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 v_NonEmpty:S:S N:S:S X:S:S XS:S:S Y:S:S YS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (incr 1) 0.001/0.001 (oddNs) 0.001/0.001 (pairNs) 0.001/0.001 (repItems 1) 0.001/0.001 (tail 1) 0.001/0.001 (take 1 2) 0.001/0.001 (zip 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 (pair 1 2) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 incr(cons(X:S:S,XS:S:S)) -> cons(s(X:S:S),incr(XS:S:S)) 0.001/0.001 oddNs -> incr(pairNs) 0.001/0.001 pairNs -> cons(num0,incr(oddNs)) 0.001/0.001 repItems(cons(X:S:S,XS:S:S)) -> cons(X:S:S,cons(X:S:S,repItems(XS:S:S))) 0.001/0.001 repItems(nil) -> nil 0.001/0.001 tail(cons(X:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(num0,XS:S:S) -> nil 0.001/0.001 take(s(N:S:S),cons(X:S:S,XS:S:S)) -> cons(X:S:S,take(N:S:S,XS:S:S)) 0.001/0.001 zip(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(pair(X:S:S,Y:S:S),zip(XS:S:S,YS:S:S)) 0.001/0.001 zip(nil,XS:S:S) -> nil 0.001/0.001 zip(X:S:S,nil) -> nil 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 N:S:S X:S:S XS:S:S Y:S:S YS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (incr 1) 0.001/0.001 (oddNs) 0.001/0.001 (pairNs) 0.001/0.001 (repItems 1) 0.001/0.001 (tail 1) 0.001/0.001 (take 1 2) 0.001/0.001 (zip 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 (pair 1 2) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 incr(cons(X:S:S,XS:S:S)) -> cons(s(X:S:S),incr(XS:S:S)) 0.001/0.001 oddNs -> incr(pairNs) 0.001/0.001 pairNs -> cons(num0,incr(oddNs)) 0.001/0.001 repItems(cons(X:S:S,XS:S:S)) -> cons(X:S:S,cons(X:S:S,repItems(XS:S:S))) 0.001/0.001 repItems(nil) -> nil 0.001/0.001 tail(cons(X:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(num0,XS:S:S) -> nil 0.001/0.001 take(s(N:S:S),cons(X:S:S,XS:S:S)) -> cons(X:S:S,take(N:S:S,XS:S:S)) 0.001/0.001 zip(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(pair(X:S:S,Y:S:S),zip(XS:S:S,YS:S:S)) 0.001/0.001 zip(nil,XS:S:S) -> nil 0.001/0.001 zip(X:S:S,nil) -> nil 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 N:S:S X:S:S XS:S:S Y:S:S YS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (incr 1) 0.001/0.001 (oddNs) 0.001/0.001 (pairNs) 0.001/0.001 (repItems 1) 0.001/0.001 (tail 1) 0.001/0.001 (take 1 2) 0.001/0.001 (zip 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 (pair 1 2) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 incr(cons(X:S:S,XS:S:S)) -> cons(s(X:S:S),incr(XS:S:S)) 0.001/0.001 oddNs -> incr(pairNs) 0.001/0.001 pairNs -> cons(num0,incr(oddNs)) 0.001/0.001 repItems(cons(X:S:S,XS:S:S)) -> cons(X:S:S,cons(X:S:S,repItems(XS:S:S))) 0.001/0.001 repItems(nil) -> nil 0.001/0.001 tail(cons(X:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(num0,XS:S:S) -> nil 0.001/0.001 take(s(N:S:S),cons(X:S:S,XS:S:S)) -> cons(X:S:S,take(N:S:S,XS:S:S)) 0.001/0.001 zip(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(pair(X:S:S,Y:S:S),zip(XS:S:S,YS:S:S)) 0.001/0.001 zip(nil,XS:S:S) -> nil 0.001/0.001 zip(X:S:S,nil) -> nil 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 incr(cons(X:S:S,XS:S:S)) -> cons(s(X:S:S),incr(XS:S:S)) 0.001/0.001 oddNs -> incr(pairNs) 0.001/0.001 pairNs -> cons(num0,incr(oddNs)) 0.001/0.001 repItems(cons(X:S:S,XS:S:S)) -> cons(X:S:S,cons(X:S:S,repItems(XS:S:S))) 