3.33/1.74 MAYBE 3.33/1.74 3.33/1.74 Proof: 3.33/1.74 ConCon could not decide confluence of the system. 3.33/1.74 \cite{ALS94}, Theorem 4.1 does not apply. 3.33/1.74 This system is of type 3 or smaller. 3.33/1.74 This system is strongly deterministic. 3.33/1.74 This system is quasi-decreasing. 3.33/1.74 By \cite{A14}, Theorem 11.5.9. 3.33/1.74 This system is of type 3 or smaller. 3.33/1.74 This system is deterministic. 3.33/1.74 System R transformed to V(R) + Emb. 3.33/1.74 This system is terminating. 3.33/1.74 Call external tool: 3.33/1.74 ./ttt2.sh 3.33/1.74 Input: 3.33/1.74 (VAR x) 3.33/1.74 (RULES 3.33/1.74 a -> c 3.33/1.74 a -> d 3.33/1.74 f(x) -> x 3.33/1.74 f(x) -> d 3.33/1.74 f(x) -> x 3.33/1.74 ) 3.33/1.74 3.33/1.74 Polynomial Interpretation Processor: 3.33/1.74 dimension: 1 3.33/1.74 interpretation: 3.33/1.74 [f](x0) = 2x0 + 4, 3.33/1.74 3.33/1.74 [d] = 0, 3.33/1.74 3.33/1.74 [c] = 0, 3.33/1.74 3.33/1.74 [a] = 4 3.33/1.74 orientation: 3.33/1.74 a() = 4 >= 0 = c() 3.33/1.74 3.33/1.74 a() = 4 >= 0 = d() 3.33/1.74 3.33/1.74 f(x) = 2x + 4 >= x = x 3.33/1.74 3.33/1.74 f(x) = 2x + 4 >= 0 = d() 3.33/1.74 problem: 3.33/1.74 3.33/1.74 Qed 3.33/1.74 ConCon could not decide whether all 2 critical pairs are joinable or not. 3.33/1.74 Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {}) 3.33/1.74 CP: c = d 3.33/1.74 ConCon could not decide context-joinability of this critical pair. 3.33/1.74 3.33/1.77 EOF