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 X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (div 1 2) 0.001/0.001 (geq 1 2) 0.001/0.001 (if 1) 0.001/0.001 (minus 1 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 div(num0,s(Y:S:S)) -> num0 0.001/0.001 div(s(X:S:S),s(Y:S:S)) -> if(geq(X:S:S,Y:S:S),s(div(minus(X:S:S,Y:S:S),s(Y:S:S))),num0) 0.001/0.001 geq(num0,s(Y:S:S)) -> ffalse 0.001/0.001 geq(s(X:S:S),s(Y:S:S)) -> geq(X:S:S,Y:S:S) 0.001/0.001 geq(X:S:S,num0) -> ftrue 0.001/0.001 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.001/0.001 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.001/0.001 minus(num0,Y:S:S) -> num0 0.001/0.001 minus(s(X:S:S),s(Y:S:S)) -> minus(X:S:S,Y: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 X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (div 1 2) 0.001/0.001 (geq 1 2) 0.001/0.001 (if 1) 0.001/0.001 (minus 1 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 div(num0,s(Y:S:S)) -> num0 0.001/0.001 div(s(X:S:S),s(Y:S:S)) -> if(geq(X:S:S,Y:S:S),s(div(minus(X:S:S,Y:S:S),s(Y:S:S))),num0) 0.001/0.001 geq(num0,s(Y:S:S)) -> ffalse 0.001/0.001 geq(s(X:S:S),s(Y:S:S)) -> geq(X:S:S,Y:S:S) 0.001/0.001 geq(X:S:S,num0) -> ftrue 0.001/0.001 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.001/0.001 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.001/0.001 minus(num0,Y:S:S) -> num0 0.001/0.001 minus(s(X:S:S),s(Y:S:S)) -> minus(X:S:S,Y: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 X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (div 1 2) 0.001/0.001 (geq 1 2) 0.001/0.001 (if 1) 0.001/0.001 (minus 1 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (ffalse) 0.001/0.001 (ftrue) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 div(num0,s(Y:S:S)) -> num0 0.001/0.001 div(s(X:S:S),s(Y:S:S)) -> if(geq(X:S:S,Y:S:S),s(div(minus(X:S:S,Y:S:S),s(Y:S:S))),num0) 0.001/0.001 geq(num0,s(Y:S:S)) -> ffalse 0.001/0.001 geq(s(X:S:S),s(Y:S:S)) -> geq(X:S:S,Y:S:S) 0.001/0.001 geq(X:S:S,num0) -> ftrue 0.001/0.001 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.001/0.001 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.001/0.001 minus(num0,Y:S:S) -> num0 0.001/0.001 minus(s(X:S:S),s(Y:S:S)) -> minus(X:S:S,Y: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 div(num0,s(Y:S:S)) -> num0 0.001/0.001 div(s(X:S:S),s(Y:S:S)) -> if(geq(X:S:S,Y:S:S),s(div(minus(X:S:S,Y:S:S),s(Y:S:S))),num0) 0.001/0.001 geq(num0,s(Y:S:S)) -> ffalse 0.001/0.001 geq(s(X:S:S),s(Y:S:S)) -> geq(X:S:S,Y:S:S) 0.001/0.001 geq(X:S:S,num0) -> ftrue 0.001/0.001 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.001/0.001 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.001/0.001 minus(num0,Y:S:S) -> num0 0.001/0.001 minus(s(X:S:S),s(Y:S:S)) -> minus(X:S:S,Y:S:S) 0.001/0.001 -> Vars: 0.001/0.001 Y:S, X:S, Y:S, Y:S, X:S, Y:S, X:S, X:S, Y:S, X:S, Y:S, Y:S, X:S, Y:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [X:S, Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [X:S, Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [X:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [Y:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [X:S, Y:S], UV-LFrozen: [X:S, Y:S], 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 Y:S: [x4, x6, x7, x9, x12, x14, x15, x17], X:S: [x5, x8, x10, x11, x13, x16] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: div(num0,s(x4:S)) -> num0, id: 1, possubterms: div(num0,s(x4:S))->[], num0->[1], s(x4:S)->[2]) 0.001/0.001 (rule: div(s(x5:S),s(x6:S)) -> if(geq(x5:S,x6:S),s(div(minus(x5:S,x6:S),s(x6:S))),num0), id: 2, possubterms: div(s(x5:S),s(x6:S))->[], s(x5:S)->[1], s(x6:S)->[2]) 0.001/0.001 (rule: geq(num0,s(x7:S)) -> ffalse, id: 3, possubterms: geq(num0,s(x7:S))->[], num0->[1], s(x7:S)->[2]) 0.001/0.001 (rule: geq(s(x8:S),s(x9:S)) -> geq(x8:S,x9:S), id: 4, possubterms: geq(s(x8:S),s(x9:S))->[], s(x8:S)->[1], s(x9:S)->[2]) 0.001/0.001 (rule: geq(x10:S,num0) -> ftrue, id: 5, possubterms: geq(x10:S,num0)->[], num0->[2]) 0.001/0.001 (rule: if(ffalse,x11:S,x12:S) -> x12:S, id: 6, possubterms: if(ffalse,x11:S,x12:S)->[], ffalse->[1]) 0.001/0.001 (rule: if(ftrue,x13:S,x14:S) -> x13:S, id: 7, possubterms: if(ftrue,x13:S,x14:S)->[], ftrue->[1]) 0.001/0.001 (rule: minus(num0,x15:S) -> num0, id: 8, possubterms: minus(num0,x15:S)->[], num0->[1]) 0.001/0.001 (rule: minus(s(x16:S),s(x17:S)) -> minus(x16:S,x17:S), id: 9, possubterms: minus(s(x16:S),s(x17:S))->[], s(x16:S)->[1], s(x17: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 50%CPU (0avgtext+0avgdata 8488maxresident)k 0.001/0.001 8inputs+0outputs (0major+686minor)pagefaults 0swaps