3.34/1.73 MAYBE 3.34/1.73 3.34/1.73 Proof: 3.34/1.73 ConCon could not decide confluence of the system. 3.34/1.73 \cite{ALS94}, Theorem 4.1 does not apply. 3.34/1.73 This system is of type 3 or smaller. 3.34/1.73 This system is strongly deterministic. 3.34/1.73 This system is quasi-decreasing. 3.34/1.73 By \cite{A14}, Theorem 11.5.9. 3.34/1.73 This system is of type 3 or smaller. 3.34/1.73 This system is deterministic. 3.34/1.73 System R transformed to V(R) + Emb. 3.34/1.73 This system is terminating. 3.34/1.73 Call external tool: 3.34/1.73 ./ttt2.sh 3.34/1.73 Input: 3.34/1.73 (VAR x) 3.34/1.73 (RULES 3.34/1.73 a -> c 3.34/1.73 a -> d 3.34/1.73 f(x) -> x 3.34/1.73 f(x) -> d 3.34/1.73 f(x) -> x 3.34/1.73 ) 3.34/1.73 3.34/1.73 Polynomial Interpretation Processor: 3.34/1.73 dimension: 1 3.34/1.73 interpretation: 3.34/1.73 [f](x0) = 2x0 + 4, 3.34/1.73 3.34/1.73 [d] = 0, 3.34/1.73 3.34/1.73 [c] = 0, 3.34/1.73 3.34/1.73 [a] = 4 3.34/1.73 orientation: 3.34/1.73 a() = 4 >= 0 = c() 3.34/1.73 3.34/1.73 a() = 4 >= 0 = d() 3.34/1.73 3.34/1.73 f(x) = 2x + 4 >= x = x 3.34/1.73 3.34/1.73 f(x) = 2x + 4 >= 0 = d() 3.34/1.73 problem: 3.34/1.73 3.34/1.73 Qed 3.34/1.73 ConCon could not decide whether all 2 critical pairs are joinable or not. 3.34/1.73 Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {}) 3.34/1.73 CP: c = d 3.34/1.73 ConCon could not decide context-joinability of this critical pair. 3.34/1.73 3.34/1.74 EOF