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 (adx 1) 0.001/0.001 (hd 1) 0.001/0.001 (incr 1) 0.001/0.001 (nats) 0.001/0.001 (tl 1) 0.001/0.001 (zeros) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 adx(cons(X:S:S,Y:S:S)) -> incr(cons(X:S:S,adx(Y:S:S))) 0.001/0.001 hd(cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 incr(cons(X:S:S,Y:S:S)) -> cons(s(X:S:S),incr(Y:S:S)) 0.001/0.001 nats -> adx(zeros) 0.001/0.001 tl(cons(X:S:S,Y:S:S)) -> Y:S:S 0.001/0.001 zeros -> cons(num0,zeros) 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 (adx 1) 0.001/0.001 (hd 1) 0.001/0.001 (incr 1) 0.001/0.001 (nats) 0.001/0.001 (tl 1) 0.001/0.001 (zeros) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 adx(cons(X:S:S,Y:S:S)) -> incr(cons(X:S:S,adx(Y:S:S))) 0.001/0.001 hd(cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 incr(cons(X:S:S,Y:S:S)) -> cons(s(X:S:S),incr(Y:S:S)) 0.001/0.001 nats -> adx(zeros) 0.001/0.001 tl(cons(X:S:S,Y:S:S)) -> Y:S:S 0.001/0.001 zeros -> cons(num0,zeros) 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 (adx 1) 0.001/0.001 (hd 1) 0.001/0.001 (incr 1) 0.001/0.001 (nats) 0.001/0.001 (tl 1) 0.001/0.001 (zeros) 0.001/0.001 (cons) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s 1) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 adx(cons(X:S:S,Y:S:S)) -> incr(cons(X:S:S,adx(Y:S:S))) 0.001/0.001 hd(cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 incr(cons(X:S:S,Y:S:S)) -> cons(s(X:S:S),incr(Y:S:S)) 0.001/0.001 nats -> adx(zeros) 0.001/0.001 tl(cons(X:S:S,Y:S:S)) -> Y:S:S 0.001/0.001 zeros -> cons(num0,zeros) 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 adx(cons(X:S:S,Y:S:S)) -> incr(cons(X:S:S,adx(Y:S:S))) 0.001/0.001 hd(cons(X:S:S,Y:S:S)) -> X:S:S 0.001/0.001 incr(cons(X:S:S,Y:S:S)) -> cons(s(X:S:S),incr(Y:S:S)) 0.001/0.001 nats -> adx(zeros) 0.001/0.001 tl(cons(X:S:S,Y:S:S)) -> Y:S:S 0.001/0.001 zeros -> cons(num0,zeros) 0.001/0.001 -> Vars: 0.001/0.001 X:S, Y:S, X:S, Y:S, X: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: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x4, x5, x6, x7, x8, x9, x10, x11 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x4, x6, x8, x10], Y:S: [x5, x7, x9, x11] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: adx(cons(x4:S,x5:S)) -> incr(cons(x4:S,adx(x5:S))), id: 1, possubterms: adx(cons(x4:S,x5:S))->[], cons(x4:S,x5:S)->[1]) 0.001/0.001 (rule: hd(cons(x6:S,x7:S)) -> x6:S, id: 2, possubterms: hd(cons(x6:S,x7:S))->[], cons(x6:S,x7:S)->[1]) 0.001/0.001 (rule: incr(cons(x8:S,x9:S)) -> cons(s(x8:S),incr(x9:S)), id: 3, possubterms: incr(cons(x8:S,x9:S))->[], cons(x8:S,x9:S)->[1]) 0.001/0.001 (rule: nats -> adx(zeros), id: 4, possubterms: nats->[]) 0.001/0.001 (rule: tl(cons(x10:S,x11:S)) -> x11:S, id: 5, possubterms: tl(cons(x10:S,x11:S))->[], cons(x10:S,x11:S)->[1]) 0.001/0.001 (rule: zeros -> cons(num0,zeros), id: 6, possubterms: zeros->[]) 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, Right linear, 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 41%CPU (0avgtext+0avgdata 8500maxresident)k 0.001/0.001 8inputs+0outputs (0major+686minor)pagefaults 0swaps