0.001/0.001 NO 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S x:S:S y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (f_1 2) 0.001/0.001 (g_1) 0.001/0.001 (a_0) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (i_0 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f_1(x:S:S,i_0(g_1(x:S:S))) -> a_0 0.001/0.001 f_1(x:S:S,i_0(x:S:S)) -> f_1(x:S:S,x:S:S) 0.001/0.001 f_1(x:S:S,x:S:S) -> f_1(i_0(x:S:S),g_1(g_1(x:S:S))) 0.001/0.001 f_1(x:S:S,y:S:S) -> x:S:S 0.001/0.001 g_1(x:S:S) -> i_0(x:S:S) 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 CleanTRS Processor: 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S x:S:S y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (f_1 2) 0.001/0.001 (g_1) 0.001/0.001 (a_0) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (i_0 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f_1(x:S:S,i_0(g_1(x:S:S))) -> a_0 0.001/0.001 f_1(x:S:S,i_0(x:S:S)) -> f_1(x:S:S,x:S:S) 0.001/0.001 f_1(x:S:S,x:S:S) -> f_1(i_0(x:S:S),g_1(g_1(x:S:S))) 0.001/0.001 f_1(x:S:S,y:S:S) -> x:S:S 0.001/0.001 g_1(x:S:S) -> i_0(x:S:S) 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 Modular Confluence Combinations Decomposition Processor: 0.001/0.001 It is a CTRS -> No modular confluence 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 CS-TRS Processor: 0.001/0.001 R is a CS-TRS 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S x:S:S y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (f_1 2) 0.001/0.001 (g_1) 0.001/0.001 (a_0) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (i_0 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f_1(x:S:S,i_0(g_1(x:S:S))) -> a_0 0.001/0.001 f_1(x:S:S,i_0(x:S:S)) -> f_1(x:S:S,x:S:S) 0.001/0.001 f_1(x:S:S,x:S:S) -> f_1(i_0(x:S:S),g_1(g_1(x:S:S))) 0.001/0.001 f_1(x:S:S,y:S:S) -> x:S:S 0.001/0.001 g_1(x:S:S) -> i_0(x:S:S) 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 f_1(x:S:S,i_0(g_1(x:S:S))) -> a_0 0.001/0.001 f_1(x:S:S,i_0(x:S:S)) -> f_1(x:S:S,x:S:S) 0.001/0.001 f_1(x:S:S,x:S:S) -> f_1(i_0(x:S:S),g_1(g_1(x:S:S))) 0.001/0.001 f_1(x:S:S,y:S:S) -> x:S:S 0.001/0.001 g_1(x:S:S) -> i_0(x:S:S) 0.001/0.001 -> Vars: 0.001/0.001 x:S, x:S, x:S, x:S, y:S, x:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [x:S], UV-RActive: [x:S], UV-LFrozen: [x:S], UV-RFrozen: [x:S]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [x:S], UV-RActive: [], UV-LFrozen: [x:S], UV-RFrozen: [x:S]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [y:S], UV-RActive: [x:S], UV-LFrozen: [x:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [x:S], UV-LFrozen: [x:S], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x4, x5, x6, x7, x8, x9 0.001/0.001 -> PVars: 0.001/0.001 x:S: [x4, x5, x6, x7, x9], y:S: [x8] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: f_1(x4:S,i_0(g_1(x4:S))) -> a_0, id: 1, possubterms: f_1(x4:S,i_0(g_1(x4:S)))->[], i_0(g_1(x4:S))->[2], g_1(x4:S)->[2, 1]) 0.001/0.001 (rule: f_1(x5:S,i_0(x5:S)) -> f_1(x5:S,x5:S), id: 2, possubterms: f_1(x5:S,i_0(x5:S))->[], i_0(x5:S)->[2]) 0.001/0.001 (rule: f_1(x6:S,x6:S) -> f_1(i_0(x6:S),g_1(g_1(x6:S))), id: 3, possubterms: f_1(x6:S,x6:S)->[]) 0.001/0.001 (rule: f_1(x7:S,x8:S) -> x7:S, id: 4, possubterms: f_1(x7:S,x8:S)->[]) 0.001/0.001 (rule: g_1(x9:S) -> i_0(x9:S), id: 5, possubterms: g_1(x9:S)->[]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R1 unifies with R5 at p: [2,1], l: f_1(x4:S,i_0(g_1(x4:S))), lp: g_1(x4:S), sig: {x4:S -> x:S:S}, l': g_1(x:S:S), r: a_0, r': i_0(x:S:S)) 0.001/0.001 (R4 unifies with R1 at p: [], l: f_1(x7:S,x8:S), lp: f_1(x7:S,x8:S), sig: {x7:S -> x:S:S,x8:S -> i_0(g_1(x:S:S))}, l': f_1(x:S:S,i_0(g_1(x:S:S))), r: x7:S, r': a_0) 0.001/0.001 (R4 unifies with R2 at p: [], l: f_1(x7:S,x8:S), lp: f_1(x7:S,x8:S), sig: {x7:S -> x:S:S,x8:S -> i_0(x:S:S)}, l': f_1(x:S:S,i_0(x:S:S)), r: x7:S, r': f_1(x:S:S,x:S:S)) 0.001/0.001 (R4 unifies with R3 at p: [], l: f_1(x7:S,x8:S), lp: f_1(x7:S,x8:S), sig: {x7:S -> x:S:S,x8:S -> x:S:S}, l': f_1(x:S:S,x:S:S), r: x7:S, r': f_1(i_0(x:S:S),g_1(g_1(x:S:S)))) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Not trivial, Overlay, NW0, N1 0.001/0.001 => Not trivial, Not overlay, NW0, N2 0.001/0.001 => Not trivial, Overlay, NW0, N3 0.001/0.001 => Not trivial, Overlay, NW0, N4 0.001/0.001 0.001/0.001 -> Problem conclusions: 0.001/0.001 Not left linear, Not right linear, Not linear 0.001/0.001 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.001/0.001 Not Huet-Levy confluent, Not Newman confluent 0.001/0.001 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 Different Normal CP Terms Processor: 0.001/0.001 => Not trivial, Overlay, NW0, N1, Normal and not trivial cp 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 50%CPU (0avgtext+0avgdata 9232maxresident)k 0.001/0.001 98inputs+0outputs (0major+759minor)pagefaults 0swaps