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 Z:S: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 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (num01) 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(num0) -> num0 0.001/0.001 dbl(s(X:S:S)) -> s(s(dbl(X:S:S))) 0.001/0.001 dbl1(num0) -> num01 0.001/0.001 dbl1(s(X:S:S)) -> s1(s1(dbl1(X:S:S))) 0.001/0.001 dbls(cons(X:S:S,Y:S:S)) -> cons(dbl(X:S:S),dbls(Y:S:S)) 0.001/0.001 dbls(nil) -> nil 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 indx(cons(X:S:S,Y:S:S),Z:S:S) -> cons(sel(X:S:S,Z:S:S),indx(Y:S:S,Z:S:S)) 0.001/0.001 indx(nil,X:S:S) -> nil 0.001/0.001 quote(dbl(X:S:S)) -> dbl1(X:S:S) 0.001/0.001 quote(sel(X:S:S,Y:S:S)) -> sel1(X:S:S,Y:S:S) 0.001/0.001 quote(num0) -> num01 0.001/0.001 quote(s(X:S:S)) -> s1(quote(X:S:S)) 0.001/0.001 sel(num0,cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 sel(s(X:S:S),cons(Y:S:S,Z:S:S)) -> sel(X:S:S,Z:S:S) 0.001/0.001 sel1(num0,cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 sel1(s(X:S:S),cons(Y:S:S,Z:S:S)) -> sel1(X:S:S,Z: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 Z:S: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 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (num01) 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(num0) -> num0 0.001/0.001 dbl(s(X:S:S)) -> s(s(dbl(X:S:S))) 0.001/0.001 dbl1(num0) -> num01 0.001/0.001 dbl1(s(X:S:S)) -> s1(s1(dbl1(X:S:S))) 0.001/0.001 dbls(cons(X:S:S,Y:S:S)) -> cons(dbl(X:S:S),dbls(Y:S:S)) 0.001/0.001 dbls(nil) -> nil 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 indx(cons(X:S:S,Y:S:S),Z:S:S) -> cons(sel(X:S:S,Z:S:S),indx(Y:S:S,Z:S:S)) 0.001/0.001 indx(nil,X:S:S) -> nil 0.001/0.001 quote(dbl(X:S:S)) -> dbl1(X:S:S) 0.001/0.001 quote(sel(X:S:S,Y:S:S)) -> sel1(X:S:S,Y:S:S) 0.001/0.001 quote(num0) -> num01 0.001/0.001 quote(s(X:S:S)) -> s1(quote(X:S:S)) 0.001/0.001 sel(num0,cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 sel(s(X:S:S),cons(Y:S:S,Z:S:S)) -> sel(X:S:S,Z:S:S) 0.001/0.001 sel1(num0,cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 sel1(s(X:S:S),cons(Y:S:S,Z:S:S)) -> sel1(X:S:S,Z: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 Y:S:S Z:S: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 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (num01) 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(num0) -> num0 0.001/0.001 dbl(s(X:S:S)) -> s(s(dbl(X:S:S))) 0.001/0.001 dbl1(num0) -> num01 0.001/0.001 dbl1(s(X:S:S)) -> s1(s1(dbl1(X:S:S))) 0.001/0.001 dbls(cons(X:S:S,Y:S:S)) -> cons(dbl(X:S:S),dbls(Y:S:S)) 0.001/0.001 dbls(nil) -> nil 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 indx(cons(X:S:S,Y:S:S),Z:S:S) -> cons(sel(X:S:S,Z:S:S),indx(Y:S:S,Z:S:S)) 0.001/0.001 indx(nil,X:S:S) -> nil 0.001/0.001 quote(dbl(X:S:S)) -> dbl1(X:S:S) 0.001/0.001 quote(sel(X:S:S,Y:S:S)) -> sel1(X:S:S,Y:S:S) 0.001/0.001 