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 I:S P:S X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (__ 1 2) 0.001/0.001 (isNePal 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt) -> U12(tt) 0.001/0.001 U12(tt) -> tt 0.001/0.001 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.001/0.001 __(nil,X:S) -> X:S 0.001/0.001 __(X:S,nil) -> X:S 0.001/0.001 isNePal(__(I:S,__(P:S,I:S))) -> U11(tt) 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 I:S P:S X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (__ 1 2) 0.001/0.001 (isNePal 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt) -> U12(tt) 0.001/0.001 U12(tt) -> tt 0.001/0.001 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.001/0.001 __(nil,X:S) -> X:S 0.001/0.001 __(X:S,nil) -> X:S 0.001/0.001 isNePal(__(I:S,__(P:S,I:S))) -> U11(tt) 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 0.001/0.001 No usable combinations 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 Not CS-TRS Processor: 0.001/0.001 R is not 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 I:S P:S X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (__ 1 2) 0.001/0.001 (isNePal 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (nil) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt) -> U12(tt) 0.001/0.001 U12(tt) -> tt 0.001/0.001 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.001/0.001 __(nil,X:S) -> X:S 0.001/0.001 __(X:S,nil) -> X:S 0.001/0.001 isNePal(__(I:S,__(P:S,I:S))) -> U11(tt) 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 U11(tt) -> U12(tt) 0.001/0.001 U12(tt) -> tt 0.001/0.001 __(__(X:S,Y:S),Z:S) -> __(X:S,__(Y:S,Z:S)) 0.001/0.001 __(nil,X:S) -> X:S 0.001/0.001 __(X:S,nil) -> X:S 0.001/0.001 isNePal(__(I:S,__(P:S,I:S))) -> U11(tt) 0.001/0.001 -> Vars: 0.001/0.001 X, Y, Z, X, X, I, P 0.001/0.001 -> FVars: 0.001/0.001 x6, x7, x8, x9, x10, x11, x12 0.001/0.001 -> PVars: 0.001/0.001 X: [x6, x9, x10], Y: [x7], Z: [x8], I: [x11], P: [x12] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: U11(tt) -> U12(tt), id: 1, possubterms: U11(tt)->[], tt->[1]) 0.001/0.001 (rule: U12(tt) -> tt, id: 2, possubterms: U12(tt)->[], tt->[1]) 0.001/0.001 (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]) 0.001/0.001 (rule: __(nil,x9:S) -> x9:S, id: 4, possubterms: __(nil,x9:S)->[], nil->[1]) 0.001/0.001 (rule: __(x10:S,nil) -> x10:S, id: 5, possubterms: __(x10:S,nil)->[], nil->[2]) 0.001/0.001 (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]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (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))) 0.001/0.001 (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) 0.001/0.001 (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) 0.001/0.001 (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))) 0.001/0.001 (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) 0.001/0.001 (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))) 0.001/0.001 (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) 0.001/0.001 (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))) 0.001/0.001 (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) 0.001/0.001 (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) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Not trivial, Not overlay, NW0, N1 0.001/0.001 <__(__(X:S,__(Y:S,Z:S)),Z:S),__(__(X:S,Y:S),__(Z:S,Z:S))> => 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 <__(X:S,Z:S),__(X:S,__(nil,Z:S))> => Not trivial, Not overlay, NW0, N5 0.001/0.001 <__(X:S,__(Y:S,nil)),__(X:S,Y:S)> => Not trivial, Overlay, NW0, N6 0.001/0.001 => Not trivial, Not overlay, NW0, N7 0.001/0.001 <__(X:S,Z:S),__(nil,__(X:S,Z:S))> => Not trivial, Not overlay, NW0, N8 0.001/0.001 => Not trivial, Not overlay, NW0, N9 0.001/0.001 => Trivial, Overlay, NW0, N10 0.001/0.001 0.001/0.001 -> Problem conclusions: 0.001/0.001 Not left linear, 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 TRS 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: isNePal(__(X:S,__(Y:S,__(P:S,__(X:S,Y:S))))) 0.001/0.001 Nodes: [0] 0.001/0.001 Edges: [] 0.001/0.001 ID: 0 => ('isNePal(__(X:S,__(Y:S,__(P:S,__(X:S,Y:S)))))', D0) 0.001/0.001 t: U11(tt) 0.001/0.001 Nodes: [0,1,2] 0.001/0.001 Edges: [(0,1),(1,2)] 0.001/0.001 ID: 0 => ('U11(tt)', D0) 0.001/0.001 ID: 1 => ('U12(tt)', D1, R1, P[], S{}), NR: 'U12(tt)' 0.001/0.001 ID: 2 => ('tt', D2, R2, P[], S{}), NR: 'tt' 0.001/0.001 isNePal(__(X:S,__(Y:S,__(P:S,__(X:S,Y:S))))) ->* no union *<- U11(tt) 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 66%CPU (0avgtext+0avgdata 10084maxresident)k 0.001/0.001 0inputs+0outputs (0major+828minor)pagefaults 0swaps