0.00/0.02 NO 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 0.00/0.02 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.00/0.02 Confluence Problem: 0.00/0.02 (VAR vNonEmpty x) 0.00/0.02 (REPLACEMENT-MAP 0.00/0.02 (a 1) 0.00/0.02 (b 1) 0.00/0.02 (fSNonEmpty) 0.00/0.02 ) 0.00/0.02 (RULES 0.00/0.02 a(a(x)) -> b(b(b(x))) 0.00/0.02 b(b(b(b(x)))) -> a(a(a(x))) 0.00/0.02 ) 0.00/0.02 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.00/0.02 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 Not CS-TRS Procedure: 0.00/0.02 R is not a CS-TRS 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.00/0.02 Confluence Problem: 0.00/0.02 (VAR vNonEmpty x) 0.00/0.02 (REPLACEMENT-MAP 0.00/0.02 (a 1) 0.00/0.02 (b 1) 0.00/0.02 (fSNonEmpty) 0.00/0.02 ) 0.00/0.02 (RULES 0.00/0.02 a(a(x)) -> b(b(b(x))) 0.00/0.02 b(b(b(b(x)))) -> a(a(a(x))) 0.00/0.02 ) 0.00/0.02 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.00/0.02 0.00/0.02 Huet Levy Procedure: 0.00/0.02 -> Rules: 0.00/0.02 a(a(x)) -> b(b(b(x))) 0.00/0.02 b(b(b(b(x)))) -> a(a(a(x))) 0.00/0.02 -> Vars: 0.00/0.02 x, x 0.00/0.02 0.00/0.02 -> Rlps: 0.00/0.02 (rule: a(a(x)) -> b(b(b(x))), id: 1, possubterms: a(a(x))->[], a(x)->[1]) 0.00/0.02 (rule: b(b(b(b(x)))) -> a(a(a(x))), id: 2, possubterms: b(b(b(b(x))))->[], b(b(b(x)))->[1], b(b(x))->[1, 1], b(x)->[1, 1, 1]) 0.00/0.02 0.00/0.02 -> Unifications: 0.00/0.02 (R1 unifies with R1 at p: [1], l: a(a(x)), lp: a(x), sig: {x -> a(x')}, l': a(a(x')), r: b(b(b(x))), r': b(b(b(x')))) 0.00/0.02 (R2 unifies with R2 at p: [1], l: b(b(b(b(x)))), lp: b(b(b(x))), sig: {x -> b(x')}, l': b(b(b(b(x')))), r: a(a(a(x))), r': a(a(a(x')))) 0.00/0.02 (R2 unifies with R2 at p: [1,1], l: b(b(b(b(x)))), lp: b(b(x)), sig: {x -> b(b(x'))}, l': b(b(b(b(x')))), r: a(a(a(x))), r': a(a(a(x')))) 0.00/0.02 (R2 unifies with R2 at p: [1,1,1], l: b(b(b(b(x)))), lp: b(x), sig: {x -> b(b(b(x')))}, l': b(b(b(b(x')))), r: a(a(a(x))), r': a(a(a(x')))) 0.00/0.02 0.00/0.02 -> Critical pairs info: 0.00/0.02 => Not trivial, Not overlay, Proper, NW0, N1 0.00/0.02 => Not trivial, Not overlay, Proper, NW0, N2 0.00/0.02 => Not trivial, Not overlay, Proper, NW0, N3 0.00/0.02 => Not trivial, Not overlay, Proper, NW0, N4 0.00/0.02 0.00/0.02 -> Problem conclusions: 0.00/0.02 Left linear, Right linear, Linear 0.00/0.02 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.00/0.02 Not Huet-Levy confluent, Not Newman confluent 0.00/0.02 R is a TRS 0.00/0.02 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 No Convergence Brute Force Procedure: 0.00/0.02 -> Rewritings: 0.00/0.02 s: a(b(b(b(x')))) 0.00/0.02 Nodes: [0] 0.00/0.02 Edges: [] 0.00/0.02 ID: 0 => ('a(b(b(b(x'))))', D0) 0.00/0.02 t: b(b(b(a(x')))) 0.00/0.02 Nodes: [0] 0.00/0.02 Edges: [] 0.00/0.02 ID: 0 => ('b(b(b(a(x'))))', D0) 0.00/0.02 a(b(b(b(x')))) ->* no union *<- b(b(b(a(x')))) 0.00/0.02 "Not joinable" 0.00/0.02 0.00/0.02 The problem is not confluent. 0.00/0.02 EOF