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 Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (2ndsneg 1 2) 0.001/0.001 (2ndspos 1 2) 0.001/0.001 (from 1) 0.001/0.001 (pi 1) 0.001/0.001 (plus 1 2) 0.001/0.001 (square 1) 0.001/0.001 (times 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (negrecip 1) 0.001/0.001 (posrecip 1) 0.001/0.001 (rcons 1 2) 0.001/0.001 (rnil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 2ndsneg(0,Z:S) -> rnil 0.001/0.001 2ndsneg(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,Z:S)) 0.001/0.001 2ndspos(0,Z:S) -> rnil 0.001/0.001 2ndspos(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 pi(X:S) -> 2ndspos(X:S,from(0)) 0.001/0.001 plus(0,Y:S) -> Y:S 0.001/0.001 plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) 0.001/0.001 square(X:S) -> times(X:S,X:S) 0.001/0.001 times(0,Y:S) -> 0 0.001/0.001 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y: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 Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (2ndsneg 1 2) 0.001/0.001 (2ndspos 1 2) 0.001/0.001 (from 1) 0.001/0.001 (pi 1) 0.001/0.001 (plus 1 2) 0.001/0.001 (square 1) 0.001/0.001 (times 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (negrecip 1) 0.001/0.001 (posrecip 1) 0.001/0.001 (rcons 1 2) 0.001/0.001 (rnil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 2ndsneg(0,Z:S) -> rnil 0.001/0.001 2ndsneg(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,Z:S)) 0.001/0.001 2ndspos(0,Z:S) -> rnil 0.001/0.001 2ndspos(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 pi(X:S) -> 2ndspos(X:S,from(0)) 0.001/0.001 plus(0,Y:S) -> Y:S 0.001/0.001 plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) 0.001/0.001 square(X:S) -> times(X:S,X:S) 0.001/0.001 times(0,Y:S) -> 0 0.001/0.001 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y: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 Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (2ndsneg 1 2) 0.001/0.001 (2ndspos 1 2) 0.001/0.001 (from 1) 0.001/0.001 (pi 1) 0.001/0.001 (plus 1 2) 0.001/0.001 (square 1) 0.001/0.001 (times 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (negrecip 1) 0.001/0.001 (posrecip 1) 0.001/0.001 (rcons 1 2) 0.001/0.001 (rnil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 2ndsneg(0,Z:S) -> rnil 0.001/0.001 2ndsneg(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,Z:S)) 0.001/0.001 2ndspos(0,Z:S) -> rnil 0.001/0.001 2ndspos(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 pi(X:S) -> 2ndspos(X:S,from(0)) 0.001/0.001 plus(0,Y:S) -> Y:S 0.001/0.001 plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) 0.001/0.001 square(X:S) -> times(X:S,X:S) 0.001/0.001 times(0,Y:S) -> 0 0.001/0.001 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y: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(x15:S) -> cons(x15:S,from(s(x15:S))) 0.001/0.001 Rule 5 (l' :-> r') => from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 Var => x15:S 0.001/0.001 Pos x15:S in l => [1] 0.001/0.001 Sigma => {x15: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(x15:S) -> cons(x15:S,from(s(x15:S))) 0.001/0.001 Rule 6 (l' :-> r') => pi(X:S) -> 2ndspos(X:S,from(0)) 0.001/0.001 Var => x15:S 0.001/0.001 Pos x15:S in l => [1] 0.001/0.001 Sigma => {x15:S -> pi(X:S)} 0.001/0.001 s => cons(pi(X:S),from(s(pi(X:S)))) 0.001/0.001 t => from(2ndspos(X:S,from(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) => from(x15:S) -> cons(x15:S,from(s(x15:S))) 