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 N:S:S X:S:S XS:S:S YS:S:S ZS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (afterNth) 0.001/0.001 (fst 1) 0.001/0.001 (head 1) 0.001/0.001 (natsFrom) 0.001/0.001 (sel) 0.001/0.001 (snd 1) 0.001/0.001 (splitAt 1 2) 0.001/0.001 (tail 1) 0.001/0.001 (take) 0.001/0.001 (u 1) 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) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 afterNth(N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.001/0.001 fst(pair(XS:S:S,YS:S:S)) -> XS:S:S 0.001/0.001 head(cons(N:S:S,XS:S:S)) -> N:S:S 0.001/0.001 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.001/0.001 sel(N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.001/0.001 snd(pair(XS:S:S,YS:S:S)) -> YS:S:S 0.001/0.001 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.001/0.001 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> u(splitAt(N:S:S,XS:S:S),N:S:S,X:S:S,XS:S:S) 0.001/0.001 tail(cons(N:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.001/0.001 u(pair(YS:S:S,ZS:S:S),N:S:S,X:S:S,XS:S:S) -> pair(cons(X:S:S,YS:S:S),ZS: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 N:S:S X:S:S XS:S:S YS:S:S ZS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (afterNth) 0.001/0.001 (fst 1) 0.001/0.001 (head 1) 0.001/0.001 (natsFrom) 0.001/0.001 (sel) 0.001/0.001 (snd 1) 0.001/0.001 (splitAt 1 2) 0.001/0.001 (tail 1) 0.001/0.001 (take) 0.001/0.001 (u 1) 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) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 afterNth(N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.001/0.001 fst(pair(XS:S:S,YS:S:S)) -> XS:S:S 0.001/0.001 head(cons(N:S:S,XS:S:S)) -> N:S:S 0.001/0.001 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.001/0.001 sel(N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.001/0.001 snd(pair(XS:S:S,YS:S:S)) -> YS:S:S 0.001/0.001 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.001/0.001 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> u(splitAt(N:S:S,XS:S:S),N:S:S,X:S:S,XS:S:S) 0.001/0.001 tail(cons(N:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.001/0.001 u(pair(YS:S:S,ZS:S:S),N:S:S,X:S:S,XS:S:S) -> pair(cons(X:S:S,YS:S:S),ZS: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 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 v_NonEmpty:S:S N:S:S X:S:S XS:S:S YS:S:S ZS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (afterNth) 0.001/0.001 (fst 1) 0.001/0.001 (head 1) 0.001/0.001 (natsFrom) 0.001/0.001 (sel) 0.001/0.001 (snd 1) 0.001/0.001 (splitAt 1 2) 0.001/0.001 (tail 1) 0.001/0.001 (take) 0.001/0.001 (u 1) 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) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 afterNth(N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.001/0.001 fst(pair(XS:S:S,YS:S:S)) -> XS:S:S 0.001/0.001 head(cons(N:S:S,XS:S:S)) -> N:S:S 0.001/0.001 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.001/0.001 sel(N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.001/0.001 snd(pair(XS:S:S,YS:S:S)) -> YS:S:S 0.001/0.001 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.001/0.001 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> u(splitAt(N:S:S,XS:S:S),N:S:S,X:S:S,XS:S:S) 0.001/0.001 tail(cons(N:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.001/0.001 u(pair(YS:S:S,ZS:S:S),N:S:S,X:S:S,XS:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Extended u-Critical Pairs NonLHRV Processor [JLAMP21]: 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => splitAt(num0,x18:S) -> pair(nil,x18:S) 0.001/0.001 Rule 7 (l' :-> r') => splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.001/0.001 Var => x18:S 0.001/0.001 Pos x18:S in l => [2] 0.001/0.001 Sigma => {x18:S -> splitAt(num0,XS:S:S)} 0.001/0.001 s => pair(nil,splitAt(num0,XS:S:S)) 0.001/0.001 t => splitAt(num0,pair(nil,XS:S:S)) 0.001/0.001 NW => 1 