0.00/0.00 YES 0.00/0.00 0.00/0.00 Problem 1: 0.00/0.00 0.00/0.00 0.00/0.00 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.00/0.00 Confluence Problem: 0.00/0.00 (VAR vNonEmpty L N X) 0.00/0.00 (REPLACEMENT-MAP 0.00/0.00 (and 1) 0.00/0.00 (length 1) 0.00/0.00 (zeros) 0.00/0.00 (0) 0.00/0.00 (cons 1) 0.00/0.00 (fSNonEmpty) 0.00/0.00 (nil) 0.00/0.00 (s 1) 0.00/0.00 (tt) 0.00/0.00 ) 0.00/0.00 (RULES 0.00/0.00 and(tt,X) -> X 0.00/0.00 length(cons(N,L)) -> s(length(L)) 0.00/0.00 length(nil) -> 0 0.00/0.00 zeros -> cons(0,zeros) 0.00/0.00 ) 0.00/0.00 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.00/0.00 0.00/0.00 0.00/0.00 Problem 1: 0.00/0.00 0.00/0.00 Problem 1: 0.00/0.00 Left-Homogeneous u-Replacing Variables Procedure: 0.00/0.00 R satisfies LHRV condition 0.00/0.00 0.00/0.00 Problem 1: 0.00/0.00 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.00/0.00 Confluence Problem: 0.00/0.00 (VAR vNonEmpty L N X) 0.00/0.00 (REPLACEMENT-MAP 0.00/0.00 (and 1) 0.00/0.00 (length 1) 0.00/0.00 (zeros) 0.00/0.00 (0) 0.00/0.00 (cons 1) 0.00/0.00 (fSNonEmpty) 0.00/0.00 (nil) 0.00/0.00 (s 1) 0.00/0.00 (tt) 0.00/0.00 ) 0.00/0.00 (RULES 0.00/0.00 and(tt,X) -> X 0.00/0.00 length(cons(N,L)) -> s(length(L)) 0.00/0.00 length(nil) -> 0 0.00/0.00 zeros -> cons(0,zeros) 0.00/0.00 ) 0.00/0.00 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.00/0.00 0.00/0.00 Huet Levy Procedure: 0.00/0.00 -> Rules: 0.00/0.00 and(tt,X) -> X 0.00/0.00 length(cons(N,L)) -> s(length(L)) 0.00/0.00 length(nil) -> 0 0.00/0.00 zeros -> cons(0,zeros) 0.00/0.00 -> Vars: 0.00/0.00 X, L, N 0.00/0.00 -> UVars: 0.00/0.00 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.00/0.00 (UV-RuleId: 2, UV-LActive: [N], UV-RActive: [L], UV-LFrozen: [L], UV-RFrozen: []) 0.00/0.00 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.00/0.00 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.00/0.00 0.00/0.00 -> Rlps: 0.00/0.00 (rule: and(tt,X) -> X, id: 1, possubterms: and(tt,X)->[], tt->[1]) 0.00/0.00 (rule: length(cons(N,L)) -> s(length(L)), id: 2, possubterms: length(cons(N,L))->[], cons(N,L)->[1]) 0.00/0.00 (rule: length(nil) -> 0, id: 3, possubterms: length(nil)->[], nil->[1]) 0.00/0.00 (rule: zeros -> cons(0,zeros), id: 4, possubterms: zeros->[]) 0.00/0.00 0.00/0.00 -> Unifications: 0.00/0.00 0.00/0.00 0.00/0.00 -> Critical pairs info: 0.00/0.00 0.00/0.00 0.00/0.00 -> Problem conclusions: 0.00/0.00 Left linear, Right linear, Linear 0.00/0.00 Weakly orthogonal, Almost orthogonal, Orthogonal 0.00/0.00 Huet-Levy confluent, Not Newman confluent 0.00/0.00 R is a CS-TRS, Left-homogeneous u-replacing variables 0.00/0.00 0.00/0.00 0.00/0.00 The problem is confluent. 0.00/0.01 EOF