quote(num0) -> num01 0.001/0.001 quote(s(X:S:S)) -> s1(quote(X:S:S)) 0.001/0.001 sel(num0,cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 sel(s(X:S:S),cons(Y:S:S,Z:S:S)) -> sel(X:S:S,Z:S:S) 0.001/0.001 sel1(num0,cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 sel1(s(X:S:S),cons(Y:S:S,Z:S:S)) -> sel1(X:S:S,Z: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 dbl(num0) -> num0 0.001/0.001 dbl(s(X:S:S)) -> s(s(dbl(X:S:S))) 0.001/0.001 dbl1(num0) -> num01 0.001/0.001 dbl1(s(X:S:S)) -> s1(s1(dbl1(X:S:S))) 0.001/0.001 dbls(cons(X:S:S,Y:S:S)) -> cons(dbl(X:S:S),dbls(Y:S:S)) 0.001/0.001 dbls(nil) -> nil 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 indx(cons(X:S:S,Y:S:S),Z:S:S) -> cons(sel(X:S:S,Z:S:S),indx(Y:S:S,Z:S:S)) 0.001/0.001 indx(nil,X:S:S) -> nil 0.001/0.001 quote(dbl(X:S:S)) -> dbl1(X:S:S) 0.001/0.001 quote(sel(X:S:S,Y:S:S)) -> sel1(X:S:S,Y:S:S) 0.001/0.001 quote(num0) -> num01 0.001/0.001 quote(s(X:S:S)) -> s1(quote(X:S:S)) 0.001/0.001 sel(num0,cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 sel(s(X:S:S),cons(Y:S:S,Z:S:S)) -> sel(X:S:S,Z:S:S) 0.001/0.001 sel1(num0,cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 sel1(s(X:S:S),cons(Y:S:S,Z:S:S)) -> sel1(X:S:S,Z:S:S) 0.001/0.001 -> Vars: 0.001/0.001 X:S, X:S, X:S, Y:S, X:S, X:S, Y:S, Z:S, X:S, X:S, X:S, Y:S, X:S, X:S, Y:S, X:S, Y:S, Z:S, X:S, Y:S, X:S, Y:S, Z:S 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:S], UV-RFrozen: [X:S]) 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:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 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:S], UV-RFrozen: [X:S]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S, Z:S], UV-RFrozen: [X:S, Y:S, Z:S]) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [X:S], UV-RActive: [X:S], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [X:S, Y:S], UV-RActive: [X:S, Y:S], 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:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [X:S, Z:S], UV-LFrozen: [X:S, Y:S, Z:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [X:S, Z:S], UV-LFrozen: [X:S, Y:S, Z:S], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x5, x6, x7, x9, x10, x13, x14, x15, x17, x18, x20, x23, x25], Y:S: [x8, x11, x16, x19, x21, x24, x26], Z:S: [x12, x22, x27] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: dbl(num0) -> num0, id: 1, possubterms: dbl(num0)->[], num0->[1]) 0.001/0.001 (rule: dbl(s(x5:S)) -> s(s(dbl(x5:S))), id: 2, possubterms: dbl(s(x5:S))->[], s(x5:S)->[1]) 0.001/0.001 (rule: dbl1(num0) -> num01, id: 3, possubterms: dbl1(num0)->[], num0->[1]) 0.001/0.001 (rule: dbl1(s(x6:S)) -> s1(s1(dbl1(x6:S))), id: 4, possubterms: dbl1(s(x6:S))->[], s(x6:S)->[1]) 0.001/0.001 (rule: dbls(cons(x7:S,x8:S)) -> cons(dbl(x7:S),dbls(x8:S)), id: 5, possubterms: dbls(cons(x7:S,x8:S))->[], cons(x7:S,x8:S)->[1]) 0.001/0.001 (rule: dbls(nil) -> nil, id: 