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 N:S X:S XS:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (2nd 1) 0.001/0.001 (from 1) 0.001/0.001 (head 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (take 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 2nd(cons(X:S,XS:S)) -> head(XS:S) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 head(cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(0,cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S) 0.001/0.001 take(0,XS:S) -> nil 0.001/0.001 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS: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 N:S X:S XS:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (2nd 1) 0.001/0.001 (from 1) 0.001/0.001 (head 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (take 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 2nd(cons(X:S,XS:S)) -> head(XS:S) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 head(cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(0,cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S) 0.001/0.001 take(0,XS:S) -> nil 0.001/0.001 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS: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 N:S X:S XS:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (2nd 1) 0.001/0.001 (from 1) 0.001/0.001 (head 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (take 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 2nd(cons(X:S,XS:S)) -> head(XS:S) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 head(cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(0,cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S) 0.001/0.001 take(0,XS:S) -> nil 0.001/0.001 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS: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) => from(x6:S) -> cons(x6:S,from(s(x6:S))) 0.001/0.001 Rule 2 (l' :-> r') => from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 Var => x6:S 0.001/0.001 Pos x6:S in l => [1] 0.001/0.001 Sigma => {x6:S -> from(X:S)} 0.001/0.001 s => cons(from(X:S),from(s(from(X:S)))) 0.001/0.001 t => from(cons(X:S,from(s(X:S)))) 0.001/0.001 NW => 0 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => from(x6:S) -> cons(x6:S,from(s(x6:S))) 0.001/0.001 Rule 3 (l' :-> r') => head(cons(X:S,XS:S)) -> X:S 0.001/0.001 Var => x6:S 0.001/0.001 Pos x6:S in l => [1] 0.001/0.001 Sigma => {x6:S -> head(cons(X:S,XS:S))} 0.001/0.001 s => cons(head(cons(X:S,XS:S)),from(s(head(cons(X:S,XS:S))))) 0.001/0.001 t => from(X:S) 0.001/0.001 NW => 0 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => from(x6:S) -> cons(x6:S,from(s(x6:S))) 0.001/0.001 Rule 4 (l' :-> r') => sel(0,cons(X:S,XS:S)) -> X:S 0.001/0.001 Var => x6:S 0.001/0.001 Pos x6:S in l => [1] 0.001/0.001 Sigma => {x6:S -> sel(0,cons(X:S,XS:S))} 0.001/0.001 s => cons(sel(0,cons(X:S,XS:S)),from(s(sel(0,cons(X:S,XS:S))))) 0.001/0.001 t => from(X:S) 0.001/0.001 NW => 0 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => from(x6:S) -> cons(x6:S,from(s(x6:S))) 0.001/0.001 Rule 5 (l' :-> r') => sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S) 0.001/0.001 Var => x6:S 0.001/0.001 Pos x6:S in l => [1] 0.001/0.001 Sigma => {x6:S -> sel(s(N:S),cons(X:S,XS:S))} 0.001/0.001 s => cons(sel(s(N:S),cons(X:S,XS:S)),from(s(sel(s(N:S),cons(X:S,XS:S))))) 0.001/0.001 t => from(sel(N:S,XS:S)) 0.001/0.001 NW => 0 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => from(x6:S) -> cons(x6:S,from(s(x6:S))) 0.001/0.001 Rule 6 (l' :-> r') => take(0,XS:S) -> nil 0.001/0.001 Var => x6:S 0.001/0.001 Pos x6:S in l => [1] 0.001/0.001 Sigma => {x6:S -> take(0,XS:S)} 0.001/0.001 s => cons(take(0,XS:S),from(s(take(0,XS:S)))) 0.001/0.001 t => from(nil) 0.001/0.001 NW => 0 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => from(x6:S) -> cons(x6:S,from(s(x6:S))) 0.001/0.001 Rule 7 (l' :-> r') => take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS:S)) 0.001/0.001 Var => x6:S 0.001/0.001 Pos x6:S in l => [1] 0.001/0.001 Sigma => {x6:S -> take(s(N:S),cons(X:S,XS:S))} 0.001/0.001 s => cons(take(s(N:S),cons(X:S,XS:S)),from(s(take(s(N:S),cons(X:S,XS:S))))) 0.001/0.001 t => from(cons(X:S,take(N:S,XS:S))) 0.001/0.001 NW => 0 0.001/0.001 0.001/0.001 0.001/0.001 ->Extended u-Critical Pair: 0.001/0.001 Rule 1 (l :-> r) => take(s(x15:S),cons(x16:S,x17:S)) -> cons(x16:S,take(x15:S,x17:S)) 0.001/0.001 Rule 7 (l' :-> r') => take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS:S)) 0.001/0.001 Var => x15:S 0.001/0.001 Pos x15:S in l => [1,1] 