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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (*top*_0 1) 0.001/0.001 (f_0 1) 0.001/0.001 (f_1 1) 0.001/0.001 (h_1) 0.001/0.001 (i_1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 *top*_0(f_1(i_1(x:S:S))) -> *top*_0(x:S:S) 0.001/0.001 f_0(f_1(i_1(x:S:S))) -> f_1(x:S:S) 0.001/0.001 f_1(h_1(x:S:S)) -> f_1(i_1(x:S:S)) 0.001/0.001 f_1(i_1(x:S:S)) -> x:S:S 0.001/0.001 h_1(x:S:S) -> f_1(h_1(x:S:S)) 0.001/0.001 i_1(x:S:S) -> h_1(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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (*top*_0 1) 0.001/0.001 (f_0 1) 0.001/0.001 (f_1 1) 0.001/0.001 (h_1) 0.001/0.001 (i_1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 *top*_0(f_1(i_1(x:S:S))) -> *top*_0(x:S:S) 0.001/0.001 f_0(f_1(i_1(x:S:S))) -> f_1(x:S:S) 0.001/0.001 f_1(h_1(x:S:S)) -> f_1(i_1(x:S:S)) 0.001/0.001 f_1(i_1(x:S:S)) -> x:S:S 0.001/0.001 h_1(x:S:S) -> f_1(h_1(x:S:S)) 0.001/0.001 i_1(x:S:S) -> h_1(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 Left-Homogeneous u-Replacing Variables Processor: 0.001/0.001 R satisfies LHRV condition 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) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (*top*_0 1) 0.001/0.001 (f_0 1) 0.001/0.001 (f_1 1) 0.001/0.001 (h_1) 0.001/0.001 (i_1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 *top*_0(f_1(i_1(x:S:S))) -> *top*_0(x:S:S) 0.001/0.001 f_0(f_1(i_1(x:S:S))) -> f_1(x:S:S) 0.001/0.001 f_1(h_1(x:S:S)) -> f_1(i_1(x:S:S)) 0.001/0.001 f_1(i_1(x:S:S)) -> x:S:S 0.001/0.001 h_1(x:S:S) -> f_1(h_1(x:S:S)) 0.001/0.001 i_1(x:S:S) -> h_1(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 *top*_0(f_1(i_1(x:S:S))) -> *top*_0(x:S:S) 0.001/0.001 f_0(f_1(i_1(x:S:S))) -> f_1(x:S:S) 0.001/0.001 f_1(h_1(x:S:S)) -> f_1(i_1(x:S:S)) 0.001/0.001 f_1(i_1(x:S:S)) -> x:S:S 0.001/0.001 h_1(x:S:S) -> f_1(h_1(x:S:S)) 0.001/0.001 i_1(x:S:S) -> h_1(x:S:S) 0.001/0.001 -> Vars: 0.001/0.001 x:S, x:S, x:S, x:S, x:S, x:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [x:S], UV-LFrozen: [x:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [x:S], UV-LFrozen: [x:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x:S], UV-RFrozen: [x:S]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [x:S], UV-LFrozen: [x:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x:S], UV-RFrozen: [x:S]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x:S], UV-RFrozen: [x:S]) 0.001/0.001 -> FVars: 0.001/0.001 x3, x4, x5, x6, x7, x8 0.001/0.001 -> PVars: 0.001/0.001 x:S: [x3, x4, x5, x6, x7, x8] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: *top*_0(f_1(i_1(x3:S))) -> *top*_0(x3:S), id: 1, possubterms: *top*_0(f_1(i_1(x3:S)))->[], f_1(i_1(x3:S))->[1], i_1(x3:S)->[1, 1]) 0.001/0.001 (rule: f_0(f_1(i_1(x4:S))) -> f_1(x4:S), id: 2, possubterms: f_0(f_1(i_1(x4:S)))->[], f_1(i_1(x4:S))->[1], i_1(x4:S)->[1, 1]) 0.001/0.001 (rule: f_1(h_1(x5:S)) -> f_1(i_1(x5:S)), id: 3, possubterms: f_1(h_1(x5:S))->[], h_1(x5:S)->[1]) 0.001/0.001 (rule: f_1(i_1(x6:S)) -> x6:S, id: 4, possubterms: f_1(i_1(x6:S))->[], i_1(x6:S)->[1]) 0.001/0.001 (rule: h_1(x7:S) -> f_1(h_1(x7:S)), id: 5, possubterms: h_1(x7:S)->[]) 0.001/0.001 (rule: i_1(x8:S) -> h_1(x8:S), id: 6, possubterms: i_1(x8:S)->[]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R1 unifies with R4 at p: [1], l: *top*_0(f_1(i_1(x3:S))), lp: f_1(i_1(x3:S)), sig: {x3:S -> x:S:S}, l': f_1(i_1(x:S:S)), r: *top*_0(x3:S), r': x:S:S) 0.001/0.001 (R1 unifies with R6 at p: [1,1], l: *top*_0(f_1(i_1(x3:S))), lp: i_1(x3:S), sig: {x3:S -> x:S:S}, l': i_1(x:S:S), r: *top*_0(x3:S), r': h_1(x:S:S)) 0.001/0.001 (R2 unifies with R4 at p: [1], l: f_0(f_1(i_1(x4:S))), lp: f_1(i_1(x4:S)), sig: {x4:S -> x:S:S}, l': f_1(i_1(x:S:S)), r: f_1(x4:S), r': x:S:S) 0.001/0.001 (R2 unifies with R6 at p: [1,1], l: f_0(f_1(i_1(x4:S))), lp: i_1(x4:S), sig: {x4:S -> x:S:S}, l': i_1(x:S:S), r: f_1(x4:S), r': h_1(x:S:S)) 0.001/0.001 (R3 unifies with R5 at p: [1], l: f_1(h_1(x5:S)), lp: h_1(x5:S), sig: {x5:S -> x:S:S}, l': h_1(x:S:S), r: f_1(i_1(x5:S)), r': f_1(h_1(x:S:S))) 0.001/0.001 (R4 unifies with R6 at p: [1], l: f_1(i_1(x6:S)), lp: i_1(x6:S), sig: {x6:S -> x:S:S}, l': i_1(x:S:S), r: x6:S, r': h_1(x:S:S)) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 <*top*_0(f_1(h_1(x:S:S))),*top*_0(x:S:S)> => Not trivial, Not overlay, NW0, N1 0.001/0.001 => Not trivial, Not overlay, NW0, N2 0.001/0.001 <*top*_0(x:S:S),*top*_0(x:S:S)> => Trivial, Not overlay, NW0, N3 0.001/0.001 => Not trivial, Not overlay, NW0, N4 0.001/0.001 => Not trivial, Not overlay, NW0, N5 0.001/0.001 => Not trivial, Not overlay, NW0, N6 0.001/0.001 0.001/0.001 -> Problem conclusions: 0.001/0.001 Left linear, Right linear, 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, 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, Not overlay, NW0, N2, 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 9628maxresident)k 0.001/0.001 8inputs+0outputs (0major+795minor)pagefaults 0swaps