3.68/1.86 MAYBE 3.68/1.86 3.68/1.86 Proof: 3.68/1.86 ConCon could not decide confluence of the system. 3.68/1.86 Inlined conditions in System R. 3.68/1.86 \cite{ALS94}, Theorem 4.1 does not apply. 3.68/1.86 This system is of type 3 or smaller. 3.68/1.86 This system is strongly deterministic. 3.68/1.86 This system is quasi-decreasing. 3.68/1.86 By \cite{O02}, p. 214, Proposition 7.2.50. 3.68/1.86 This system is of type 3 or smaller. 3.68/1.86 This system is deterministic. 3.68/1.86 System R transformed to optimized U(R). 3.68/1.86 This system is terminating. 3.68/1.86 Call external tool: 3.68/1.86 ./ttt2.sh 3.68/1.86 Input: 3.68/1.86 (VAR x) 3.68/1.86 (RULES 3.68/1.86 c -> t(k) 3.68/1.86 f(x) -> s(x) 3.68/1.86 c -> t(l) 3.68/1.86 s(b) -> c 3.68/1.86 g(x, x) -> h(x, x) 3.68/1.86 s(a) -> c 3.68/1.86 ) 3.68/1.86 3.68/1.86 Polynomial Interpretation Processor: 3.68/1.86 dimension: 1 3.68/1.86 interpretation: 3.68/1.86 [a] = 2, 3.68/1.86 3.68/1.86 [h](x0, x1) = 3x0 + 5x1 + 2x0x0, 3.68/1.86 3.68/1.86 [g](x0, x1) = 7x0 + 6x1 + 2x1x1 + 2, 3.68/1.86 3.68/1.86 [b] = 4, 3.68/1.86 3.68/1.86 [l] = 0, 3.68/1.86 3.68/1.86 [s](x0) = x0 + 4x0x0 + 4, 3.68/1.86 3.68/1.86 [f](x0) = 4x0 + 7x0x0 + 6, 3.68/1.86 3.68/1.86 [t](x0) = 5x0 + x0x0, 3.68/1.86 3.68/1.86 [k] = 0, 3.68/1.86 3.68/1.86 [c] = 4 3.68/1.86 orientation: 3.68/1.86 c() = 4 >= 0 = t(k()) 3.68/1.86 3.68/1.86 f(x) = 4x + 7x*x + 6 >= x + 4x*x + 4 = s(x) 3.68/1.86 3.68/1.86 c() = 4 >= 0 = t(l()) 3.68/1.86 3.68/1.86 s(b()) = 72 >= 4 = c() 3.68/1.86 3.68/1.86 g(x,x) = 13x + 2x*x + 2 >= 8x + 2x*x = h(x,x) 3.79/1.86 3.79/1.87 s(a()) = 22 >= 4 = c() 3.79/1.87 problem: 3.79/1.87 3.79/1.87 Qed 3.79/1.87 ConCon could not decide whether all 2 critical pairs are joinable or not. 3.79/1.87 Overlap: (rule1: c -> t(l), rule2: c -> t(k), pos: ε, mgu: {}) 3.79/1.87 CP: t(k) = t(l) 3.79/1.87 ConCon could not decide context-joinability of this critical pair. 3.79/1.87 3.79/1.87 EOF