0.004/0.004 YES 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 0.004/0.004 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 Confluence Problem: 0.004/0.004 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S) 0.004/0.004 (STRATEGY CONTEXTSENSITIVE 0.004/0.004 (div 1 2) 0.004/0.004 (gt 1 2) 0.004/0.004 (if 1) 0.004/0.004 (minus) 0.004/0.004 (p 1) 0.004/0.004 (fSNonEmpty) 0.004/0.004 (ffalse) 0.004/0.004 (ftrue) 0.004/0.004 (num0) 0.004/0.004 (s) 0.004/0.004 ) 0.004/0.004 (RULES 0.004/0.004 div(num0,s(Y:S:S)) -> num0 0.004/0.004 div(s(X:S:S),s(Y:S:S)) -> s(div(minus(X:S:S,Y:S:S),s(Y:S:S))) 0.004/0.004 gt(num0,Y:S:S) -> ffalse 0.004/0.004 gt(s(X:S:S),num0) -> ftrue 0.004/0.004 gt(s(X:S:S),s(Y:S:S)) -> gt(X:S:S,Y:S:S) 0.004/0.004 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.004/0.004 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.004/0.004 minus(X:S:S,Y:S:S) -> if(gt(Y:S:S,num0),minus(p(X:S:S),p(Y:S:S)),X:S:S) 0.004/0.004 p(num0) -> num0 0.004/0.004 p(s(X:S:S)) -> X:S:S 0.004/0.004 ) 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 0.004/0.004 CleanTRS Processor: 0.004/0.004 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 Confluence Problem: 0.004/0.004 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S) 0.004/0.004 (STRATEGY CONTEXTSENSITIVE 0.004/0.004 (div 1 2) 0.004/0.004 (gt 1 2) 0.004/0.004 (if 1) 0.004/0.004 (minus) 0.004/0.004 (p 1) 0.004/0.004 (fSNonEmpty) 0.004/0.004 (ffalse) 0.004/0.004 (ftrue) 0.004/0.004 (num0) 0.004/0.004 (s) 0.004/0.004 ) 0.004/0.004 (RULES 0.004/0.004 div(num0,s(Y:S:S)) -> num0 0.004/0.004 div(s(X:S:S),s(Y:S:S)) -> s(div(minus(X:S:S,Y:S:S),s(Y:S:S))) 0.004/0.004 gt(num0,Y:S:S) -> ffalse 0.004/0.004 gt(s(X:S:S),num0) -> ftrue 0.004/0.004 gt(s(X:S:S),s(Y:S:S)) -> gt(X:S:S,Y:S:S) 0.004/0.004 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.004/0.004 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.004/0.004 minus(X:S:S,Y:S:S) -> if(gt(Y:S:S,num0),minus(p(X:S:S),p(Y:S:S)),X:S:S) 0.004/0.004 p(num0) -> num0 0.004/0.004 p(s(X:S:S)) -> X:S:S 0.004/0.004 ) 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 0.004/0.004 Modular Confluence Combinations Decomposition Processor: 0.004/0.004 It is a CTRS -> No modular confluence 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 Left-Homogeneous u-Replacing Variables Processor: 0.004/0.004 R satisfies LHRV condition 0.004/0.004 0.004/0.004 Problem 1: 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 Confluence Problem: 0.004/0.004 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S) 0.004/0.004 (STRATEGY CONTEXTSENSITIVE 0.004/0.004 (div 1 2) 0.004/0.004 (gt 1 2) 0.004/0.004 (if 1) 0.004/0.004 (minus) 0.004/0.004 (p 1) 0.004/0.004 (fSNonEmpty) 0.004/0.004 (ffalse) 0.004/0.004 (ftrue) 0.004/0.004 (num0) 0.004/0.004 (s) 0.004/0.004 ) 0.004/0.004 (RULES 0.004/0.004 div(num0,s(Y:S:S)) -> num0 0.004/0.004 div(s(X:S:S),s(Y:S:S)) -> s(div(minus(X:S:S,Y:S:S),s(Y:S:S))) 0.004/0.004 gt(num0,Y:S:S) -> ffalse 0.004/0.004 gt(s(X:S:S),num0) -> ftrue 0.004/0.004 gt(s(X:S:S),s(Y:S:S)) -> gt(X:S:S,Y:S:S) 0.004/0.004 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.004/0.004 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.004/0.004 minus(X:S:S,Y:S:S) -> if(gt(Y:S:S,num0),minus(p(X:S:S),p(Y:S:S)),X:S:S) 0.004/0.004 p(num0) -> num0 0.004/0.004 p(s(X:S:S)) -> X:S:S 0.004/0.004 ) 0.004/0.004 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.004/0.004 