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 (from) 0.001/0.001 (minus 1 2) 0.001/0.001 (quot 1 2) 0.001/0.001 (sel 1 2) 0.001/0.001 (zWquot 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 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 minus(s(X:S:S),s(Y:S:S)) -> minus(X:S:S,Y:S:S) 0.001/0.001 minus(X:S:S,num0) -> num0 0.001/0.001 quot(num0,s(Y:S:S)) -> num0 0.001/0.001 quot(s(X:S:S),s(Y:S:S)) -> s(quot(minus(X:S:S,Y:S:S),s(Y:S:S))) 0.001/0.001 sel(num0,cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 sel(s(N:S:S),cons(X:S:S,XS:S:S)) -> sel(N:S:S,XS:S:S) 0.001/0.001 zWquot(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(quot(X:S:S,Y:S:S),zWquot(XS:S:S,YS:S:S)) 0.001/0.001 zWquot(nil,XS:S:S) -> nil 0.001/0.001 zWquot(XS: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 (from) 0.001/0.001 (minus 1 2) 0.001/0.001 (quot 1 2) 0.001/0.001 (sel 1 2) 0.001/0.001 (zWquot 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 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 minus(s(X:S:S),s(Y:S:S)) -> minus(X:S:S,Y:S:S) 0.001/0.001 minus(X:S:S,num0) -> num0 0.001/0.001 quot(num0,s(Y:S:S)) -> num0 0.001/0.001 quot(s(X:S:S),s(Y:S:S)) -> s(quot(minus(X:S:S,Y:S:S),s(Y:S:S))) 0.001/0.001 sel(num0,cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 sel(s(N:S:S),cons(X:S:S,XS:S:S)) -> sel(N:S:S,XS:S:S) 0.001/0.001 zWquot(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(quot(X:S:S,Y:S:S),zWquot(XS:S:S,YS:S:S)) 0.001/0.001 zWquot(nil,XS:S:S) -> nil 0.001/0.001 zWquot(XS: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 (from) 0.001/0.001 (minus 1 2) 0.001/0.001 (quot 1 2) 0.001/0.001 (sel 1 2) 0.001/0.001 (zWquot 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 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 minus(s(X:S:S),s(Y:S:S)) -> minus(X:S:S,Y:S:S) 0.001/0.001 minus(X:S:S,num0) -> num0 0.001/0.001 quot(num0,s(Y:S:S)) -> num0 0.001/0.001 quot(s(X:S:S),s(Y:S:S)) -> s(quot(minus(X:S:S,Y:S:S),s(Y:S:S))) 0.001/0.001 sel(num0,cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 sel(s(N:S:S),cons(X:S:S,XS:S:S)) -> sel(N:S:S,XS:S:S) 0.001/0.001 zWquot(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(quot(X:S:S,Y:S:S),zWquot(XS:S:S,YS:S:S)) 0.001/0.001 zWquot(nil,XS:S:S) -> nil 0.001/0.001 zWquot(XS: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 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 minus(s(X:S:S),s(Y:S:S)) -> minus(X:S:S,Y:S:S) 0.001/0.001 minus(X:S:S,num0) -> num0 0.001/0.001 quot(num0,s(Y:S:S)) -> num0 0.001/0.001 quot(s(X:S:S),s(Y:S:S)) -> s(quot(minus(X:S:S,Y:S:S),s(Y:S:S))) 0.001/0.001 sel(num0,cons(X:S:S,XS:S:S)) -> X:S:S 0.001/0.001 sel(s(N:S:S),cons(X:S:S,XS:S:S)) -> sel(N:S:S,XS:S:S) 0.001/0.001 zWquot(cons(X:S:S,XS:S:S),cons(Y:S:S,YS:S:S)) -> cons(quot(X:S:S,Y:S:S),zWquot(XS:S:S,YS:S:S)) 0.001/0.001 zWquot(nil,XS:S:S) -> nil 0.001/0.001 zWquot(XS:S:S,nil) -> nil 0.001/0.001 -> Vars: 0.001/0.001 X:S, X:S, Y:S, X:S, Y:S, X:S, Y:S, X:S, XS:S, N:S, X:S, XS:S, X:S, XS:S, Y:S, YS:S, XS:S, XS:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 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], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y: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: [X:S], UV-LFrozen: [X:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [N:S, XS:S], UV-LFrozen: [N:S, X:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, 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: 9, UV-LActive: [XS:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [XS: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, x23, x24 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x7, x8, x10, x12, x14, x17, x19], Y:S: [x9, x11, x13, x21], XS:S: [x15, x18, x20, x23, x24], N:S: [x16], YS:S: [x22] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: from(x7:S) -> cons(x7:S,from(s(x7:S))), id: 1, possubterms: from(x7:S)->[]) 0.001/0.001 (rule: minus(s(x8:S),s(x9:S)) -> minus(x8:S,x9:S), id: 2, possubterms: minus(s(x8:S),s(x9:S))->[], s(x8:S)->[1], s(x9:S)->[2]) 0.001/0.001 (rule: minus(x10:S,num0) -> num0, id: 3, possubterms: minus(x10:S,num0)->[], num0->[2]) 0.001/0.001 (rule: quot(num0,s(x11:S)) -> num0, id: 4, possubterms: quot(num0,s(x11:S))->[], num0->[1], s(x11:S)->[2]) 0.001/0.001 (rule: quot(s(x12:S),s(x13:S)) -> s(quot(minus(x12:S,x13:S),s(x13:S))), id: 5, possubterms: quot(s(x12:S),s(x13:S))->[], s(x12:S)->[1], s(x13:S)->[2]) 0.001/0.001 (rule: sel(num0,cons(x14:S,x15:S)) -> x14:S, id: 6, possubterms: sel(num0,cons(x14:S,x15:S))->[], num0->[1], cons(x14:S,x15:S)->[2]) 0.001/0.001 (rule: sel(s(x16:S),cons(x17:S,x18:S)) -> sel(x16:S,x18:S), id: 7, possubterms: sel(s(x16:S),cons(x17:S,x18:S))->[], s(x16:S)->[1], cons(x17:S,x18:S)->[2]) 0.001/0.001 (rule: zWquot(cons(x19:S,x20:S),cons(x21:S,x22:S)) -> cons(quot(x19:S,x21:S),zWquot(x20:S,x22:S)), id: 8, possubterms: zWquot(cons(x19:S,x20:S),cons(x21:S,x22:S))->[], cons(x19:S,x20:S)->[1], cons(x21:S,x22:S)->[2]) 0.001/0.001 (rule: zWquot(nil,x23:S) -> nil, id: 9, possubterms: zWquot(nil,x23:S)->[], nil->[1]) 0.001/0.001 (rule: zWquot(x24:S,nil) -> nil, id: 10, possubterms: zWquot(x24:S,nil)->[], nil->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R10 unifies with R9 at p: [], l: zWquot(x24:S,nil), lp: zWquot(x24:S,nil), sig: {XS:S:S -> nil,x24:S -> nil}, l': zWquot(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 58%CPU (0avgtext+0avgdata 8464maxresident)k 0.001/0.001 8inputs+0outputs (0major+731minor)pagefaults 0swaps