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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (f 1) 0.001/0.001 (g 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f(X:S) -> cons(X:S,f(g(X:S))) 0.001/0.001 g(0) -> s(0) 0.001/0.001 g(s(X:S)) -> s(s(g(X:S))) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z: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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (f 1) 0.001/0.001 (g 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f(X:S) -> cons(X:S,f(g(X:S))) 0.001/0.001 g(0) -> s(0) 0.001/0.001 g(s(X:S)) -> s(s(g(X:S))) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z: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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (f 1) 0.001/0.001 (g 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f(X:S) -> cons(X:S,f(g(X:S))) 0.001/0.001 g(0) -> s(0) 0.001/0.001 g(s(X:S)) -> s(s(g(X:S))) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z: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) => f(x4:S) -> cons(x4:S,f(g(x4:S))) 0.001/0.001 Rule 1 (l' :-> r') => f(X:S) -> cons(X:S,f(g(X:S))) 0.001/0.001 Var => x4:S 0.001/0.001 Pos x4:S in l => [1] 0.001/0.001 Sigma => {x4:S -> f(X:S)} 0.001/0.001 s => cons(f(X:S),f(g(f(X:S)))) 0.001/0.001 t => f(cons(X:S,f(g(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) => f(x4:S) -> cons(x4:S,f(g(x4:S))) 0.001/0.001 Rule 2 (l' :-> r') => g(0) -> s(0) 0.001/0.001 Var => x4:S 0.001/0.001 Pos x4:S in l => [1] 0.001/0.001 Sigma => {x4:S -> g(0)} 0.001/0.001 s => cons(g(0),f(g(g(0)))) 0.001/0.001 t => f(s(0)) 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) => f(x4:S) -> cons(x4:S,f(g(x4:S))) 0.001/0.001 Rule 3 (l' :-> r') => g(s(X:S)) -> s(s(g(X:S))) 0.001/0.001 Var => x4:S 0.001/0.001 Pos x4:S in l => [1] 0.001/0.001 Sigma => {x4:S -> g(s(X:S))} 0.001/0.001 s => cons(g(s(X:S)),f(g(g(s(X:S))))) 0.001/0.001 t => f(s(s(g(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) => f(x4:S) -> cons(x4:S,f(g(x4:S))) 0.001/0.001 Rule 4 (l' :-> r') => sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 Var => x4:S 0.001/0.001 Pos x4:S in l => [1] 0.001/0.001 Sigma => {x4:S -> sel(0,cons(X:S,Y:S))} 0.001/0.001 s => cons(sel(0,cons(X:S,Y:S)),f(g(sel(0,cons(X:S,Y:S))))) 0.001/0.001 t => f(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) => f(x4:S) -> cons(x4:S,f(g(x4:S))) 0.001/0.001 Rule 5 (l' :-> r') => sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S) 0.001/0.001 Var => x4:S 0.001/0.001 Pos x4:S in l => [1] 0.001/0.001 Sigma => {x4:S -> sel(s(X:S),cons(Y:S,Z:S))} 0.001/0.001 s => cons(sel(s(X:S),cons(Y:S,Z:S)),f(g(sel(s(X:S),cons(Y:S,Z:S))))) 0.001/0.001 t => f(sel(X:S,Z:S)) 0.001/0.001 NW => 0 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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (f 1) 0.001/0.001 (g 1) 0.001/0.001 (sel 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 f(X:S) -> cons(X:S,f(g(X:S))) 0.001/0.001 g(0) -> s(0) 0.001/0.001 g(s(X:S)) -> s(s(g(X:S))) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z: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 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 f(X:S) -> cons(X:S,f(g(X:S))) 0.001/0.001 g(0) -> s(0) 0.001/0.001 g(s(X:S)) -> s(s(g(X:S))) 0.001/0.001 sel(0,cons(X:S,Y:S)) -> X:S 0.001/0.001 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S) 0.001/0.001 -> Vars: 0.001/0.001 X, X, X, Y, X, Y, Z 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: [X]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [Y], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [X, Y], UV-RActive: [X, Z], UV-LFrozen: [Z], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x4, x5, x6, x7, x8, x9, x10 0.001/0.001 -> PVars: 0.001/0.001 X: [x4, x5, x6, x8], Y: [x7, x9], Z: [x10] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: f(x4:S) -> cons(x4:S,f(g(x4:S))), id: 1, possubterms: f(x4:S)->[]) 0.001/0.001 (rule: g(0) -> s(0), id: 2, possubterms: g(0)->[], 0->[1]) 0.001/0.001 (rule: g(s(x5:S)) -> s(s(g(x5:S))), id: 3, possubterms: g(s(x5:S))->[], s(x5:S)->[1]) 0.001/0.001 (rule: sel(0,cons(x6:S,x7:S)) -> x6:S, id: 4, possubterms: sel(0,cons(x6:S,x7:S))->[], 0->[1], cons(x6:S,x7:S)->[2]) 0.001/0.001 (rule: sel(s(x8:S),cons(x9:S,x10:S)) -> sel(x8:S,x10:S), id: 5, possubterms: sel(s(x8:S),cons(x9:S,x10:S))->[], s(x8:S)->[1], cons(x9:S,x10: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, NW0, N4 0.001/0.001 => Not trivial, Not overlay, NW0, 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: cons(sel(s(X:S),cons(Y:S,Z:S)),f(g(sel(s(X:S),cons(Y:S,Z:S))))) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('cons(sel(s(X:S),cons(Y:S,Z:S)),f(g(sel(s(X:S),cons(Y:S,Z:S)))))', D0) 0.001/0.001 ID: 1 => ('cons(sel(X:S,Z:S),f(g(sel(s(X:S),cons(Y:S,Z:S)))))', D1, R5, P[1], S{x8:S -> X:S, x9:S -> Y:S, x10:S -> Z:S}), NR: 'sel(X:S,Z:S)' 0.001/0.001 t: f(sel(X:S,Z:S)) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('f(sel(X:S,Z:S))', D0) 0.001/0.001 ID: 1 => ('cons(sel(X:S,Z:S),f(g(sel(X:S,Z:S))))', D1, R1, P[], S{x4:S -> sel(X:S,Z:S)}), NR: 'cons(sel(X:S,Z:S),f(g(sel(X:S,Z:S))))' 0.001/0.001 cons(sel(s(X:S),cons(Y:S,Z:S)),f(g(sel(s(X:S),cons(Y:S,Z:S))))) ->* no union *<- f(sel(X:S,Z: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 58%CPU (0avgtext+0avgdata 9812maxresident)k 0.001/0.001 0inputs+0outputs (0major+854minor)pagefaults 0swaps