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 X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (filter 1 2) 0.001/0.001 (nats) 0.001/0.001 (sieve 1) 0.001/0.001 (zprimes) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 filter(cons(X:S:S,Y:S:S),num0,M:S:S) -> cons(num0,filter(Y:S:S,M:S:S,M:S:S)) 0.001/0.001 filter(cons(X:S:S,Y:S:S),s(N:S:S),M:S:S) -> cons(X:S:S,filter(Y:S:S,N:S:S,M:S:S)) 0.001/0.001 nats(N:S:S) -> cons(N:S:S,nats(s(N:S:S))) 0.001/0.001 sieve(cons(num0,Y:S:S)) -> cons(num0,sieve(Y:S:S)) 0.001/0.001 sieve(cons(s(N:S:S),Y:S:S)) -> cons(s(N:S:S),sieve(filter(Y:S:S,N:S:S,N:S:S))) 0.001/0.001 zprimes -> sieve(nats(s(s(num0)))) 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 X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (filter 1 2) 0.001/0.001 (nats) 0.001/0.001 (sieve 1) 0.001/0.001 (zprimes) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 filter(cons(X:S:S,Y:S:S),num0,M:S:S) -> cons(num0,filter(Y:S:S,M:S:S,M:S:S)) 0.001/0.001 filter(cons(X:S:S,Y:S:S),s(N:S:S),M:S:S) -> cons(X:S:S,filter(Y:S:S,N:S:S,M:S:S)) 0.001/0.001 nats(N:S:S) -> cons(N:S:S,nats(s(N:S:S))) 0.001/0.001 sieve(cons(num0,Y:S:S)) -> cons(num0,sieve(Y:S:S)) 0.001/0.001 sieve(cons(s(N:S:S),Y:S:S)) -> cons(s(N:S:S),sieve(filter(Y:S:S,N:S:S,N:S:S))) 0.001/0.001 zprimes -> sieve(nats(s(s(num0)))) 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 X:S:S Y:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (filter 1 2) 0.001/0.001 (nats) 0.001/0.001 (sieve 1) 0.001/0.001 (zprimes) 0.001/0.001 (cons 1) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 filter(cons(X:S:S,Y:S:S),num0,M:S:S) -> cons(num0,filter(Y:S:S,M:S:S,M:S:S)) 0.001/0.001 filter(cons(X:S:S,Y:S:S),s(N:S:S),M:S:S) -> cons(X:S:S,filter(Y:S:S,N:S:S,M:S:S)) 0.001/0.001 nats(N:S:S) -> cons(N:S:S,nats(s(N:S:S))) 0.001/0.001 sieve(cons(num0,Y:S:S)) -> cons(num0,sieve(Y:S:S)) 0.001/0.001 sieve(cons(s(N:S:S),Y:S:S)) -> cons(s(N:S:S),sieve(filter(Y:S:S,N:S:S,N:S:S))) 0.001/0.001 zprimes -> sieve(nats(s(s(num0)))) 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 filter(cons(X:S:S,Y:S:S),num0,M:S:S) -> cons(num0,filter(Y:S:S,M:S:S,M:S:S)) 0.001/0.001 filter(cons(X:S:S,Y:S:S),s(N:S:S),M:S:S) -> cons(X:S:S,filter(Y:S:S,N:S:S,M:S:S)) 0.001/0.001 nats(N:S:S) -> cons(N:S:S,nats(s(N:S:S))) 0.001/0.001 sieve(cons(num0,Y:S:S)) -> cons(num0,sieve(Y:S:S)) 0.001/0.001 sieve(cons(s(N:S:S),Y:S:S)) -> cons(s(N:S:S),sieve(filter(Y:S:S,N:S:S,N:S:S))) 0.001/0.001 zprimes -> sieve(nats(s(s(num0)))) 0.001/0.001 -> Vars: 0.001/0.001 M:S, X:S, Y:S, M:S, N:S, X:S, Y:S, N:S, Y:S, N:S, Y:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [X:S], UV-RActive: [], UV-LFrozen: [M:S, Y:S], UV-RFrozen: [M:S, Y:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [X:S], UV-RActive: [X:S], UV-LFrozen: [M:S, N:S, Y:S], UV-RFrozen: [M:S, N:S, Y:S]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y:S], UV-RFrozen: [Y:S]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, Y:S], UV-RFrozen: [N:S, Y:S]) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 -> FVars: 0.001/0.001 x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16 0.001/0.001 -> PVars: 0.001/0.001 M:S: [x6, x9], X:S: [x7, x11], Y:S: [x8, x12, x14, x16], N:S: [x10, x13, x15] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: filter(cons(x7:S,x8:S),num0,x6:S) -> cons(num0,filter(x8:S,x6:S,x6:S)), id: 1, possubterms: filter(cons(x7:S,x8:S),num0,x6:S)->[], cons(x7:S,x8:S)->[1], num0->[2]) 0.001/0.001 (rule: filter(cons(x11:S,x12:S),s(x10:S),x9:S) -> cons(x11:S,filter(x12:S,x10:S,x9:S)), id: 2, possubterms: filter(cons(x11:S,x12:S),s(x10:S),x9:S)->[], cons(x11:S,x12:S)->[1], s(x10:S)->[2]) 0.001/0.001 (rule: nats(x13:S) -> cons(x13:S,nats(s(x13:S))), id: 3, possubterms: nats(x13:S)->[]) 0.001/0.001 (rule: sieve(cons(num0,x14:S)) -> cons(num0,sieve(x14:S)), id: 4, possubterms: sieve(cons(num0,x14:S))->[], cons(num0,x14:S)->[1], num0->[1, 1]) 0.001/0.001 (rule: sieve(cons(s(x15:S),x16:S)) -> cons(s(x15:S),sieve(filter(x16:S,x15:S,x15:S))), id: 5, possubterms: sieve(cons(s(x15:S),x16:S))->[], cons(s(x15:S),x16:S)->[1], s(x15:S)->[1, 1]) 0.001/0.001 (rule: zprimes -> sieve(nats(s(s(num0)))), id: 6, possubterms: zprimes->[]) 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 58%CPU (0avgtext+0avgdata 8672maxresident)k 0.001/0.001 8inputs+0outputs (0major+689minor)pagefaults 0swaps