0.001/0.001 Rule 7 (l' :-> r') => plus(0,Y:S) -> Y:S 0.001/0.001 Var => x15:S 0.001/0.001 Pos x15:S in l => [1] 0.001/0.001 Sigma => {x15:S -> plus(0,Y:S)} 0.001/0.001 s => cons(plus(0,Y:S),from(s(plus(0,Y:S)))) 0.001/0.001 t => from(Y: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(x15:S) -> cons(x15:S,from(s(x15:S))) 0.001/0.001 Rule 8 (l' :-> r') => plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) 0.001/0.001 Var => x15:S 0.001/0.001 Pos x15:S in l => [1] 0.001/0.001 Sigma => {x15:S -> plus(s(X:S),Y:S)} 0.001/0.001 s => cons(plus(s(X:S),Y:S),from(s(plus(s(X:S),Y:S)))) 0.001/0.001 t => from(s(plus(X:S,Y: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(x15:S) -> cons(x15:S,from(s(x15:S))) 0.001/0.001 Rule 9 (l' :-> r') => square(X:S) -> times(X:S,X:S) 0.001/0.001 Var => x15:S 0.001/0.001 Pos x15:S in l => [1] 0.001/0.001 Sigma => {x15:S -> square(X:S)} 0.001/0.001 s => cons(square(X:S),from(s(square(X:S)))) 0.001/0.001 t => from(times(X: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(x15:S) -> cons(x15:S,from(s(x15:S))) 0.001/0.001 Rule 10 (l' :-> r') => times(0,Y:S) -> 0 0.001/0.001 Var => x15:S 0.001/0.001 Pos x15:S in l => [1] 0.001/0.001 Sigma => {x15:S -> times(0,Y:S)} 0.001/0.001 s => cons(times(0,Y:S),from(s(times(0,Y:S)))) 0.001/0.001 t => from(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) => from(x15:S) -> cons(x15:S,from(s(x15:S))) 0.001/0.001 Rule 11 (l' :-> r') => times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S)) 0.001/0.001 Var => x15:S 0.001/0.001 Pos x15:S in l => [1] 0.001/0.001 Sigma => {x15:S -> times(s(X:S),Y:S)} 0.001/0.001 s => cons(times(s(X:S),Y:S),from(s(times(s(X:S),Y:S)))) 0.001/0.001 t => from(plus(Y:S,times(X:S,Y: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 Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (2ndsneg 1 2) 0.001/0.001 (2ndspos 1 2) 0.001/0.001 (from 1) 0.001/0.001 (pi 1) 0.001/0.001 (plus 1 2) 0.001/0.001 (square 1) 0.001/0.001 (times 1 2) 0.001/0.001 (0) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (negrecip 1) 0.001/0.001 (posrecip 1) 0.001/0.001 (rcons 1 2) 0.001/0.001 (rnil) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 2ndsneg(0,Z:S) -> rnil 0.001/0.001 2ndsneg(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,Z:S)) 0.001/0.001 2ndspos(0,Z:S) -> rnil 0.001/0.001 2ndspos(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 pi(X:S) -> 2ndspos(X:S,from(0)) 0.001/0.001 plus(0,Y:S) -> Y:S 0.001/0.001 plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) 0.001/0.001 square(X:S) -> times(X:S,X:S) 0.001/0.001 times(0,Y:S) -> 0 0.001/0.001 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y: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, NW0, 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 2ndsneg(0,Z:S) -> rnil 0.001/0.001 2ndsneg(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,Z:S)) 0.001/0.001 2ndspos(0,Z:S) -> rnil 0.001/0.001 2ndspos(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 pi(X:S) -> 2ndspos(X:S,from(0)) 0.001/0.001 plus(0,Y:S) -> Y:S 0.001/0.001 plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) 0.001/0.001 square(X:S) -> times(X:S,X:S) 0.001/0.001 times(0,Y:S) -> 0 0.001/0.001 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S)) 0.001/0.001 -> Vars: 0.001/0.001 Z, N, X, Y, Z, Z, N, X, Y, Z, X, X, Y, X, Y, X, Y, X, Y 