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 L:S:S X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (eq 1 2) 0.001/0.001 (inf) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 eq(num0,num0) -> ftrue 0.001/0.001 eq(s(X:S:S),s(Y:S:S)) -> eq(X:S:S,Y:S:S) 0.001/0.001 eq(X:S:S,Y:S:S) -> ffalse 0.001/0.001 inf(X:S:S) -> cons(X:S:S,inf(s(X:S:S))) 0.001/0.001 length(cons(X:S:S,L:S:S)) -> s(length(L:S:S)) 0.001/0.001 length(nil) -> num0 0.001/0.001 take(num0,X:S:S) -> nil 0.001/0.001 take(s(X:S:S),cons(Y:S:S,L:S:S)) -> cons(Y:S:S,take(X:S:S,L: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 L:S:S X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (eq 1 2) 0.001/0.001 (inf) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 eq(num0,num0) -> ftrue 0.001/0.001 eq(s(X:S:S),s(Y:S:S)) -> eq(X:S:S,Y:S:S) 0.001/0.001 eq(X:S:S,Y:S:S) -> ffalse 0.001/0.001 inf(X:S:S) -> cons(X:S:S,inf(s(X:S:S))) 0.001/0.001 length(cons(X:S:S,L:S:S)) -> s(length(L:S:S)) 0.001/0.001 length(nil) -> num0 0.001/0.001 take(num0,X:S:S) -> nil 0.001/0.001 take(s(X:S:S),cons(Y:S:S,L:S:S)) -> cons(Y:S:S,take(X:S:S,L: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 L:S:S X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (eq 1 2) 0.001/0.001 (inf) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (nil) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 eq(num0,num0) -> ftrue 0.001/0.001 eq(s(X:S:S),s(Y:S:S)) -> eq(X:S:S,Y:S:S) 0.001/0.001 eq(X:S:S,Y:S:S) -> ffalse 0.001/0.001 inf(X:S:S) -> cons(X:S:S,inf(s(X:S:S))) 0.001/0.001 length(cons(X:S:S,L:S:S)) -> s(length(L:S:S)) 0.001/0.001 length(nil) -> num0 0.001/0.001 take(num0,X:S:S) -> nil 0.001/0.001 take(s(X:S:S),cons(Y:S:S,L:S:S)) -> cons(Y:S:S,take(X:S:S,L: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 eq(num0,num0) -> ftrue 0.001/0.001 eq(s(X:S:S),s(Y:S:S)) -> eq(X:S:S,Y:S:S) 0.001/0.001 eq(X:S:S,Y:S:S) -> ffalse 0.001/0.001 inf(X:S:S) -> cons(X:S:S,inf(s(X:S:S))) 0.001/0.001 length(cons(X:S:S,L:S:S)) -> s(length(L:S:S)) 0.001/0.001 length(nil) -> num0 0.001/0.001 take(num0,X:S:S) -> nil 0.001/0.001 take(s(X:S:S),cons(Y:S:S,L:S:S)) -> cons(Y:S:S,take(X:S:S,L:S:S)) 0.001/0.001 -> Vars: 0.001/0.001 X:S, Y:S, X:S, Y:S, X:S, L:S, X:S, X:S, L:S, X:S, Y: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: [X:S, Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [X:S, Y:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L:S, X:S], UV-RFrozen: [L: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: [X:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L:S, X:S, Y:S], UV-RFrozen: [L:S, X:S, Y:S]) 0.001/0.001 -> FVars: 0.001/0.001 x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x5, x7, x9, x11, x12, x14], Y:S: [x6, x8, x15], L:S: [x10, x13] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: eq(num0,num0) -> ftrue, id: 1, possubterms: eq(num0,num0)->[], num0->[1], num0->[2]) 0.001/0.001 (rule: eq(s(x5:S),s(x6:S)) -> eq(x5:S,x6:S), id: 2, possubterms: eq(s(x5:S),s(x6:S))->[], s(x5:S)->[1], s(x6:S)->[2]) 0.001/0.001 (rule: eq(x7:S,x8:S) -> ffalse, id: 3, possubterms: eq(x7:S,x8:S)->[]) 0.001/0.001 (rule: inf(x9:S) -> cons(x9:S,inf(s(x9:S))), id: 4, possubterms: inf(x9:S)->[]) 0.001/0.001 (rule: length(cons(x11:S,x10:S)) -> s(length(x10:S)), id: 5, possubterms: length(cons(x11:S,x10:S))->[], cons(x11:S,x10:S)->[1]) 0.001/0.001 (rule: length(nil) -> num0, id: 6, possubterms: length(nil)->[], nil->[1]) 0.001/0.001 (rule: take(num0,x12:S) -> nil, id: 7, possubterms: take(num0,x12:S)->[], num0->[1]) 0.001/0.001 (rule: take(s(x14:S),cons(x15:S,x13:S)) -> cons(x15:S,take(x14:S,x13:S)), id: 8, possubterms: take(s(x14:S),cons(x15:S,x13:S))->[], s(x14:S)->[1], cons(x15:S,x13:S)->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R3 unifies with R1 at p: [], l: eq(x7:S,x8:S), lp: eq(x7:S,x8:S), sig: {x7:S -> num0,x8:S -> num0}, l': eq(num0,num0), r: ffalse, r': ftrue) 0.001/0.001 (R3 unifies with R2 at p: [], l: eq(x7:S,x8:S), lp: eq(x7:S,x8:S), sig: {x7:S -> s(X:S:S),x8:S -> s(Y:S:S)}, l': eq(s(X:S:S),s(Y:S:S)), r: ffalse, r': eq(X:S:S,Y:S:S)) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Not trivial, Overlay, NW0, N1 0.001/0.001 => Not trivial, Overlay, NW0, N2 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 Different Normal CP Terms Processor: 0.001/0.001 => Not trivial, Overlay, NW0, N2, Normal and not trivial cp 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 41%CPU (0avgtext+0avgdata 8732maxresident)k 0.001/0.001 8inputs+0outputs (0major+701minor)pagefaults 0swaps