0.001/0.001 repItems(nil) -> nil 0.001/0.001 tail(cons(X:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(num0,XS:S:S) -> nil 0.001/0.001 take(s(N:S:S),cons(X:S:S,XS:S:S)) -> cons(X:S:S,take(N:S:S,XS:S:S)) 0.001/0.001 zip(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(pair(X:S:S,Y:S:S),zip(XS:S:S,YS:S:S)) 0.001/0.001 zip(nil,XS:S:S) -> nil 0.001/0.001 zip(X:S:S,nil) -> nil 0.001/0.001 -> Vars: 0.001/0.001 X:S, XS:S, X:S, XS:S, X:S, XS:S, XS:S, N:S, X:S, XS:S, X:S, XS:S, Y:S, YS:S, XS:S, X:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, XS:S], UV-RFrozen: [X:S, XS:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 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: [], UV-LFrozen: [X:S, XS:S], UV-RFrozen: [X:S, XS:S]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [XS:S], UV-LFrozen: [X:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [XS:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, X:S, XS:S], UV-RFrozen: [N:S, X:S, XS:S]) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, XS:S, Y:S, YS:S], UV-RFrozen: [X:S, XS:S, Y:S, YS:S]) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [XS:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [X:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x7, x9, x11, x15, x17, x22], XS:S: [x8, x10, x12, x13, x16, x18, x21], N:S: [x14], Y:S: [x19], YS:S: [x20] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: incr(cons(x7:S,x8:S)) -> cons(s(x7:S),incr(x8:S)), id: 1, possubterms: incr(cons(x7:S,x8:S))->[], cons(x7:S,x8:S)->[1]) 0.001/0.001 (rule: oddNs -> incr(pairNs), id: 2, possubterms: oddNs->[]) 0.001/0.001 (rule: pairNs -> cons(num0,incr(oddNs)), id: 3, possubterms: pairNs->[]) 0.001/0.001 (rule: repItems(cons(x9:S,x10:S)) -> cons(x9:S,cons(x9:S,repItems(x10:S))), id: 4, possubterms: repItems(cons(x9:S,x10:S))->[], cons(x9:S,x10:S)->[1]) 0.001/0.001 (rule: repItems(nil) -> nil, id: 5, possubterms: repItems(nil)->[], nil->[1]) 0.001/0.001 (rule: tail(cons(x11:S,x12:S)) -> x12:S, id: 6, possubterms: tail(cons(x11:S,x12:S))->[], cons(x11:S,x12:S)->[1]) 0.001/0.001 (rule: take(num0,x13:S) -> nil, id: 7, possubterms: take(num0,x13:S)->[], num0->[1]) 0.001/0.001 (rule: take(s(x14:S),cons(x15:S,x16:S)) -> cons(x15:S,take(x14:S,x16:S)), id: 8, possubterms: take(s(x14:S),cons(x15:S,x16:S))->[], s(x14:S)->[1], cons(x15:S,x16:S)->[2]) 0.001/0.001 (rule: zip(cons(x17:S,x18:S),cons(x19:S,x20:S)) -> cons(pair(x17:S,x19:S),zip(x18:S,x20:S)), id: 9, possubterms: zip(cons(x17:S,x18:S),cons(x19:S,x20:S))->[], cons(x17:S,x18:S)->[1], cons(x19:S,x20:S)->[2]) 0.001/0.001 (rule: zip(nil,x21:S) -> nil, id: 10, possubterms: zip(nil,x21:S)->[], nil->[1]) 0.001/0.001 (rule: zip(x22:S,nil) -> nil, id: 11, possubterms: zip(x22:S,nil)->[], nil->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R11 unifies with R10 at p: [], l: zip(x22:S,nil), lp: zip(x22:S,nil), sig: {XS:S:S -> nil,x22:S -> nil}, l': zip(nil,XS:S:S), r: nil, r': nil) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Trivial, Overlay, NW0, N1 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, Not 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 69%CPU (0avgtext+0avgdata 8652maxresident)k 0.001/0.001 8inputs+0outputs (0major+727minor)pagefaults 0swaps