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 v_NonEmpty:S:S M:S:S N:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt,M:S:S,N:S:S) -> U12(tt,M:S:S,N:S:S) 0.001/0.001 U12(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U21(tt,M:S:S,N:S:S) -> U22(tt,M:S:S,N:S:S) 0.001/0.001 U22(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 plus(N:S:S,num0) -> N:S:S 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U11(tt,M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> num0 0.001/0.001 x(N:S:S,s(M:S:S)) -> U21(tt,M:S:S,N:S: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 v_NonEmpty:S:S M:S:S N:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt,M:S:S,N:S:S) -> U12(tt,M:S:S,N:S:S) 0.001/0.001 U12(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U21(tt,M:S:S,N:S:S) -> U22(tt,M:S:S,N:S:S) 0.001/0.001 U22(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 plus(N:S:S,num0) -> N:S:S 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U11(tt,M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> num0 0.001/0.001 x(N:S:S,s(M:S:S)) -> U21(tt,M:S:S,N:S: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 v_NonEmpty:S:S M:S:S N:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U12 1) 0.001/0.001 (U21 1) 0.001/0.001 (U22 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt,M:S:S,N:S:S) -> U12(tt,M:S:S,N:S:S) 0.001/0.001 U12(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U21(tt,M:S:S,N:S:S) -> U22(tt,M:S:S,N:S:S) 0.001/0.001 U22(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 plus(N:S:S,num0) -> N:S:S 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U11(tt,M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> num0 0.001/0.001 x(N:S:S,s(M:S:S)) -> U21(tt,M:S:S,N:S: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 U11(tt,M:S:S,N:S:S) -> U12(tt,M:S:S,N:S:S) 0.001/0.001 U12(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U21(tt,M:S:S,N:S:S) -> U22(tt,M:S:S,N:S:S) 0.001/0.001 U22(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 plus(N:S:S,num0) -> N:S:S 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U11(tt,M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> num0 0.001/0.001 x(N:S:S,s(M:S:S)) -> U21(tt,M:S:S,N:S:S) 0.001/0.001 -> Vars: 0.001/0.001 M:S, N:S, M:S, N:S, M:S, N:S, M:S, N:S, N:S, M:S, N:S, N:S, M:S, N:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 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 M:S: [x4, x6, x8, x10, x13, x16], N:S: [x5, x7, x9, x11, x12, x14, x15, x17] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: U11(tt,x4:S,x5:S) -> U12(tt,x4:S,x5:S), id: 1, possubterms: U11(tt,x4:S,x5:S)->[], tt->[1]) 0.001/0.001 (rule: U12(tt,x6:S,x7:S) -> s(plus(x7:S,x6:S)), id: 2, possubterms: U12(tt,x6:S,x7:S)->[], tt->[1]) 0.001/0.001 (rule: U21(tt,x8:S,x9:S) -> U22(tt,x8:S,x9:S), id: 3, possubterms: U21(tt,x8:S,x9:S)->[], tt->[1]) 0.001/0.001 (rule: U22(tt,x10:S,x11:S) -> plus(x(x11:S,x10:S),x11:S), id: 4, possubterms: U22(tt,x10:S,x11:S)->[], tt->[1]) 0.001/0.001 (rule: plus(x12:S,num0) -> x12:S, id: 5, possubterms: plus(x12:S,num0)->[], num0->[2]) 0.001/0.001 (rule: plus(x14:S,s(x13:S)) -> U11(tt,x13:S,x14:S), id: 6, possubterms: plus(x14:S,s(x13:S))->[], s(x13:S)->[2]) 0.001/0.001 (rule: x(x15:S,num0) -> num0, id: 7, possubterms: x(x15:S,num0)->[], num0->[2]) 0.001/0.001 (rule: x(x17:S,s(x16:S)) -> U21(tt,x16:S,x17:S), id: 8, possubterms: x(x17:S,s(x16:S))->[], s(x16:S)->[2]) 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 33%CPU (0avgtext+0avgdata 8576maxresident)k 0.001/0.001 8inputs+0outputs (0major+688minor)pagefaults 0swaps