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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (dbl 1) 0.001/0.001 (dbl1 1) 0.001/0.001 (dbls 1) 0.001/0.001 (from) 0.001/0.001 (indx 1) 0.001/0.001 (quote 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (sel1 1 2) 0.001/0.001 (0) 0.001/0.001 (01) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (s1 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 dbl(0) -> 0 0.001/0.001 dbl(s(X:S)) -> s(s(dbl(X:S))) 0.001/0.001 dbl1(0) -> 01 0.001/0.001 dbl1(s(X:S)) -> s1(s1(dbl1(X:S))) 0.001/0.001 dbls(cons(X:S,Y:S)) -> cons(dbl(X:S),dbls(Y:S)) 0.001/0.001 dbls(nil) -> nil 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 indx(cons(X:S,Y:S),Z:S) -> cons(sel(X:S,Z:S),indx(Y:S,Z:S)) 0.001/0.001 indx(nil,X:S) -> nil 0.001/0.001 quote(dbl(X:S)) -> dbl1(X:S) 0.001/0.001 quote(sel(X:S,Y:S)) -> sel1(X:S,Y:S) 0.001/0.001 quote(0) -> 01 0.001/0.001 quote(s(X:S)) -> s1(quote(X:S)) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S) 0.001/0.001 sel1(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel1(s(X:S),cons(Y:S,Z:S)) -> sel1(X:S,Z: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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (dbl 1) 0.001/0.001 (dbl1 1) 0.001/0.001 (dbls 1) 0.001/0.001 (from) 0.001/0.001 (indx 1) 0.001/0.001 (quote 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (sel1 1 2) 0.001/0.001 (0) 0.001/0.001 (01) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (s1 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 dbl(0) -> 0 0.001/0.001 dbl(s(X:S)) -> s(s(dbl(X:S))) 0.001/0.001 dbl1(0) -> 01 0.001/0.001 dbl1(s(X:S)) -> s1(s1(dbl1(X:S))) 0.001/0.001 dbls(cons(X:S,Y:S)) -> cons(dbl(X:S),dbls(Y:S)) 0.001/0.001 dbls(nil) -> nil 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 indx(cons(X:S,Y:S),Z:S) -> cons(sel(X:S,Z:S),indx(Y:S,Z:S)) 0.001/0.001 indx(nil,X:S) -> nil 0.001/0.001 quote(dbl(X:S)) -> dbl1(X:S) 0.001/0.001 quote(sel(X:S,Y:S)) -> sel1(X:S,Y:S) 0.001/0.001 quote(0) -> 01 0.001/0.001 quote(s(X:S)) -> s1(quote(X:S)) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S) 0.001/0.001 sel1(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel1(s(X:S),cons(Y:S,Z:S)) -> sel1(X:S,Z: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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (dbl 1) 0.001/0.001 (dbl1 1) 0.001/0.001 (dbls 1) 0.001/0.001 (from) 0.001/0.001 (indx 1) 0.001/0.001 (quote 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (sel1 1 2) 0.001/0.001 (0) 0.001/0.001 (01) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (s1 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 dbl(0) -> 0 0.001/0.001 dbl(s(X:S)) -> s(s(dbl(X:S))) 0.001/0.001 dbl1(0) -> 01 0.001/0.001 dbl1(s(X:S)) -> s1(s1(dbl1(X:S))) 0.001/0.001 dbls(cons(X:S,Y:S)) -> cons(dbl(X:S),dbls(Y:S)) 0.001/0.001 dbls(nil) -> nil 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 indx(cons(X:S,Y:S),Z:S) -> cons(sel(X:S,Z:S),indx(Y:S,Z:S)) 