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [Z], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [N, X], UV-RActive: [N, Y, Z], UV-LFrozen: [Y, Z], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [Z], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [N, X], UV-RActive: [N, Y, Z], UV-LFrozen: [Y, Z], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: [X]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [Y], UV-RActive: [Y], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [X, Y], UV-RActive: [X, Y], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [Y], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [X, Y], UV-RActive: [X, Y], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23 0.001/0.001 -> PVars: 0.001/0.001 Z: [x5, x9, x10, x14], N: [x6, x11], X: [x7, x12, x15, x16, x18, x20, x22], Y: [x8, x13, x17, x19, x21, x23] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: 2ndsneg(0,x5:S) -> rnil, id: 1, possubterms: 2ndsneg(0,x5:S)->[], 0->[1]) 0.001/0.001 (rule: 2ndsneg(s(x6:S),cons(x7:S,cons(x8:S,x9:S))) -> rcons(negrecip(x8:S),2ndspos(x6:S,x9:S)), id: 2, possubterms: 2ndsneg(s(x6:S),cons(x7:S,cons(x8:S,x9:S)))->[], s(x6:S)->[1], cons(x7:S,cons(x8:S,x9:S))->[2]) 0.001/0.001 (rule: 2ndspos(0,x10:S) -> rnil, id: 3, possubterms: 2ndspos(0,x10:S)->[], 0->[1]) 0.001/0.001 (rule: 2ndspos(s(x11:S),cons(x12:S,cons(x13:S,x14:S))) -> rcons(posrecip(x13:S),2ndsneg(x11:S,x14:S)), id: 4, possubterms: 2ndspos(s(x11:S),cons(x12:S,cons(x13:S,x14:S)))->[], s(x11:S)->[1], cons(x12:S,cons(x13:S,x14:S))->[2]) 0.001/0.001 (rule: from(x15:S) -> cons(x15:S,from(s(x15:S))), id: 5, possubterms: from(x15:S)->[]) 0.001/0.001 (rule: pi(x16:S) -> 2ndspos(x16:S,from(0)), id: 6, possubterms: pi(x16:S)->[]) 0.001/0.001 (rule: plus(0,x17:S) -> x17:S, id: 7, possubterms: plus(0,x17:S)->[], 0->[1]) 0.001/0.001 (rule: plus(s(x18:S),x19:S) -> s(plus(x18:S,x19:S)), id: 8, possubterms: plus(s(x18:S),x19:S)->[], s(x18:S)->[1]) 0.001/0.001 (rule: square(x20:S) -> times(x20:S,x20:S), id: 9, possubterms: square(x20:S)->[]) 0.001/0.001 (rule: times(0,x21:S) -> 0, id: 10, possubterms: times(0,x21:S)->[], 0->[1]) 0.001/0.001 (rule: times(s(x22:S),x23:S) -> plus(x23:S,times(x22:S,x23:S)), id: 11, possubterms: times(s(x22:S),x23:S)->[], s(x22: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, 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, 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(times(s(X:S),Y:S),from(s(times(s(X:S),Y:S)))) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('cons(times(s(X:S),Y:S),from(s(times(s(X:S),Y:S))))', D0) 0.001/0.001 ID: 1 => ('cons(plus(Y:S,times(X:S,Y:S)),from(s(times(s(X:S),Y:S))))', D1, R11, P[1], S{x22:S -> X:S, x23:S -> Y:S}), NR: 'plus(Y:S,times(X:S,Y:S))' 0.001/0.001 t: from(plus(Y:S,times(X:S,Y:S))) 0.001/0.001 Nodes: [0,1] 0.001/0.001 Edges: [(0,1)] 0.001/0.001 ID: 0 => ('from(plus(Y:S,times(X:S,Y:S)))', D0) 0.001/0.001 ID: 1 => ('cons(plus(Y:S,times(X:S,Y:S)),from(s(plus(Y:S,times(X:S,Y:S)))))', D1, R5, P[], S{x15:S -> plus(Y:S,times(X:S,Y:S))}), NR: 'cons(plus(Y:S,times(X:S,Y:S)),from(s(plus(Y:S,times(X:S,Y:S)))))' 0.001/0.001 cons(times(s(X:S),Y:S),from(s(times(s(X:S),Y:S)))) ->* no union *<- from(plus(Y:S,times(X: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 0.00user 0.00system 0:00.01elapsed 75%CPU (0avgtext+0avgdata 11160maxresident)k 0.001/0.001 0inputs+0outputs (0major+1046minor)pagefaults 0swaps