6, possubterms: dbls(nil)->[], nil->[1]) 0.001/0.001 (rule: from(x9:S) -> cons(x9:S,from(s(x9:S))), id: 7, possubterms: from(x9:S)->[]) 0.001/0.001 (rule: indx(cons(x10:S,x11:S),x12:S) -> cons(sel(x10:S,x12:S),indx(x11:S,x12:S)), id: 8, possubterms: indx(cons(x10:S,x11:S),x12:S)->[], cons(x10:S,x11:S)->[1]) 0.001/0.001 (rule: indx(nil,x13:S) -> nil, id: 9, possubterms: indx(nil,x13:S)->[], nil->[1]) 0.001/0.001 (rule: quote(dbl(x14:S)) -> dbl1(x14:S), id: 10, possubterms: quote(dbl(x14:S))->[], dbl(x14:S)->[1]) 0.001/0.001 (rule: quote(sel(x15:S,x16:S)) -> sel1(x15:S,x16:S), id: 11, possubterms: quote(sel(x15:S,x16:S))->[], sel(x15:S,x16:S)->[1]) 0.001/0.001 (rule: quote(num0) -> num01, id: 12, possubterms: quote(num0)->[], num0->[1]) 0.001/0.001 (rule: quote(s(x17:S)) -> s1(quote(x17:S)), id: 13, possubterms: quote(s(x17:S))->[], s(x17:S)->[1]) 0.001/0.001 (rule: sel(num0,cons(x18:S,x19:S)) -> x18:S, id: 14, possubterms: sel(num0,cons(x18:S,x19:S))->[], num0->[1], cons(x18:S,x19:S)->[2]) 0.001/0.001 (rule: sel(s(x20:S),cons(x21:S,x22:S)) -> sel(x20:S,x22:S), id: 15, possubterms: sel(s(x20:S),cons(x21:S,x22:S))->[], s(x20:S)->[1], cons(x21:S,x22:S)->[2]) 0.001/0.001 (rule: sel1(num0,cons(x23:S,x24:S)) -> x23:S, id: 16, possubterms: sel1(num0,cons(x23:S,x24:S))->[], num0->[1], cons(x23:S,x24:S)->[2]) 0.001/0.001 (rule: sel1(s(x25:S),cons(x26:S,x27:S)) -> sel1(x25:S,x27:S), id: 17, possubterms: sel1(s(x25:S),cons(x26:S,x27:S))->[], s(x25:S)->[1], cons(x26:S,x27: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(x14:S)), lp: dbl(x14:S), sig: {x14:S -> num0}, l': dbl(num0), r: dbl1(x14:S), r': num0) 0.001/0.001 (R10 unifies with R2 at p: [1], l: quote(dbl(x14:S)), lp: dbl(x14:S), sig: {x14:S -> s(X:S:S)}, l': dbl(s(X:S:S)), r: dbl1(x14:S), r': s(s(dbl(X:S:S)))) 0.001/0.001 (R11 unifies with R14 at p: [1], l: quote(sel(x15:S,x16:S)), lp: sel(x15:S,x16:S), sig: {x15:S -> num0,x16:S -> cons(X:S:S,Y:S:S)}, l': sel(num0,cons(X:S:S,Y:S:S)), r: sel1(x15:S,x16:S), r': X:S:S) 0.001/0.001 (R11 unifies with R15 at p: [1], l: quote(sel(x15:S,x16:S)), lp: sel(x15:S,x16:S), sig: {x15:S -> s(X:S:S),x16:S -> cons(Y:S:S,Z:S:S)}, l': sel(s(X:S:S),cons(Y:S:S,Z:S:S)), r: sel1(x15:S,x16:S), r': sel(X:S:S,Z:S: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:S) 0.001/0.001 Nodes: [0] 0.001/0.001 Edges: [] 0.001/0.001 ID: 0 => ('quote(X:S:S)', D0) 0.001/0.001 t: sel1(num0,cons(X:S:S,Y:S:S)) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('sel1(num0,cons(X:S:S,Y:S:S))', D0) 0.001/0.001 ID: 1 => ('X:S:S', D1, R16, P[], S{x23:S -> X:S:S, x24:S -> Y:S:S}), NR: 'X:S:S' 0.001/0.001 quote(X:S:S) ->* no union *<- sel1(num0,cons(X:S:S,Y:S:S)) 0.001/0.001 "Not joinable" 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.01user 0.00system 0:00.01elapsed 91%CPU (0avgtext+0avgdata 10128maxresident)k 0.001/0.001 8inputs+0outputs (0major+880minor)pagefaults 0swaps