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => splitAt(num0,x18:S) -> pair(nil,x18:S) 0.001/0.001 Rule 8 (l' :-> r') => splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> u(splitAt(N:S:S,XS:S:S),N:S:S,X:S:S,XS:S:S) 0.001/0.001 Var => x18:S 0.001/0.001 Pos x18:S in l => [2] 0.001/0.001 Sigma => {x18:S -> splitAt(s(N:S:S),cons(X:S:S,XS:S:S))} 0.001/0.001 s => pair(nil,splitAt(s(N:S:S),cons(X:S:S,XS:S:S))) 0.001/0.001 t => splitAt(num0,u(splitAt(N:S:S,XS:S:S),N:S:S,X:S:S,XS:S:S)) 0.001/0.001 NW => 1 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => splitAt(num0,x18:S) -> pair(nil,x18:S) 0.001/0.001 Rule 9 (l' :-> r') => tail(cons(N:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 Var => x18:S 0.001/0.001 Pos x18:S in l => [2] 0.001/0.001 Sigma => {x18:S -> tail(cons(N:S:S,XS:S:S))} 0.001/0.001 s => pair(nil,tail(cons(N:S:S,XS:S:S))) 0.001/0.001 t => splitAt(num0,XS:S:S) 0.001/0.001 NW => 1 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => splitAt(num0,x18:S) -> pair(nil,x18:S) 0.001/0.001 Rule 10 (l' :-> r') => take(N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.001/0.001 Var => x18:S 0.001/0.001 Pos x18:S in l => [2] 0.001/0.001 Sigma => {x18:S -> take(N:S:S,XS:S:S)} 0.001/0.001 s => pair(nil,take(N:S:S,XS:S:S)) 0.001/0.001 t => splitAt(num0,fst(splitAt(N:S:S,XS:S:S))) 0.001/0.001 NW => 1 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => splitAt(num0,x18:S) -> pair(nil,x18:S) 0.001/0.001 Rule 11 (l' :-> r') => u(pair(YS:S:S,ZS:S:S),N:S:S,X:S:S,XS:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.001/0.001 Var => x18:S 0.001/0.001 Pos x18:S in l => [2] 0.001/0.001 Sigma => {x18:S -> u(pair(YS:S:S,ZS:S:S),N:S:S,X:S:S,XS:S:S)} 0.001/0.001 s => pair(nil,u(pair(YS:S:S,ZS:S:S),N:S:S,X:S:S,XS:S:S)) 0.001/0.001 t => splitAt(num0,pair(cons(X:S:S,YS:S:S),ZS:S:S)) 0.001/0.001 NW => 1 0.001/0.001 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 YS:S:S ZS:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (afterNth) 0.001/0.001 (fst 1) 0.001/0.001 (head 1) 0.001/0.001 (natsFrom) 0.001/0.001 (sel) 0.001/0.001 (snd 1) 0.001/0.001 (splitAt 1 2) 0.001/0.001 (tail 1) 0.001/0.001 (take) 0.001/0.001 (u 1) 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) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 afterNth(N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.001/0.001 fst(pair(XS:S:S,YS:S:S)) -> XS:S:S 0.001/0.001 head(cons(N:S:S,XS:S:S)) -> N:S:S 0.001/0.001 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.001/0.001 sel(N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.001/0.001 snd(pair(XS:S:S,YS:S:S)) -> YS:S:S 0.001/0.001 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.001/0.001 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> u(splitAt(N:S:S,XS:S:S),N:S:S,X:S:S,XS:S:S) 0.001/0.001 tail(cons(N:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.001/0.001 u(pair(YS:S:S,ZS:S:S),N:S:S,X:S:S,XS:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.001/0.001 ) 0.001/0.001 Critical Pairs: 0.001/0.001 => Not trivial, Not overlay, NW1, N1 0.001/0.001 => Not trivial, Not overlay, NW1, N2 0.001/0.001 => Not trivial, Not overlay, NW1, N3 0.001/0.001 => Not trivial, Not overlay, NW1, N4 0.001/0.001 => Not trivial, Not overlay, NW1, N5 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 afterNth(N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.001/0.001 fst(pair(XS:S:S,YS:S:S)) -> XS:S:S 0.001/0.001 head(cons(N:S:S,XS:S:S)) -> N:S:S 0.001/0.001 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.001/0.001 sel(N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.001/0.001 snd(pair(XS:S:S,YS:S:S)) -> YS:S:S 0.001/0.001 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.001/0.001 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> u(splitAt(N:S:S,XS:S:S),N:S:S,X:S:S,XS:S:S) 0.001/0.001 tail(cons(N:S:S,XS:S:S)) -> XS:S:S 0.001/0.001 