0.001/0.001 indx(nil,X:S) -> nil 0.001/0.001 quote(dbl(X:S)) -> dbl1(X:S) 0.001/0.001 quote(sel(X:S,Y:S)) -> sel1(X:S,Y:S) 0.001/0.001 quote(0) -> 01 0.001/0.001 quote(s(X:S)) -> s1(quote(X:S)) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S) 0.001/0.001 sel1(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel1(s(X:S),cons(Y:S,Z:S)) -> sel1(X:S,Z: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 dbl(0) -> 0 0.001/0.001 dbl(s(X:S)) -> s(s(dbl(X:S))) 0.001/0.001 dbl1(0) -> 01 0.001/0.001 dbl1(s(X:S)) -> s1(s1(dbl1(X:S))) 0.001/0.001 dbls(cons(X:S,Y:S)) -> cons(dbl(X:S),dbls(Y:S)) 0.001/0.001 dbls(nil) -> nil 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 indx(cons(X:S,Y:S),Z:S) -> cons(sel(X:S,Z:S),indx(Y:S,Z:S)) 0.001/0.001 indx(nil,X:S) -> nil 0.001/0.001 quote(dbl(X:S)) -> dbl1(X:S) 0.001/0.001 quote(sel(X:S,Y:S)) -> sel1(X:S,Y:S) 0.001/0.001 quote(0) -> 01 0.001/0.001 quote(s(X:S)) -> s1(quote(X:S)) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S) 0.001/0.001 sel1(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel1(s(X:S),cons(Y:S,Z:S)) -> sel1(X:S,Z:S) 0.001/0.001 -> Vars: 0.001/0.001 X, X, X, Y, X, X, Y, Z, X, X, X, Y, X, X, Y, X, Y, Z, X, Y, X, Y, Z 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X], UV-RFrozen: [X]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: [X, Y]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X], UV-RFrozen: [X]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y, Z], UV-RFrozen: [X, Y, Z]) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [X, Y], UV-RActive: [X, Y], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X, Y], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [X, Z], UV-LFrozen: [X, Y, Z], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X, Y], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [X, Z], UV-LFrozen: [X, Y, Z], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26 0.001/0.001 -> PVars: 0.001/0.001 X: [x4, x5, x6, x8, x9, x12, x13, x14, x16, x17, x19, x22, x24], Y: [x7, x10, x15, x18, x20, x23, x25], Z: [x11, x21, x26] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: dbl(0) -> 0, id: 1, possubterms: dbl(0)->[], 0->[1]) 0.001/0.001 (rule: dbl(s(x4:S)) -> s(s(dbl(x4:S))), id: 2, possubterms: dbl(s(x4:S))->[], s(x4:S)->[1]) 0.001/0.001 (rule: dbl1(0) -> 01, id: 3, possubterms: dbl1(0)->[], 0->[1]) 0.001/0.001 (rule: dbl1(s(x5:S)) -> s1(s1(dbl1(x5:S))), id: 4, possubterms: dbl1(s(x5:S))->[], s(x5:S)->[1]) 0.001/0.001 (rule: dbls(cons(x6:S,x7:S)) -> cons(dbl(x6:S),dbls(x7:S)), id: 5, possubterms: dbls(cons(x6:S,x7:S))->[], cons(x6:S,x7:S)->[1]) 0.001/0.001 (rule: dbls(nil) -> nil, id: 6, possubterms: dbls(nil)->[], nil->[1]) 0.001/0.001 (rule: from(x8:S) -> cons(x8:S,from(s(x8:S))), id: 7, possubterms: from(x8:S)->[]) 0.001/0.001 (rule: indx(cons(x9:S,x10:S),x11:S) -> cons(sel(x9:S,x11:S),indx(x10:S,x11:S)), id: 8, possubterms: indx(cons(x9:S,x10:S),x11:S)->[], cons(x9:S,x10:S)->[1]) 