0.009/0.009 NO 0.009/0.009 0.009/0.009 Problem 1: 0.009/0.009 0.009/0.009 0.009/0.009 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.009/0.009 Confluence Problem: 0.009/0.009 (VAR vNonEmpty:S v_NonEmpty:S:S I:S:S P:S:S X:S:S Y:S:S Z:S:S) 0.009/0.009 (STRATEGY CONTEXTSENSITIVE 0.009/0.009 (U11 1) 0.009/0.009 (U12 1) 0.009/0.009 (__ 1 2) 0.009/0.009 (isNePal 1) 0.009/0.009 (fSNonEmpty) 0.009/0.009 (nil) 0.009/0.009 (tt) 0.009/0.009 ) 0.009/0.009 (RULES 0.009/0.009 U11(tt) -> U12(tt) 0.009/0.009 U12(tt) -> tt 0.009/0.009 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.009/0.009 __(nil,X:S:S) -> X:S:S 0.009/0.009 __(X:S:S,nil) -> X:S:S 0.009/0.009 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> U11(tt) 0.009/0.009 ) 0.009/0.009 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.009/0.009 0.009/0.009 0.009/0.009 Problem 1: 0.009/0.009 0.009/0.009 CleanTRS Processor: 0.009/0.009 0.009/0.009 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.009/0.009 Confluence Problem: 0.009/0.009 (VAR vNonEmpty:S v_NonEmpty:S:S I:S:S P:S:S X:S:S Y:S:S Z:S:S) 0.009/0.009 (STRATEGY CONTEXTSENSITIVE 0.009/0.009 (U11 1) 0.009/0.009 (U12 1) 0.009/0.009 (__ 1 2) 0.009/0.009 (isNePal 1) 0.009/0.009 (fSNonEmpty) 0.009/0.009 (nil) 0.009/0.009 (tt) 0.009/0.009 ) 0.009/0.009 (RULES 0.009/0.009 U11(tt) -> U12(tt) 0.009/0.009 U12(tt) -> tt 0.009/0.009 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.009/0.009 __(nil,X:S:S) -> X:S:S 0.009/0.009 __(X:S:S,nil) -> X:S:S 0.009/0.009 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> U11(tt) 0.009/0.009 ) 0.009/0.009 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.009/0.009 0.009/0.009 0.009/0.009 Problem 1: 0.009/0.009 0.009/0.009 Modular Confluence Combinations Decomposition Processor: 0.009/0.009 0.009/0.009 No usable combinations 0.009/0.009 0.009/0.009 Problem 1: 0.009/0.009 Not CS-TRS Processor: 0.009/0.009 R is not a CS-TRS 0.009/0.009 0.009/0.009 Problem 1: 0.009/0.009 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.009/0.009 Confluence Problem: 0.009/0.009 (VAR vNonEmpty:S v_NonEmpty:S:S I:S:S P:S:S X:S:S Y:S:S Z:S:S) 0.009/0.009 (STRATEGY CONTEXTSENSITIVE 0.009/0.009 (U11 1) 0.009/0.009 (U12 1) 0.009/0.009 (__ 1 2) 0.009/0.009 (isNePal 1) 0.009/0.009 (fSNonEmpty) 0.009/0.009 (nil) 0.009/0.009 (tt) 0.009/0.009 ) 0.009/0.009 (RULES 0.009/0.009 U11(tt) -> U12(tt) 0.009/0.009 U12(tt) -> tt 0.009/0.009 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.009/0.009 __(nil,X:S:S) -> X:S:S 0.009/0.009 __(X:S:S,nil) -> X:S:S 0.009/0.009 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> U11(tt) 0.009/0.009 ) 0.009/0.009 