0.004/0.004 Huet Levy Processor: 0.004/0.004 -> Rules: 0.004/0.004 div(num0,s(Y:S:S)) -> num0 0.004/0.004 div(s(X:S:S),s(Y:S:S)) -> s(div(minus(X:S:S,Y:S:S),s(Y:S:S))) 0.004/0.004 gt(num0,Y:S:S) -> ffalse 0.004/0.004 gt(s(X:S:S),num0) -> ftrue 0.004/0.004 gt(s(X:S:S),s(Y:S:S)) -> gt(X:S:S,Y:S:S) 0.004/0.004 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.004/0.004 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.004/0.004 minus(X:S:S,Y:S:S) -> if(gt(Y:S:S,num0),minus(p(X:S:S),p(Y:S:S)),X:S:S) 0.004/0.004 p(num0) -> num0 0.004/0.004 p(s(X:S:S)) -> X:S:S 0.004/0.004 -> Vars: 0.004/0.004 Y:S, X:S, Y:S, Y:S, X:S, X:S, Y:S, X:S, Y:S, X:S, Y:S, X:S, Y:S, X:S 0.004/0.004 -> UVars: 0.004/0.004 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y:S], UV-RFrozen: []) 0.004/0.004 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.004/0.004 (UV-RuleId: 3, UV-LActive: [Y:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.004/0.004 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: []) 0.004/0.004 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [X:S, Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.004/0.004 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.004/0.004 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.004/0.004 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.004/0.004 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.004/0.004 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.004/0.004 -> FVars: 0.004/0.004 x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17 0.004/0.004 -> PVars: 0.004/0.004 Y:S: [x4, x6, x7, x10, x12, x14, x16], X:S: [x5, x8, x9, x11, x13, x15, x17] 0.004/0.004 0.004/0.004 -> Rlps: 0.004/0.004 (rule: div(num0,s(x4:S)) -> num0, id: 1, possubterms: div(num0,s(x4:S))->[], num0->[1], s(x4:S)->[2]) 0.004/0.004 (rule: div(s(x5:S),s(x6:S)) -> s(div(minus(x5:S,x6:S),s(x6:S))), id: 2, possubterms: div(s(x5:S),s(x6:S))->[], s(x5:S)->[1], s(x6:S)->[2]) 0.004/0.004 (rule: gt(num0,x7:S) -> ffalse, id: 3, possubterms: gt(num0,x7:S)->[], num0->[1]) 0.004/0.004 (rule: gt(s(x8:S),num0) -> ftrue, id: 4, possubterms: gt(s(x8:S),num0)->[], s(x8:S)->[1], num0->[2]) 0.004/0.004 (rule: gt(s(x9:S),s(x10:S)) -> gt(x9:S,x10:S), id: 5, possubterms: gt(s(x9:S),s(x10:S))->[], s(x9:S)->[1], s(x10:S)->[2]) 0.004/0.004 (rule: if(ffalse,x11:S,x12:S) -> x12:S, id: 6, possubterms: if(ffalse,x11:S,x12:S)->[], ffalse->[1]) 0.004/0.004 (rule: if(ftrue,x13:S,x14:S) -> x13:S, id: 7, possubterms: if(ftrue,x13:S,x14:S)->[], ftrue->[1]) 0.004/0.004 (rule: minus(x15:S,x16:S) -> if(gt(x16:S,num0),minus(p(x15:S),p(x16:S)),x15:S), id: 8, possubterms: minus(x15:S,x16:S)->[]) 0.004/0.004 (rule: p(num0) -> num0, id: 9, possubterms: p(num0)->[], num0->[1]) 0.004/0.004 (rule: p(s(x17:S)) -> x17:S, id: 10, possubterms: p(s(x17:S))->[], s(x17:S)->[1]) 0.004/0.004 0.004/0.004 -> Unifications: 0.004/0.004 0.004/0.004 0.004/0.004 -> Critical pairs info: 0.004/0.004 0.004/0.004 0.004/0.004 -> Problem conclusions: 0.004/0.004 Left linear, Not right linear, Not linear 0.004/0.004 Weakly orthogonal, Almost orthogonal, Orthogonal 0.004/0.004 Huet-Levy confluent, Not Newman confluent 0.004/0.004 R is a CS-TRS, Left-homogeneous u-replacing variables 0.004/0.004 0.004/0.004 0.004/0.004 The problem is joinable. 0.004/0.004 0.00user 0.01system 0:00.04elapsed 34%CPU (0avgtext+0avgdata 8172maxresident)k 0.004/0.004 11312inputs+0outputs (45major+666minor)pagefaults 0swaps