12.12/4.74 MAYBE 12.12/4.74 12.12/4.74 Proof: 12.12/4.74 ConCon could not decide confluence of the system. 12.12/4.75 \cite{ALS94}, Theorem 4.1 does not apply. 12.12/4.75 This system is of type 3 or smaller. 12.12/4.75 This system is strongly deterministic. 12.12/4.75 This system is quasi-decreasing. 12.12/4.75 By \cite{A14}, Theorem 11.5.9. 12.12/4.75 This system is of type 3 or smaller. 12.12/4.75 This system is deterministic. 12.12/4.75 System R transformed to V(R) + Emb. 12.12/4.75 This system is terminating. 12.12/4.75 Call external tool: 12.12/4.75 ./ttt2.sh -s COMP[30] -ext trs - 12.12/4.75 Input: 12.12/4.75 (VAR x) 12.12/4.75 (RULES 12.12/4.75 e(0) -> true 12.12/4.75 e(s(x)) -> true 12.12/4.75 e(s(x)) -> o(x) 12.12/4.75 e(s(x)) -> false 12.12/4.75 e(s(x)) -> e(x) 12.12/4.75 o(0) -> false 12.12/4.75 o(s(x)) -> true 12.12/4.75 o(s(x)) -> e(x) 12.12/4.75 o(s(x)) -> false 12.12/4.75 o(s(x)) -> o(x) 12.12/4.75 s(x) -> x 12.12/4.75 o(x) -> x 12.12/4.75 e(x) -> x 12.12/4.75 ) 12.12/4.75 12.12/4.75 Matrix Interpretation Processor: dim=3 12.12/4.75 12.12/4.75 interpretation: 12.12/4.75 12.12/4.75 [o](x0) = x0 12.12/4.75 , 12.12/4.75 12.12/4.75 12.12/4.75 [e](x0) = x0 12.12/4.75 , 12.12/4.75 12.12/4.75 [1] 12.12/4.75 [s](x0) = x0 + [0] 12.12/4.75 [0], 12.12/4.75 12.12/4.75 [0] 12.12/4.75 [false] = [0] 12.12/4.75 [0], 12.12/4.75 12.12/4.75 [1] 12.12/4.75 [0] = [0] 12.12/4.75 [0], 12.12/4.75 12.12/4.75 [0] 12.12/4.75 [true] = [0] 12.12/4.75 [0] 12.12/4.75 orientation: 12.12/4.75 [1] [0] 12.12/4.75 e(0()) = [0] >= [0] = true() 12.12/4.75 [0] [0] 12.12/4.75 12.12/4.75 [1] [0] 12.12/4.75 e(s(x)) = x + [0] >= [0] = true() 12.12/4.75 [0] [0] 12.12/4.75 12.12/4.75 [1] 12.12/4.75 e(s(x)) = x + [0] >= x = o(x) 12.12/4.75 [0] 12.12/4.75 12.12/4.75 [1] [0] 12.12/4.75 e(s(x)) = x + [0] >= [0] = false() 12.12/4.75 [0] [0] 12.12/4.75 12.12/4.75 [1] 12.12/4.75 e(s(x)) = x + [0] >= x = e(x) 12.12/4.75 [0] 12.12/4.75 12.12/4.75 [1] [0] 12.12/4.75 o(0()) = [0] >= [0] = false() 12.12/4.75 [0] [0] 12.12/4.75 12.12/4.75 [1] [0] 12.12/4.75 o(s(x)) = x + [0] >= [0] = true() 12.12/4.75 [0] [0] 12.12/4.75 12.12/4.75 [1] 12.12/4.75 o(s(x)) = x + [0] >= x = e(x) 12.12/4.75 [0] 12.12/4.75 12.12/4.75 [1] [0] 12.12/4.75 o(s(x)) = x + [0] >= [0] = false() 12.12/4.75 [0] [0] 12.12/4.75 12.12/4.75 [1] 12.12/4.75 o(s(x)) = x + [0] >= x = o(x) 12.12/4.75 [0] 12.12/4.75 12.12/4.75 [1] 12.12/4.75 s(x) = x + [0] >= x = x 12.12/4.75 [0] 12.12/4.75 12.12/4.75 12.12/4.75 o(x) = x >= x = x 12.12/4.75 12.12/4.75 12.12/4.75 12.12/4.75 e(x) = x >= x = x 12.12/4.75 12.12/4.75 problem: 12.12/4.75 o(x) -> x 12.12/4.75 e(x) -> x 12.12/4.75 Matrix Interpretation Processor: dim=3 12.12/4.75 12.12/4.75 interpretation: 12.12/4.75 12.12/4.75 [o](x0) = x0 12.12/4.75 , 12.12/4.75 12.12/4.75 [1] 12.12/4.75 [e](x0) = x0 + [0] 12.12/4.75 [0] 12.12/4.75 orientation: 12.12/4.75 12.12/4.75 o(x) = x >= x = x 12.12/4.75 12.12/4.75 12.12/4.75 [1] 12.12/4.75 e(x) = x + [0] >= x = x 12.12/4.75 [0] 12.12/4.75 problem: 12.12/4.75 o(x) -> x 12.12/4.75 Matrix Interpretation Processor: dim=3 12.12/4.75 12.12/4.75 interpretation: 12.12/4.75 [1] 12.12/4.75 [o](x0) = x0 + [0] 12.12/4.75 [0] 12.12/4.75 orientation: 12.12/4.75 [1] 12.12/4.75 o(x) = x + [0] >= x = x 12.12/4.75 [0] 12.12/4.75 problem: 12.12/4.75 12.12/4.75 Qed 12.12/4.75 This critical pair is conditional. 12.12/4.75 This critical pair has some non-trivial conditions. 12.12/4.75 ConCon could not decide whether all 4 critical pairs are joinable or not. 12.12/4.75 Overlap: (rule1: e(s(y)) -> false <= e(y) = true, rule2: e(s(z)) -> true <= o(z) = true, pos: ε, mgu: {(y,z)}) 12.12/4.75 CP: true = false <= e(z) = true, o(z) = true 12.12/4.75 ConCon could not decide infeasibility of this critical pair. 12.12/4.75 maedmax: MAYBE 12.12/4.75 12.24/4.77 EOF