0.004/0.004 NO 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 0.004/0.004 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 Confluence Problem: 0.004/0.004 (VAR vNonEmpty:S I:S P:S X:S Y:S Z:S) 0.004/0.004 (STRATEGY CONTEXTSENSITIVE 0.004/0.004 (U11 1) 0.004/0.004 (U12 1) 0.004/0.004 (__ 1 2) 0.004/0.004 (isNePal 1) 0.004/0.004 (fSNonEmpty) 0.004/0.004 (nil) 0.004/0.004 (tt) 0.004/0.004 ) 0.004/0.004 (RULES 0.004/0.004 U11(tt) -> U12(tt) 0.004/0.004 U12(tt) -> tt 0.004/0.004 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.004/0.004 __(nil,X:S) -> X:S 0.004/0.004 __(X:S,nil) -> X:S 0.004/0.004 isNePal(__(I:S,__(P:S,I:S))) -> U11(tt) 0.004/0.004 ) 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 0.004/0.004 CleanTRS Processor: 0.004/0.004 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 Confluence Problem: 0.004/0.004 (VAR vNonEmpty:S I:S P:S X:S Y:S Z:S) 0.004/0.004 (STRATEGY CONTEXTSENSITIVE 0.004/0.004 (U11 1) 0.004/0.004 (U12 1) 0.004/0.004 (__ 1 2) 0.004/0.004 (isNePal 1) 0.004/0.004 (fSNonEmpty) 0.004/0.004 (nil) 0.004/0.004 (tt) 0.004/0.004 ) 0.004/0.004 (RULES 0.004/0.004 U11(tt) -> U12(tt) 0.004/0.004 U12(tt) -> tt 0.004/0.004 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.004/0.004 __(nil,X:S) -> X:S 0.004/0.004 __(X:S,nil) -> X:S 0.004/0.004 isNePal(__(I:S,__(P:S,I:S))) -> U11(tt) 0.004/0.004 ) 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 0.004/0.004 Modular Confluence Combinations Decomposition Processor: 0.004/0.004 0.004/0.004 No usable combinations 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 Not CS-TRS Processor: 0.004/0.004 R is not a CS-TRS 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 Confluence Problem: 0.004/0.004 (VAR vNonEmpty:S I:S P:S X:S Y:S Z:S) 0.004/0.004 (STRATEGY CONTEXTSENSITIVE 0.004/0.004 (U11 1) 0.004/0.004 (U12 1) 0.004/0.004 (__ 1 2) 0.004/0.004 (isNePal 1) 0.004/0.004 (fSNonEmpty) 0.004/0.004 (nil) 0.004/0.004 (tt) 0.004/0.004 ) 0.004/0.004 (RULES 0.004/0.004 U11(tt) -> U12(tt) 0.004/0.004 U12(tt) -> tt 0.004/0.004 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.004/0.004 __(nil,X:S) -> X:S 0.004/0.004 __(X:S,nil) -> X:S 0.004/0.004 isNePal(__(I:S,__(P:S,I:S))) -> U11(tt) 0.004/0.004 ) 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 0.004/0.004 Huet Levy Processor: 0.004/0.004 -> Rules: 0.004/0.004 U11(tt) -> U12(tt) 0.004/0.004 U12(tt) -> tt 0.004/0.004 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.004/0.004 __(nil,X:S) -> X:S 0.004/0.004 __(X:S,nil) -> X:S 0.004/0.004 isNePal(__(I:S,__(P:S,I:S))) -> U11(tt) 0.004/0.004 -> Vars: 0.004/0.004 X, Y, Z, X, X, I, P 0.004/0.004 -> FVars: 0.004/0.004 x6, x7, x8, x9, x10, x11, x12 0.004/0.004 -> PVars: 0.004/0.004 X: [x6, x9, x10], Y: [x7], Z: [x8], I: [x11], P: [x12] 0.004/0.004 0.004/0.004 -> Rlps: 0.004/0.004 (rule: U11(tt) -> U12(tt), id: 1, possubterms: U11(tt)->[], tt->[1]) 0.004/0.004 (rule: U12(tt) -> tt, id: 2, possubterms: U12(tt)->[], tt->[1]) 0.004/0.004 (rule: __(__(x6:S,x7:S),x8:S) -> __(x6:S,__(x7:S,x8:S)), id: 3, possubterms: __(__(x6:S,x7:S),x8:S)->[], __(x6:S,x7:S)->[1]) 0.004/0.004 (rule: __(nil,x9:S) -> x9:S, id: 4, possubterms: __(nil,x9:S)->[], nil->[1]) 0.004/0.004 (rule: __(x10:S,nil) -> x10:S, id: 5, possubterms: __(x10:S,nil)->[], nil->[2]) 0.004/0.004 (rule: isNePal(__(x11:S,__(x12:S,x11:S))) -> U11(tt), id: 6, possubterms: isNePal(__(x11:S,__(x12:S,x11:S)))->[], __(x11:S,__(x12:S,x11:S))->[1], __(x12:S,x11:S)->[1, 2]) 0.004/0.004 0.004/0.004 -> Unifications: 0.004/0.004 (R3 unifies with R3 at p: [1], l: __(__(x6:S,x7:S),x8:S), lp: __(x6:S,x7:S), sig: {x6:S -> __(X:S,Y:S),x7:S -> Z:S}, l': __(__(X:S,Y:S),Z:S), r: __(x6:S,__(x7:S,x8:S)), r': __(X:S,__(Y:S,Z:S))) 0.004/0.004 (R3 unifies with R4 at p: [1], l: __(__(x6:S,x7:S),x8:S), lp: __(x6:S,x7:S), sig: {x6:S -> nil,x7:S -> X:S}, l': __(nil,X:S), r: __(x6:S,__(x7:S,x8:S)), r': X:S) 0.004/0.004 (R3 unifies with R5 at p: [1], l: __(__(x6:S,x7:S),x8:S), lp: __(x6:S,x7:S), sig: {x6:S -> X:S,x7:S -> nil}, l': __(X:S,nil), r: __(x6:S,__(x7:S,x8:S)), r': X:S) 0.004/0.004 (R5 unifies with R3 at p: [], l: __(x10:S,nil), lp: __(x10:S,nil), sig: {Z:S -> nil,x10:S -> __(X:S,Y:S)}, l': __(__(X:S,Y:S),Z:S), r: x10:S, r': __(X:S,__(Y:S,Z:S))) 0.004/0.004 (R5 unifies with R4 at p: [], l: __(x10:S,nil), lp: __(x10:S,nil), sig: {X:S -> nil,x10:S -> nil}, l': __(nil,X:S), r: x10:S, r': X:S) 0.004/0.004 (R6 unifies with R3 at p: [1], l: isNePal(__(x11:S,__(x12:S,x11:S))), lp: __(x11:S,__(x12:S,x11:S)), sig: {Z:S -> __(x12:S,__(X:S,Y:S)),x11:S -> __(X:S,Y:S)}, l': __(__(X:S,Y:S),Z:S), r: U11(tt), r': __(X:S,__(Y:S,Z:S))) 0.004/0.004 (R6 unifies with R4 at p: [1], l: isNePal(__(x11:S,__(x12:S,x11:S))), lp: __(x11:S,__(x12:S,x11:S)), sig: {X:S -> __(x12:S,nil),x11:S -> nil}, l': __(nil,X:S), r: U11(tt), r': X:S) 0.004/0.004 (R6 unifies with R3 at p: [1,2], l: isNePal(__(x11:S,__(x12:S,x11:S))), lp: __(x12:S,x11:S), sig: {x11:S -> Z:S,x12:S -> __(X:S,Y:S)}, l': __(__(X:S,Y:S),Z:S), r: U11(tt), r': __(X:S,__(Y:S,Z:S))) 0.004/0.004 (R6 unifies with R4 at p: [1,2], l: isNePal(__(x11:S,__(x12:S,x11:S))), lp: __(x12:S,x11:S), sig: {x11:S -> X:S,x12:S -> nil}, l': __(nil,X:S), r: U11(tt), r': X:S) 0.004/0.004 (R6 unifies with R5 at p: [1,2], l: isNePal(__(x11:S,__(x12:S,x11:S))), lp: __(x12:S,x11:S), sig: {x11:S -> nil,x12:S -> X:S}, l': __(X:S,nil), r: U11(tt), r': X:S) 0.004/0.004 0.004/0.004 -> Critical pairs info: 0.004/0.004 <__(X:S,__(Y:S,nil)),__(X:S,Y:S)> => Not trivial, Overlay, NW0, N1 0.004/0.004 => Not trivial, Not overlay, NW0, N2 0.004/0.004 => Not trivial, Not overlay, NW0, N3 0.004/0.004 => Not trivial, Not overlay, NW0, N4 0.004/0.004 => Trivial, Overlay, NW0, N5 0.004/0.004 <__(X:S,Z:S),__(nil,__(X:S,Z:S))> => Not trivial, Not overlay, NW0, N6 0.004/0.004 <__(__(X:S,__(Y:S,Z:S)),Z:S),__(__(X:S,Y:S),__(Z:S,Z:S))> => Not trivial, Not overlay, NW0, N7 0.004/0.004 <__(X:S,Z:S),__(X:S,__(nil,Z:S))> => Not trivial, Not overlay, NW0, N8 0.004/0.004 => Not trivial, Not overlay, NW0, N9 0.004/0.004 => Not trivial, Not overlay, NW0, N10 0.004/0.004 0.004/0.004 -> Problem conclusions: 0.004/0.004 Not left linear, Right linear, Not linear 0.004/0.004 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.004/0.004 Not Huet-Levy confluent, Not Newman confluent 0.004/0.004 R is a TRS 0.004/0.004 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 No Convergence Brute Force Processor: 0.004/0.004 -> Rewritings: 0.004/0.004 s: isNePal(__(X:S,X:S)) 0.004/0.004 Nodes: [0] 0.004/0.004 Edges: [] 0.004/0.004 ID: 0 => ('isNePal(__(X:S,X:S))', D0) 0.004/0.004 t: U11(tt) 0.004/0.004 Nodes: [0,1,2] 0.004/0.004 Edges: [(0,1),(1,2)] 0.004/0.004 ID: 0 => ('U11(tt)', D0) 0.004/0.004 ID: 1 => ('U12(tt)', D1, R1, P[], S{}), NR: 'U12(tt)' 0.004/0.004 ID: 2 => ('tt', D2, R2, P[], S{}), NR: 'tt' 0.004/0.004 isNePal(__(X:S,X:S)) ->* no union *<- U11(tt) 0.004/0.004 "Not joinable" 0.004/0.004 0.004/0.004 The problem is not joinable. 0.004/0.004 0.02user 0.01system 0:00.04elapsed 81%CPU (0avgtext+0avgdata 10644maxresident)k 0.004/0.004 0inputs+0outputs (0major+3312minor)pagefaults 0swaps