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 v_NonEmpty:S:S I:S:S P:S:S X:S:S Y:S:S Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (__ 1 2) 0.001/0.001 (and 1) 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 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.001/0.001 __(nil,X:S:S) -> X:S:S 0.001/0.001 __(X:S:S,nil) -> X:S:S 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> 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 v_NonEmpty:S:S I:S:S P:S:S X:S:S Y:S:S Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (__ 1 2) 0.001/0.001 (and 1) 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 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.001/0.001 __(nil,X:S:S) -> X:S:S 0.001/0.001 __(X:S:S,nil) -> X:S:S 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> 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 It is a CTRS -> No modular confluence 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 Left-Homogeneous u-Replacing Variables Processor: 0.001/0.001 R satisfies LHRV condition 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 v_NonEmpty:S:S I:S:S P:S:S X:S:S Y:S:S Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (__ 1 2) 0.001/0.001 (and 1) 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 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.001/0.001 __(nil,X:S:S) -> X:S:S 0.001/0.001 __(X:S:S,nil) -> X:S:S 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> 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 __(__(X:S:S,Y:S:S),Z:S:S) -> __(X:S:S,__(Y:S:S,Z:S:S)) 0.001/0.001 __(nil,X:S:S) -> X:S:S 0.001/0.001 __(X:S:S,nil) -> X:S:S 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNePal(__(I:S:S,__(P:S:S,I:S:S))) -> tt 0.001/0.001 -> Vars: 0.001/0.001 X:S, Y:S, Z:S, X:S, X:S, X:S, I:S, P:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [X:S, Y:S, Z:S], UV-RActive: [X:S, Y:S, Z:S], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [X:S], UV-RActive: [X:S], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [X:S], UV-RActive: [X:S], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [I:S, P:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x7, x8, x9, x10, x11, x12, x13, x14 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x7, x10, x11, x12], Y:S: [x8], Z:S: [x9], I:S: [x13], P:S: [x14] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: __(__(x7:S,x8:S),x9:S) -> __(x7:S,__(x8:S,x9:S)), id: 1, possubterms: __(__(x7:S,x8:S),x9:S)->[], __(x7:S,x8:S)->[1]) 0.001/0.001 (rule: __(nil,x10:S) -> x10:S, id: 2, possubterms: __(nil,x10:S)->[], nil->[1]) 0.001/0.001 (rule: __(x11:S,nil) -> x11:S, id: 3, possubterms: __(x11:S,nil)->[], nil->[2]) 0.001/0.001 (rule: and(tt,x12:S) -> x12:S, id: 4, possubterms: and(tt,x12:S)->[], tt->[1]) 0.001/0.001 (rule: isNePal(__(x13:S,__(x14:S,x13:S))) -> tt, id: 5, possubterms: isNePal(__(x13:S,__(x14:S,x13:S)))->[], __(x13:S,__(x14:S,x13:S))->[1], __(x14:S,x13:S)->[1, 2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R1 unifies with R1 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))) 0.001/0.001 (R1 unifies with R2 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) 0.001/0.001 (R1 unifies with R3 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) 0.001/0.001 (R3 unifies with R1 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))) 0.001/0.001 (R3 unifies with R2 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) 0.001/0.001 (R5 unifies with R1 at p: [1], l: isNePal(__(x13:S,__(x14:S,x13:S))), lp: __(x13:S,__(x14:S,x13:S)), sig: {Z:S:S -> __(x14:S,__(X:S:S,Y:S:S)),x13:S -> __(X:S:S,Y:S:S)}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: tt, r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.001/0.001 (R5 unifies with R2 at p: [1], l: isNePal(__(x13:S,__(x14:S,x13:S))), lp: __(x13:S,__(x14:S,x13:S)), sig: {X:S:S -> __(x14:S,nil),x13:S -> nil}, l': __(nil,X:S:S), r: tt, r': X:S:S) 0.001/0.001 (R5 unifies with R1 at p: [1,2], l: isNePal(__(x13:S,__(x14:S,x13:S))), lp: __(x14:S,x13:S), sig: {x13:S -> Z:S:S,x14:S -> __(X:S:S,Y:S:S)}, l': __(__(X:S:S,Y:S:S),Z:S:S), r: tt, r': __(X:S:S,__(Y:S:S,Z:S:S))) 0.001/0.001 (R5 unifies with R2 at p: [1,2], l: isNePal(__(x13:S,__(x14:S,x13:S))), lp: __(x14:S,x13:S), sig: {x13:S -> X:S:S,x14:S -> nil}, l': __(nil,X:S:S), r: tt, r': X:S:S) 0.001/0.001 (R5 unifies with R3 at p: [1,2], l: isNePal(__(x13:S,__(x14:S,x13:S))), lp: __(x14:S,x13:S), sig: {x13:S -> nil,x14:S -> X:S:S}, l': __(X:S:S,nil), r: tt, r': X:S:S) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 <__(X:S:S,Z:S:S),__(nil,__(X:S:S,Z:S:S))> => Not trivial, Not overlay, NW0, N1 0.001/0.001 => Not trivial, Not overlay, NW0, N2 0.001/0.001 <__(__(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, N3 0.001/0.001 => Not trivial, Not overlay, NW0, N4 0.001/0.001 <__(X:S:S,__(Y:S:S,nil)),__(X:S:S,Y:S:S)> => Not trivial, Overlay, NW0, N5 0.001/0.001 => Trivial, Overlay, NW0, N6 0.001/0.001 => Not trivial, Not overlay, NW0, N7 0.001/0.001 => Not trivial, Not overlay, NW0, N8 0.001/0.001 => Not trivial, Not overlay, NW0, N9 0.001/0.001 <__(X:S:S,Z:S:S),__(X:S:S,__(nil,Z:S:S))> => Not trivial, Not 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 CS-TRS, Left-homogeneous u-replacing variables 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 Different Normal CP Terms Processor: 0.001/0.001 => Not trivial, Not overlay, NW0, N2, Normal and not trivial cp 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 50%CPU (0avgtext+0avgdata 8908maxresident)k 0.001/0.001 8inputs+0outputs (0major+736minor)pagefaults 0swaps