0.001/0.001 YES 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 (dbls 1) 0.001/0.001 (from) 0.001/0.001 (indx 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s) 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 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 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 ) 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 (dbls 1) 0.001/0.001 (from) 0.001/0.001 (indx 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s) 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 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 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 ) 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 (dbls 1) 0.001/0.001 (from) 0.001/0.001 (indx 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s) 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 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 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 ) 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 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 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 -> Vars: 0.001/0.001 X, X, Y, X, X, Y, Z, X, 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: [X, Y], UV-RFrozen: [X, Y]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X], UV-RFrozen: [X]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y, Z], UV-RFrozen: [X, Y, Z]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X, Y], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, 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 0.001/0.001 -> PVars: 0.001/0.001 X: [x4, x5, x7, x8, x11, x12, x14], Y: [x6, x9, x13, x15], Z: [x10, x16] 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: dbls(cons(x5:S,x6:S)) -> cons(dbl(x5:S),dbls(x6:S)), id: 3, possubterms: dbls(cons(x5:S,x6:S))->[], cons(x5:S,x6:S)->[1]) 0.001/0.001 (rule: dbls(nil) -> nil, id: 4, possubterms: dbls(nil)->[], nil->[1]) 0.001/0.001 (rule: from(x7:S) -> cons(x7:S,from(s(x7:S))), id: 5, possubterms: from(x7:S)->[]) 0.001/0.001 (rule: indx(cons(x8:S,x9:S),x10:S) -> cons(sel(x8:S,x10:S),indx(x9:S,x10:S)), id: 6, possubterms: indx(cons(x8:S,x9:S),x10:S)->[], cons(x8:S,x9:S)->[1]) 0.001/0.001 (rule: indx(nil,x11:S) -> nil, id: 7, possubterms: indx(nil,x11:S)->[], nil->[1]) 0.001/0.001 (rule: sel(0,cons(x12:S,x13:S)) -> x12:S, id: 8, possubterms: sel(0,cons(x12:S,x13:S))->[], 0->[1], cons(x12:S,x13:S)->[2]) 0.001/0.001 (rule: sel(s(x14:S),cons(x15:S,x16:S)) -> sel(x14:S,x16:S), id: 9, possubterms: sel(s(x14:S),cons(x15:S,x16:S))->[], s(x14:S)->[1], cons(x15:S,x16:S)->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 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 Weakly orthogonal, Almost orthogonal, Orthogonal 0.001/0.001 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 The problem is joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 50%CPU (0avgtext+0avgdata 8496maxresident)k 0.001/0.001 0inputs+0outputs (0major+684minor)pagefaults 0swaps