0.001/0.001 (rule: indx(nil,x12:S) -> nil, id: 9, possubterms: indx(nil,x12:S)->[], nil->[1]) 0.001/0.001 (rule: quote(dbl(x13:S)) -> dbl1(x13:S), id: 10, possubterms: quote(dbl(x13:S))->[], dbl(x13:S)->[1]) 0.001/0.001 (rule: quote(sel(x14:S,x15:S)) -> sel1(x14:S,x15:S), id: 11, possubterms: quote(sel(x14:S,x15:S))->[], sel(x14:S,x15:S)->[1]) 0.001/0.001 (rule: quote(0) -> 01, id: 12, possubterms: quote(0)->[], 0->[1]) 0.001/0.001 (rule: quote(s(x16:S)) -> s1(quote(x16:S)), id: 13, possubterms: quote(s(x16:S))->[], s(x16:S)->[1]) 0.001/0.001 (rule: sel(0,cons(x17:S,x18:S)) -> x17:S, id: 14, possubterms: sel(0,cons(x17:S,x18:S))->[], 0->[1], cons(x17:S,x18:S)->[2]) 0.001/0.001 (rule: sel(s(x19:S),cons(x20:S,x21:S)) -> sel(x19:S,x21:S), id: 15, possubterms: sel(s(x19:S),cons(x20:S,x21:S))->[], s(x19:S)->[1], cons(x20:S,x21:S)->[2]) 0.001/0.001 (rule: sel1(0,cons(x22:S,x23:S)) -> x22:S, id: 16, possubterms: sel1(0,cons(x22:S,x23:S))->[], 0->[1], cons(x22:S,x23:S)->[2]) 0.001/0.001 (rule: sel1(s(x24:S),cons(x25:S,x26:S)) -> sel1(x24:S,x26:S), id: 17, possubterms: sel1(s(x24:S),cons(x25:S,x26:S))->[], s(x24:S)->[1], cons(x25:S,x26:S)->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R10 unifies with R1 at p: [1], l: quote(dbl(x13:S)), lp: dbl(x13:S), sig: {x13:S -> 0}, l': dbl(0), r: dbl1(x13:S), r': 0) 0.001/0.001 (R10 unifies with R2 at p: [1], l: quote(dbl(x13:S)), lp: dbl(x13:S), sig: {x13:S -> s(X:S)}, l': dbl(s(X:S)), r: dbl1(x13:S), r': s(s(dbl(X:S)))) 0.001/0.001 (R11 unifies with R14 at p: [1], l: quote(sel(x14:S,x15:S)), lp: sel(x14:S,x15:S), sig: {x14:S -> 0,x15:S -> cons(X:S,Y:S)}, l': sel(0,cons(X:S,Y:S)), r: sel1(x14:S,x15:S), r': X:S) 0.001/0.001 (R11 unifies with R15 at p: [1], l: quote(sel(x14:S,x15:S)), lp: sel(x14:S,x15:S), sig: {x14:S -> s(X:S),x15:S -> cons(Y:S,Z:S)}, l': sel(s(X:S),cons(Y:S,Z:S)), r: sel1(x14:S,x15:S), r': sel(X:S,Z:S)) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Not trivial, Not overlay, NW0, N1 0.001/0.001 => Not trivial, Not overlay, NW0, N2 0.001/0.001 => Not trivial, Not overlay, NW0, N3 0.001/0.001 => Not trivial, Not overlay, NW0, N4 0.001/0.001 0.001/0.001 -> Problem conclusions: 0.001/0.001 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, Left-homogeneous u-replacing variables 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 No Convergence Brute Force Processor: 0.001/0.001 -> Rewritings: 0.001/0.001 s: quote(X:S) 0.001/0.001 Nodes: [0] 0.001/0.001 Edges: [] 0.001/0.001 ID: 0 => ('quote(X:S)', D0) 0.001/0.001 t: sel1(0,cons(X:S,Y:S)) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('sel1(0,cons(X:S,Y:S))', D0) 0.001/0.001 ID: 1 => ('X:S', D1, R16, P[], S{x22:S -> X:S, x23:S -> Y:S}), NR: 'X:S' 0.001/0.001 quote(X:S) ->* no union *<- sel1(0,cons(X:S,Y:S)) 0.001/0.001 "Not joinable" 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 71%CPU (0avgtext+0avgdata 10072maxresident)k 0.001/0.001 0inputs+0outputs (0major+862minor)pagefaults 0swaps