take(N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.001/0.001 u(pair(YS:S:S,ZS:S:S),N:S:S,X:S:S,XS:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.001/0.001 -> Vars: 0.001/0.001 N:S, XS:S, XS:S, YS:S, N:S, XS:S, N:S, N:S, XS:S, XS:S, YS:S, XS:S, N:S, X:S, XS:S, N:S, XS:S, N:S, XS:S, N:S, X:S, XS:S, YS:S, ZS:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [N:S, XS:S], UV-LFrozen: [N:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [XS:S], UV-LFrozen: [XS:S, YS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S, XS:S]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [YS:S], UV-LFrozen: [XS:S, YS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [XS:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [XS:S]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [N:S, XS:S], 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: [XS:S], UV-LFrozen: [N:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [N:S, XS:S], UV-LFrozen: [N:S, XS:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, X:S, XS:S, YS:S, ZS:S], UV-RFrozen: [X:S, YS:S, ZS:S]) 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, x25, x26, x27, x28, x29, x30 0.001/0.001 -> PVars: 0.001/0.001 N:S: [x7, x11, x13, x14, x19, x22, x24, x26], XS:S: [x8, x9, x12, x15, x16, x18, x21, x23, x25, x28], YS:S: [x10, x17, x29], X:S: [x20, x27], ZS:S: [x30] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: afterNth(x7:S,x8:S) -> snd(splitAt(x7:S,x8:S)), id: 1, possubterms: afterNth(x7:S,x8:S)->[]) 0.001/0.001 (rule: fst(pair(x9:S,x10:S)) -> x9:S, id: 2, possubterms: fst(pair(x9:S,x10:S))->[], pair(x9:S,x10:S)->[1]) 0.001/0.001 (rule: head(cons(x11:S,x12:S)) -> x11:S, id: 3, possubterms: head(cons(x11:S,x12:S))->[], cons(x11:S,x12:S)->[1]) 0.001/0.001 (rule: natsFrom(x13:S) -> cons(x13:S,natsFrom(s(x13:S))), id: 4, possubterms: natsFrom(x13:S)->[]) 0.001/0.001 (rule: sel(x14:S,x15:S) -> head(afterNth(x14:S,x15:S)), id: 5, possubterms: sel(x14:S,x15:S)->[]) 0.001/0.001 (rule: snd(pair(x16:S,x17:S)) -> x17:S, id: 6, possubterms: snd(pair(x16:S,x17:S))->[], pair(x16:S,x17:S)->[1]) 0.001/0.001 (rule: splitAt(num0,x18:S) -> pair(nil,x18:S), id: 7, possubterms: splitAt(num0,x18:S)->[], num0->[1]) 0.001/0.001 (rule: splitAt(s(x19:S),cons(x20:S,x21:S)) -> u(splitAt(x19:S,x21:S),x19:S,x20:S,x21:S), id: 8, possubterms: splitAt(s(x19:S),cons(x20:S,x21:S))->[], s(x19:S)->[1], cons(x20:S,x21:S)->[2]) 0.001/0.001 (rule: tail(cons(x22:S,x23:S)) -> x23:S, id: 9, possubterms: tail(cons(x22:S,x23:S))->[], cons(x22:S,x23:S)->[1]) 0.001/0.001 (rule: take(x24:S,x25:S) -> fst(splitAt(x24:S,x25:S)), id: 10, possubterms: take(x24:S,x25:S)->[]) 0.001/0.001 (rule: u(pair(x29:S,x30:S),x26:S,x27:S,x28:S) -> pair(cons(x27:S,x29:S),x30:S), id: 11, possubterms: u(pair(x29:S,x30:S),x26:S,x27:S,x28:S)->[], pair(x29:S,x30:S)->[1]) 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 => Not trivial, Not overlay, NW1, N1 0.001/0.001 => Not trivial, Not overlay, NW1, N2 0.001/0.001 => Not trivial, Not overlay, NW1, N3 0.001/0.001 => Not trivial, Not overlay, NW1, N4 0.001/0.001 => Not trivial, Not overlay, NW1, N5 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 No Convergence Brute Force Processor: 0.001/0.001 -> Rewritings: 0.001/0.001 s: pair(nil,tail(cons(N:S:S,XS:S:S))) 0.001/0.001 Nodes: [0] 0.001/0.001 Edges: [] 0.001/0.001 ID: 0 => ('pair(nil,tail(cons(N:S:S,XS:S:S)))', D0) 0.001/0.001 t: splitAt(num0,XS:S:S) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('splitAt(num0,XS:S:S)', D0) 0.001/0.001 ID: 1 => ('pair(nil,XS:S:S)', D1, R7, P[], S{x18:S -> XS:S:S}), NR: 'pair(nil,XS:S:S)' 0.001/0.001 pair(nil,tail(cons(N:S:S,XS:S:S))) ->* no union *<- splitAt(num0,XS:S:S) 0.001/0.001 "Not joinable" 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 75%CPU (0avgtext+0avgdata 10448maxresident)k 0.001/0.001 8inputs+0outputs (0major+922minor)pagefaults 0swaps