VAR x) 3.65/1.85 (RULES 3.65/1.85 f(x) -> x 3.65/1.85 f(x) -> s(x) 3.65/1.85 s(a) -> t(b) 3.65/1.85 a -> b 3.65/1.85 s(x) -> x 3.65/1.85 t(x) -> x 3.65/1.85 f(x) -> x 3.65/1.85 ) 3.65/1.85 3.65/1.85 Polynomial Interpretation Processor: 3.65/1.85 dimension: 1 3.65/1.85 interpretation: 3.65/1.85 [t](x0) = x0 + 4, 3.65/1.85 3.65/1.85 [b] = 4, 3.65/1.85 3.65/1.85 [a] = 7, 3.65/1.85 3.65/1.85 [s](x0) = x0 + 2, 3.65/1.85 3.65/1.85 [f](x0) = x0 + 4 3.65/1.85 orientation: 3.65/1.85 f(x) = x + 4 >= x = x 3.65/1.85 3.65/1.85 f(x) = x + 4 >= x + 2 = s(x) 3.65/1.85 3.65/1.85 s(a()) = 9 >= 8 = t(b()) 3.65/1.85 3.65/1.85 a() = 7 >= 4 = b() 3.65/1.85 3.65/1.85 s(x) = x + 2 >= x = x 3.65/1.85 3.65/1.85 t(x) = x + 4 >= x = x 3.65/1.85 problem: 3.65/1.85 3.65/1.85 Qed 3.65/1.85 ConCon could not decide whether all 1 critical pairs are joinable or not. 3.65/1.85 Overlap: (rule1: s(a) -> t(b), rule2: a -> b, pos: 1, mgu: {}) 3.65/1.85 CP: s(b) = t(b) 3.65/1.85 ConCon could not decide context-joinability of this critical pair. 3.65/1.85 3.65/1.88 EOF