0.001/0.001 YES 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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1) 0.001/0.001 (and 1) 0.001/0.001 (first 1 2) 0.001/0.001 (from) 0.001/0.001 (if 1) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 and(false,Y:S) -> false 0.001/0.001 and(true,X:S) -> X:S 0.001/0.001 first(0,X:S) -> nil 0.001/0.001 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 if(false,X:S,Y:S) -> Y:S 0.001/0.001 if(true,X:S,Y:S) -> X: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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1) 0.001/0.001 (and 1) 0.001/0.001 (first 1 2) 0.001/0.001 (from) 0.001/0.001 (if 1) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 and(false,Y:S) -> false 0.001/0.001 and(true,X:S) -> X:S 0.001/0.001 first(0,X:S) -> nil 0.001/0.001 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 if(false,X:S,Y:S) -> Y:S 0.001/0.001 if(true,X:S,Y:S) -> X: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 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 X:S Y:S Z:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (add 1) 0.001/0.001 (and 1) 0.001/0.001 (first 1 2) 0.001/0.001 (from) 0.001/0.001 (if 1) 0.001/0.001 (0) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (false) 0.001/0.001 (nil) 0.001/0.001 (s) 0.001/0.001 (true) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 and(false,Y:S) -> false 0.001/0.001 and(true,X:S) -> X:S 0.001/0.001 first(0,X:S) -> nil 0.001/0.001 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 if(false,X:S,Y:S) -> Y:S 0.001/0.001 if(true,X:S,Y:S) -> X:S 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 add(0,X:S) -> X:S 0.001/0.001 add(s(X:S),Y:S) -> s(add(X:S,Y:S)) 0.001/0.001 and(false,Y:S) -> false 0.001/0.001 and(true,X:S) -> X:S 0.001/0.001 first(0,X:S) -> nil 0.001/0.001 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S)) 0.001/0.001 from(X:S) -> cons(X:S,from(s(X:S))) 0.001/0.001 if(false,X:S,Y:S) -> Y:S 0.001/0.001 if(true,X:S,Y:S) -> X:S 0.001/0.001 -> Vars: 0.001/0.001 X, X, Y, Y, X, X, X, Y, Z, X, X, Y, X, Y 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: [X, Y]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [X], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y, Z], UV-RFrozen: [X, Y, Z]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X], UV-RFrozen: [X]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [Y], UV-LFrozen: [X, Y], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X, Y], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17 0.001/0.001 -> PVars: 0.001/0.001 X: [x4, x5, x8, x9, x10, x13, x14, x16], Y: [x6, x7, x11, x15, x17], Z: [x12] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: add(0,x4:S) -> x4:S, id: 1, possubterms: add(0,x4:S)->[], 0->[1]) 0.001/0.001 (rule: add(s(x5:S),x6:S) -> s(add(x5:S,x6:S)), id: 2, possubterms: add(s(x5:S),x6:S)->[], s(x5:S)->[1]) 0.001/0.001 (rule: and(false,x7:S) -> false, id: 3, possubterms: and(false,x7:S)->[], false->[1]) 0.001/0.001 (rule: and(true,x8:S) -> x8:S, id: 4, possubterms: and(true,x8:S)->[], true->[1]) 0.001/0.001 (rule: first(0,x9:S) -> nil, id: 5, possubterms: first(0,x9:S)->[], 0->[1]) 0.001/0.001 (rule: first(s(x10:S),cons(x11:S,x12:S)) -> cons(x11:S,first(x10:S,x12:S)), id: 6, possubterms: first(s(x10:S),cons(x11:S,x12:S))->[], s(x10:S)->[1], cons(x11:S,x12:S)->[2]) 0.001/0.001 (rule: from(x13:S) -> cons(x13:S,from(s(x13:S))), id: 7, possubterms: from(x13:S)->[]) 0.001/0.001 (rule: if(false,x14:S,x15:S) -> x15:S, id: 8, possubterms: if(false,x14:S,x15:S)->[], false->[1]) 0.001/0.001 (rule: if(true,x16:S,x17:S) -> x16:S, id: 9, possubterms: if(true,x16:S,x17:S)->[], true->[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 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 Weakly orthogonal, Almost orthogonal, Orthogonal 0.001/0.001 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 The problem is joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 61%CPU (0avgtext+0avgdata 8372maxresident)k 0.001/0.001 0inputs+0outputs (0major+685minor)pagefaults 0swaps