0.001/0.001 Sigma => {x15:S -> take(s(N:S),cons(X:S,XS:S))} 0.001/0.001 s => cons(x16:S,take(take(s(N:S),cons(X:S,XS:S)),x17:S)) 0.001/0.001 t => take(s(cons(X:S,take(N:S,XS:S))),cons(x16:S,x17: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 N:S X:S XS:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (2nd 1) 0.001/0.001 (from 1) 0.001/0.001 (head 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (take 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 2nd(cons(X:S,XS:S)) -> head(XS:S) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 head(cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(0,cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S) 0.001/0.001 take(0,XS:S) -> nil 0.001/0.001 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS:S)) 0.001/0.001 ) 0.001/0.001 Critical Pairs: 0.001/0.001 => Not trivial, Not overlay, NW0, N1 0.001/0.001 => Not trivial, Not overlay, NW0, N2 0.001/0.001 => Not trivial, Not overlay, NW0, N3 0.001/0.001 => Not trivial, Not overlay, NW0, N4 0.001/0.001 => Not trivial, Not overlay, NW0, N5 0.001/0.001 => Not trivial, Not overlay, NW0, N6 0.001/0.001 => Not trivial, Not overlay, NW1, N7 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 2nd(cons(X:S,XS:S)) -> head(XS:S) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 head(cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(0,cons(X:S,XS:S)) -> X:S 0.001/0.001 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S) 0.001/0.001 take(0,XS:S) -> nil 0.001/0.001 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS:S)) 0.001/0.001 -> Vars: 0.001/0.001 X, XS, X, X, XS, X, XS, N, X, XS, XS, N, X, XS 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [X], UV-RActive: [XS], UV-LFrozen: [XS], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: [X]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [XS], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [XS], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [N, X], UV-RActive: [N, XS], UV-LFrozen: [XS], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [N, X], UV-RActive: [X], UV-LFrozen: [XS], UV-RFrozen: [N, XS]) 0.001/0.001 -> FVars: 0.001/0.001 x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17 0.001/0.001 -> PVars: 0.001/0.001 X: [x4, x6, x7, x9, x12, x16], XS: [x5, x8, x10, x13, x14, x17], N: [x11, x15] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: 2nd(cons(x4:S,x5:S)) -> head(x5:S), id: 1, possubterms: 2nd(cons(x4:S,x5:S))->[], cons(x4:S,x5:S)->[1]) 0.001/0.001 (rule: from(x6:S) -> cons(x6:S,from(s(x6:S))), id: 2, possubterms: from(x6:S)->[]) 0.001/0.001 (rule: head(cons(x7:S,x8:S)) -> x7:S, id: 3, possubterms: head(cons(x7:S,x8:S))->[], cons(x7:S,x8:S)->[1]) 0.001/0.001 (rule: sel(0,cons(x9:S,x10:S)) -> x9:S, id: 4, possubterms: sel(0,cons(x9:S,x10:S))->[], 0->[1], cons(x9:S,x10:S)->[2]) 0.001/0.001 (rule: sel(s(x11:S),cons(x12:S,x13:S)) -> sel(x11:S,x13:S), id: 5, possubterms: sel(s(x11:S),cons(x12:S,x13:S))->[], s(x11:S)->[1], cons(x12:S,x13:S)->[2]) 0.001/0.001 (rule: take(0,x14:S) -> nil, id: 6, possubterms: take(0,x14:S)->[], 0->[1]) 0.001/0.001 (rule: take(s(x15:S),cons(x16:S,x17:S)) -> cons(x16:S,take(x15:S,x17:S)), id: 7, possubterms: take(s(x15:S),cons(x16:S,x17:S))->[], s(x15:S)->[1], cons(x16:S,x17:S)->[2]) 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, NW0, N1 0.001/0.001 => Not trivial, Not overlay, NW0, N2 0.001/0.001 => Not trivial, Not overlay, NW0, N3 0.001/0.001 => Not trivial, Not overlay, NW1, N4 0.001/0.001 => Not trivial, Not overlay, NW0, N5 0.001/0.001 => Not trivial, Not overlay, NW0, N6 0.001/0.001 => Not trivial, Not overlay, NW0, N7 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: cons(sel(0,cons(X:S,XS:S)),from(s(sel(0,cons(X:S,XS:S))))) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('cons(sel(0,cons(X:S,XS:S)),from(s(sel(0,cons(X:S,XS:S)))))', D0) 0.001/0.001 ID: 1 => ('cons(X:S,from(s(sel(0,cons(X:S,XS:S)))))', D1, R4, P[1], S{x9:S -> X:S, x10:S -> XS:S}), NR: 'X:S' 0.001/0.001 t: from(X:S) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('from(X:S)', D0) 0.001/0.001 ID: 1 => ('cons(X:S,from(s(X:S)))', D1, R2, P[], S{x6:S -> X:S}), NR: 'cons(X:S,from(s(X:S)))' 0.001/0.001 cons(sel(0,cons(X:S,XS:S)),from(s(sel(0,cons(X:S,XS:S))))) ->* no union *<- from(X:S) 0.001/0.001 "Not joinable" 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.01user 0.00system 0:00.01elapsed 100%CPU (0avgtext+0avgdata 10772maxresident)k 0.001/0.001 0inputs+0outputs (0major+1018minor)pagefaults 0swaps