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 L:S X:S Y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (eq) 0.001/0.001 (inf 1) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 eq(0,0) -> true 0.001/0.001 eq(s(X:S),s(Y:S)) -> eq(X:S,Y:S) 0.001/0.001 eq(X:S,Y:S) -> false 0.001/0.001 inf(X:S) -> cons(X:S,inf(s(X:S))) 0.001/0.001 length(cons(X:S,L:S)) -> s(length(L:S)) 0.001/0.001 length(nil) -> 0 0.001/0.001 take(0,X:S) -> nil 0.001/0.001 take(s(X:S),cons(Y:S,L:S)) -> cons(Y:S,take(X:S,L: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 L:S X:S Y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (eq) 0.001/0.001 (inf 1) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 eq(0,0) -> true 0.001/0.001 eq(s(X:S),s(Y:S)) -> eq(X:S,Y:S) 0.001/0.001 eq(X:S,Y:S) -> false 0.001/0.001 inf(X:S) -> cons(X:S,inf(s(X:S))) 0.001/0.001 length(cons(X:S,L:S)) -> s(length(L:S)) 0.001/0.001 length(nil) -> 0 0.001/0.001 take(0,X:S) -> nil 0.001/0.001 take(s(X:S),cons(Y:S,L:S)) -> cons(Y:S,take(X:S,L: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 CS-TRS Processor: 0.001/0.001 R is a CS-TRS 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 L:S X:S Y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (eq) 0.001/0.001 (inf 1) 0.001/0.001 (length 1) 0.001/0.001 (take 1 2) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 eq(0,0) -> true 0.001/0.001 eq(s(X:S),s(Y:S)) -> eq(X:S,Y:S) 0.001/0.001 eq(X:S,Y:S) -> false 0.001/0.001 inf(X:S) -> cons(X:S,inf(s(X:S))) 0.001/0.001 length(cons(X:S,L:S)) -> s(length(L:S)) 0.001/0.001 length(nil) -> 0 0.001/0.001 take(0,X:S) -> nil 0.001/0.001 take(s(X:S),cons(Y:S,L:S)) -> cons(Y:S,take(X:S,L: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(0,0) -> true 0.001/0.001 eq(s(X:S),s(Y:S)) -> eq(X:S,Y:S) 0.001/0.001 eq(X:S,Y:S) -> false 0.001/0.001 inf(X:S) -> cons(X:S,inf(s(X:S))) 0.001/0.001 length(cons(X:S,L:S)) -> s(length(L:S)) 0.001/0.001 length(nil) -> 0 0.001/0.001 take(0,X:S) -> nil 0.001/0.001 take(s(X:S),cons(Y:S,L:S)) -> cons(Y:S,take(X:S,L:S)) 0.001/0.001 -> Vars: 0.001/0.001 X, Y, X, Y, X, L, X, X, L, X, Y 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, Y], UV-RFrozen: [X, Y]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [X], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [X]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L, X], UV-RFrozen: [L]) 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], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L, X, Y], UV-RFrozen: [L, X, Y]) 0.001/0.001 -> FVars: 0.001/0.001 x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 0.001/0.001 -> PVars: 0.001/0.001 X: [x4, x6, x8, x10, x11, x13], Y: [x5, x7, x14], L: [x9, x12] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: eq(0,0) -> true, id: 1, possubterms: eq(0,0)->[]) 0.001/0.001 (rule: eq(s(x4:S),s(x5:S)) -> eq(x4:S,x5:S), id: 2, possubterms: eq(s(x4:S),s(x5:S))->[]) 0.001/0.001 (rule: eq(x6:S,x7:S) -> false, id: 3, possubterms: eq(x6:S,x7:S)->[]) 0.001/0.001 (rule: inf(x8:S) -> cons(x8:S,inf(s(x8:S))), id: 4, possubterms: inf(x8:S)->[]) 0.001/0.001 (rule: length(cons(x10:S,x9:S)) -> s(length(x9:S)), id: 5, possubterms: length(cons(x10:S,x9:S))->[], cons(x10:S,x9:S)->[1]) 0.001/0.001 (rule: length(nil) -> 0, id: 6, possubterms: length(nil)->[], nil->[1]) 0.001/0.001 (rule: take(0,x11:S) -> nil, id: 7, possubterms: take(0,x11:S)->[], 0->[1]) 0.001/0.001 (rule: take(s(x13:S),cons(x14:S,x12:S)) -> cons(x14:S,take(x13:S,x12:S)), id: 8, possubterms: take(s(x13:S),cons(x14:S,x12:S))->[], s(x13:S)->[1], cons(x14:S,x12:S)->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R3 unifies with R1 at p: [], l: eq(x6:S,x7:S), lp: eq(x6:S,x7:S), sig: {x6:S -> 0,x7:S -> 0}, l': eq(0,0), r: false, r': true) 0.001/0.001 (R3 unifies with R2 at p: [], l: eq(x6:S,x7:S), lp: eq(x6:S,x7:S), sig: {x6:S -> s(X:S),x7:S -> s(Y:S)}, l': eq(s(X:S),s(Y:S)), r: false, r': eq(X:S,Y: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, Not 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, N1, 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 50%CPU (0avgtext+0avgdata 9300maxresident)k 0.001/0.001 0inputs+0outputs (0major+749minor)pagefaults 0swaps