3.16/1.71 MAYBE 3.16/1.71 3.16/1.71 Proof: 3.16/1.71 ConCon could not decide confluence of the system. 3.16/1.71 \cite{ALS94}, Theorem 4.1 does not apply. 3.16/1.71 This system is of type 3 or smaller. 3.16/1.71 This system is strongly deterministic. 3.16/1.71 This system is quasi-decreasing. 3.16/1.71 By \cite{O02}, p. 214, Proposition 7.2.50. 3.16/1.71 This system is of type 3 or smaller. 3.16/1.71 This system is deterministic. 3.16/1.71 System R transformed to optimized U(R). 3.16/1.72 This system is terminating. 3.16/1.72 Call external tool: 3.16/1.72 ./ttt2.sh 3.16/1.72 Input: 3.16/1.72 (VAR x) 3.16/1.72 (RULES 3.16/1.72 a -> c 3.16/1.72 a -> d 3.16/1.72 f(x) -> ?1(x, x) 3.16/1.72 ?1(c, x) -> x 3.16/1.72 ) 3.16/1.72 3.16/1.72 Polynomial Interpretation Processor: 3.16/1.72 dimension: 1 3.16/1.72 interpretation: 3.16/1.72 [?1](x0, x1) = -2x0 + x1 + 4x0x0 + 4, 3.16/1.72 3.16/1.72 [f](x0) = 4x0 + 4x0x0 + 5, 3.16/1.72 3.16/1.72 [d] = 0, 3.16/1.72 3.16/1.72 [c] = 0, 3.16/1.72 3.16/1.72 [a] = 1 3.16/1.72 orientation: 3.16/1.72 a() = 1 >= 0 = c() 3.16/1.72 3.16/1.72 a() = 1 >= 0 = d() 3.16/1.72 3.16/1.72 f(x) = 4x + 4x*x + 5 >= -1x + 4x*x + 4 = ?1(x,x) 3.16/1.72 3.16/1.72 ?1(c(),x) = x + 4 >= x = x 3.16/1.72 problem: 3.16/1.72 3.16/1.72 Qed 3.16/1.72 ConCon could not decide whether all 2 critical pairs are joinable or not. 3.16/1.72 Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {}) 3.16/1.72 CP: c = d 3.16/1.72 ConCon could not decide context-joinability of this critical pair. 3.16/1.72 3.16/1.74 EOF