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.009/0.009 0.009/0.009 Huet Levy Processor: 0.009/0.009 -> Rules: 0.009/0.009 U11(tt) -> U12(tt) 0.009/0.009 U12(tt) -> tt 0.009/0.009 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.009/0.009 __(nil,X:S:S) -> X:S:S 0.009/0.009 __(X:S:S,nil) -> X:S:S 0.009/0.009 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> U11(tt) 0.009/0.009 -> Vars: 0.009/0.009 X:S, Y:S, Z:S, X:S, X:S, I:S, P:S 0.009/0.009 -> FVars: 0.009/0.009 x7, x8, x9, x10, x11, x12, x13 0.009/0.009 -> PVars: 0.009/0.009 X:S: [x7, x10, x11], Y:S: [x8], Z:S: [x9], I:S: [x12], P:S: [x13] 0.009/0.009 0.009/0.009 -> Rlps: 0.009/0.009 (rule: U11(tt) -> U12(tt), id: 1, possubterms: U11(tt)->[], tt->[1]) 0.009/0.009 (rule: U12(tt) -> tt, id: 2, possubterms: U12(tt)->[], tt->[1]) 0.009/0.009 (rule: __(__(x7:S,x8:S),x9:S) -> __(x7:S,__(x8:S,x9:S)), id: 3, possubterms: __(__(x7:S,x8:S),x9:S)->[], __(x7:S,x8:S)->[1]) 0.009/0.009 (rule: __(nil,x10:S) -> x10:S, id: 4, possubterms: __(nil,x10:S)->[], nil->[1]) 0.009/0.009 (rule: __(x11:S,nil) -> x11:S, id: 5, possubterms: __(x11:S,nil)->[], nil->[2]) 0.009/0.009 (rule: isNePal(__(x12:S,__(x13:S,x12:S))) -> U11(tt), id: 6, possubterms: isNePal(__(x12:S,__(x13:S,x12:S)))->[], __(x12:S,__(x13:S,x12:S))->[1], __(x13:S,x12:S)->[1, 2]) 0.009/0.009 0.009/0.009 -> Unifications: 0.009/0.009 (R3 unifies with R3 at p: [1], l: __(__(x7:S,x8:S),x9:S), lp: __(x7:S,x8:S), sig: {x7:S -> __(X:S:S,Y:S:S),x8:S -> Z:S:S}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: __(x7:S,__(x8:S,x9:S)), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.009/0.009 (R3 unifies with R4 at p: [1], l: __(__(x7:S,x8:S),x9:S), lp: __(x7:S,x8:S), sig: {x7:S -> nil,x8:S -> X:S:S}, l': __(nil,X:S:S), r: __(x7:S,__(x8:S,x9:S)), r': X:S:S) 0.009/0.009 (R3 unifies with R5 at p: [1], l: __(__(x7:S,x8:S),x9:S), lp: __(x7:S,x8:S), sig: {x7:S -> X:S:S,x8:S -> nil}, l': __(X:S:S,nil), r: __(x7:S,__(x8:S,x9:S)), r': X:S:S) 0.009/0.009 (R5 unifies with R3 at p: [], l: __(x11:S,nil), lp: __(x11:S,nil), sig: {Z:S:S -> nil,x11:S -> __(X:S:S,Y:S:S)}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: x11:S, r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.009/0.009 (R5 unifies with R4 at p: [], l: __(x11:S,nil), lp: __(x11:S,nil), sig: {X:S:S -> nil,x11:S -> nil}, l': __(nil,X:S:S), r: x11:S, r': X:S:S) 0.009/0.009 (R6 unifies with R3 at p: [1], l: isNePal(__(x12:S,__(x13:S,x12:S))), lp: __(x12:S,__(x13:S,x12:S)), sig: {Z:S:S -> __(x13:S,__(X:S:S,Y:S:S)),x12:S -> __(X:S:S,Y:S:S)}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: U11(tt), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.009/0.009 (R6 