2.08/1.14 MAYBE 2.08/1.14 2.08/1.14 Proof: 2.08/1.14 ConCon could not decide confluence of the system. 2.08/1.14 \cite{ALS94}, Theorem 4.1 does not apply. 2.08/1.14 This system is of type 3 or smaller. 2.08/1.14 This system is strongly deterministic. 2.08/1.14 This system is quasi-decreasing. 2.08/1.14 By \cite{O02}, p. 214, Proposition 7.2.50. 2.08/1.14 This system is of type 3 or smaller. 2.08/1.14 This system is deterministic. 2.08/1.14 System R transformed to U(R). 2.08/1.14 This system is terminating. 2.08/1.14 Call external tool: 2.08/1.14 ./ttt2.sh 2.08/1.14 Input: 2.08/1.14 a -> c 2.08/1.14 a -> d 2.08/1.14 ?1(c, x) -> x 2.08/1.14 f(x) -> ?1(x, x) 2.08/1.14 2.08/1.14 Polynomial Interpretation Processor: 2.08/1.14 dimension: 1 2.08/1.14 interpretation: 2.08/1.14 [f](x0) = 6x0x0 + 5, 2.08/1.14 2.08/1.14 [?1](x0, x1) = -4x0 + x1 + 6x0x0 + 4, 2.08/1.14 2.08/1.14 [d] = 0, 2.08/1.14 2.08/1.14 [c] = 0, 2.08/1.14 2.08/1.14 [a] = 1 2.08/1.14 orientation: 2.08/1.14 a() = 1 >= 0 = c() 2.08/1.14 2.08/1.14 a() = 1 >= 0 = d() 2.08/1.14 2.08/1.14 ?1(c(),x) = x + 4 >= x = x 2.08/1.14 2.08/1.14 f(x) = 6x*x + 5 >= -3x + 6x*x + 4 = ?1(x,x) 2.08/1.14 problem: 2.08/1.14 2.08/1.14 Qed 2.08/1.14 This critical pair is not context-joinable. 2.08/1.14 ConCon could not decide whether all 2 critical pairs are joinable or not. 2.08/1.14 Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {}) 2.08/1.14 CP: c = d 2.08/1.14 This critical pair is not context-joinable. 2.08/1.14 2.37/1.16 EOF