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 Y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1 2) 0.001/0.001 (fib 1) 0.001/0.001 (fib1 1 2) 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 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 fib(N:S) -> sel(N:S,fib1(s(0),s(0))) 0.001/0.001 fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y: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 ) 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 Y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1 2) 0.001/0.001 (fib 1) 0.001/0.001 (fib1 1 2) 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 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 fib(N:S) -> sel(N:S,fib1(s(0),s(0))) 0.001/0.001 fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y: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 ) 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 Y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1 2) 0.001/0.001 (fib 1) 0.001/0.001 (fib1 1 2) 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 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 fib(N:S) -> sel(N:S,fib1(s(0),s(0))) 0.001/0.001 fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y: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 ) 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) => fib1(x9:S,x10:S) -> cons(x9:S,fib1(x10:S,add(x9:S,x10:S))) 0.001/0.001 Rule 4 (l' :-> r') => fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y:S))) 0.001/0.001 Var => x9:S 0.001/0.001 Pos x9:S in l => [1] 0.001/0.001 Sigma => {x9:S -> fib1(X:S,Y:S)} 0.001/0.001 s => cons(fib1(X:S,Y:S),fib1(x10:S,add(fib1(X:S,Y:S),x10:S))) 0.001/0.001 t => fib1(cons(X:S,fib1(Y:S,add(X:S,Y:S))),x10: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) => fib1(x9:S,x10:S) -> cons(x9:S,fib1(x10:S,add(x9:S,x10:S))) 0.001/0.001 Rule 5 (l' :-> r') => sel(0,cons(X:S,XS:S)) -> X:S 0.001/0.001 Var => x9:S 0.001/0.001 Pos x9:S in l => [1] 0.001/0.001 Sigma => {x9:S -> sel(0,cons(X:S,XS:S))} 0.001/0.001 s => cons(sel(0,cons(X:S,XS:S)),fib1(x10:S,add(sel(0,cons(X:S,XS:S)),x10:S))) 0.001/0.001 t => fib1(X:S,x10: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) => fib1(x9:S,x10:S) -> cons(x9:S,fib1(x10:S,add(x9:S,x10:S))) 0.001/0.001 Rule 6 (l' :-> r') => sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S) 0.001/0.001 Var => x9:S 0.001/0.001 Pos x9:S in l => [1] 0.001/0.001 Sigma => {x9: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)),fib1(x10:S,add(sel(s(N:S),cons(X:S,XS:S)),x10:S))) 0.001/0.001 t => fib1(sel(N:S,XS:S),x10: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 N:S X:S XS:S Y:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1 2) 0.001/0.001 (fib 1) 0.001/0.001 (fib1 1 2) 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 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 fib(N:S) -> sel(N:S,fib1(s(0),s(0))) 0.001/0.001 fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y: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 ) 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 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 fib(N:S) -> sel(N:S,fib1(s(0),s(0))) 0.001/0.001 fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y: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 -> Vars: 0.001/0.001 X, X, Y, N, X, Y, X, XS, N, X, XS 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [X, Y], UV-RActive: [X, Y], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [N], UV-RActive: [N], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [X, Y], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: [X, Y]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [XS], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [N, X], UV-RActive: [N, XS], UV-LFrozen: [XS], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15 0.001/0.001 -> PVars: 0.001/0.001 X: [x5, x6, x9, x11, x14], Y: [x7, x10], N: [x8, x13], XS: [x12, x15] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: add(0,x5:S) -> x5:S, id: 1, possubterms: add(0,x5:S)->[], 0->[1]) 0.001/0.001 (rule: add(s(x6:S),x7:S) -> s(add(x6:S,x7:S)), id: 2, possubterms: add(s(x6:S),x7:S)->[], s(x6:S)->[1]) 0.001/0.001 (rule: fib(x8:S) -> sel(x8:S,fib1(s(0),s(0))), id: 3, possubterms: fib(x8:S)->[]) 0.001/0.001 (rule: fib1(x9:S,x10:S) -> cons(x9:S,fib1(x10:S,add(x9:S,x10:S))), id: 4, possubterms: fib1(x9:S,x10:S)->[]) 0.001/0.001 (rule: sel(0,cons(x11:S,x12:S)) -> x11:S, id: 5, possubterms: sel(0,cons(x11:S,x12:S))->[], 0->[1], cons(x11:S,x12:S)->[2]) 0.001/0.001 (rule: sel(s(x13:S),cons(x14:S,x15:S)) -> sel(x13:S,x15:S), id: 6, possubterms: sel(s(x13:S),cons(x14:S,x15:S))->[], s(x13:S)->[1], cons(x14:S,x15: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 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(N:S),cons(X:S,XS:S)),fib1(Y:S,add(sel(s(N:S),cons(X:S,XS:S)),Y:S))) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('cons(sel(s(N:S),cons(X:S,XS:S)),fib1(Y:S,add(sel(s(N:S),cons(X:S,XS:S)),Y:S)))', D0) 0.001/0.001 ID: 1 => ('cons(sel(N:S,XS:S),fib1(Y:S,add(sel(s(N:S),cons(X:S,XS:S)),Y:S)))', D1, R6, P[1], S{x13:S -> N:S, x14:S -> X:S, x15:S -> XS:S}), NR: 'sel(N:S,XS:S)' 0.001/0.001 t: fib1(sel(N:S,XS:S),Y:S) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('fib1(sel(N:S,XS:S),Y:S)', D0) 0.001/0.001 ID: 1 => ('cons(sel(N:S,XS:S),fib1(Y:S,add(sel(N:S,XS:S),Y:S)))', D1, R4, P[], S{x9:S -> sel(N:S,XS:S), x10:S -> Y:S}), NR: 'cons(sel(N:S,XS:S),fib1(Y:S,add(sel(N:S,XS:S),Y:S)))' 0.001/0.001 cons(sel(s(N:S),cons(X:S,XS:S)),fib1(Y:S,add(sel(s(N:S),cons(X:S,XS:S)),Y:S))) ->* no union *<- fib1(sel(N:S,XS:S),Y: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 83%CPU (0avgtext+0avgdata 9872maxresident)k 0.001/0.001 0inputs+0outputs (0major+863minor)pagefaults 0swaps