unifies with R4 at p: [1], l: isNePal(__(x12:S,__(x13:S,x12:S))), lp: __(x12:S,__(x13:S,x12:S)), sig: {X:S:S -> __(x13:S,nil),x12:S -> nil}, l': __(nil,X:S:S), r: U11(tt), r': X:S:S) 0.009/0.009 (R6 unifies with R3 at p: [1,2], l: isNePal(__(x12:S,__(x13:S,x12:S))), lp: __(x13:S,x12:S), sig: {x12:S -> Z:S:S,x13:S -> __(X:S:S,Y:S:S)}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: U11(tt), r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.009/0.009 (R6 unifies with R4 at p: [1,2], l: isNePal(__(x12:S,__(x13:S,x12:S))), lp: __(x13:S,x12:S), sig: {x12:S -> X:S:S,x13:S -> nil}, l': __(nil,X:S:S), r: U11(tt), r': X:S:S) 0.009/0.009 (R6 unifies with R5 at p: [1,2], l: isNePal(__(x12:S,__(x13:S,x12:S))), lp: __(x13:S,x12:S), sig: {x12:S -> nil,x13:S -> X:S:S}, l': __(X:S:S,nil), r: U11(tt), r': X:S:S) 0.009/0.009 0.009/0.009 -> Critical pairs info: 0.009/0.009 <__(__(X:S:S,__(Y:S:S,Z:S:S)),Z:S:S),__(__(X:S:S,Y:S:S),__(Z:S:S,Z:S:S))> => Not trivial, Not overlay, NW0, N1 0.009/0.009 <__(X:S:S,Z:S:S),__(X:S:S,__(nil,Z:S:S))> => Not trivial, Not overlay, NW0, N2 0.009/0.009 => Not trivial, Not overlay, NW0, N3 0.009/0.009 <__(X:S:S,Z:S:S),__(nil,__(X:S:S,Z:S:S))> => Not trivial, Not overlay, NW0, N4 0.009/0.009 => Not trivial, Not overlay, NW0, N5 0.009/0.009 <__(X:S:S,__(Y:S:S,nil)),__(X:S:S,Y:S:S)> => Not trivial, Overlay, NW0, N6 0.009/0.009 => Not trivial, Not overlay, NW0, N7 0.009/0.009 => Not trivial, Not overlay, NW0, N8 0.009/0.009 => Not trivial, Not overlay, NW0, N9 0.009/0.009 => Trivial, Overlay, NW0, N10 0.009/0.009 0.009/0.009 -> Problem conclusions: 0.009/0.009 Not left linear, Right linear, Not linear 0.009/0.009 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.009/0.009 Not Huet-Levy confluent, Not Newman confluent 0.009/0.009 R is a TRS 0.009/0.009 0.009/0.009 0.009/0.009 Problem 1: 0.009/0.009 No Convergence Brute Force Processor: 0.009/0.009 -> Rewritings: 0.009/0.009 s: isNePal(__(Z:S:S,__(X:S:S,__(Y:S:S,Z:S:S)))) 0.009/0.009 Nodes: [0] 0.009/0.009 Edges: [] 0.009/0.009 ID: 0 => ('isNePal(__(Z:S:S,__(X:S:S,__(Y:S:S,Z:S:S))))', D0) 0.009/0.009 t: U11(tt) 0.009/0.009 Nodes: [0,1,2] 0.009/0.009 Edges: [(0,1),(1,2)] 0.009/0.009 ID: 0 => ('U11(tt)', D0) 0.009/0.009 ID: 1 => ('U12(tt)', D1, R1, P[], S{}), NR: 'U12(tt)' 0.009/0.009 ID: 2 => ('tt', D2, R2, P[], S{}), NR: 'tt' 0.009/0.009 isNePal(__(Z:S:S,__(X:S:S,__(Y:S:S,Z:S:S)))) ->* no union *<- U11(tt) 0.009/0.009 "Not joinable" 0.009/0.009 0.009/0.009 The problem is not joinable. 0.009/0.009 0.05user 0.01system 0:00.09elapsed 71%CPU (0avgtext+0avgdata 10812maxresident)k 0.009/0.009 10088inputs+0outputs (41major+5061minor)pagefaults 0swaps