0.002/0.002 NO 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S Z:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (filter 1 2) 0.002/0.002 (from) 0.002/0.002 (head 1) 0.002/0.002 (if 1) 0.002/0.002 (primes) 0.002/0.002 (sieve 1) 0.002/0.002 (tail 1) 0.002/0.002 (cons) 0.002/0.002 (divides 1 2) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (ffalse) 0.002/0.002 (ftrue) 0.002/0.002 (num0) 0.002/0.002 (s 1) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)) -> if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S)))) 0.002/0.002 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.002/0.002 head(cons(X:S:S,Y:S:S)) -> X:S:S 0.002/0.002 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.002/0.002 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.002/0.002 primes -> sieve(from(s(s(num0)))) 0.002/0.002 sieve(cons(X:S:S,Y:S:S)) -> cons(X:S:S,filter(X:S:S,sieve(Y:S:S))) 0.002/0.002 tail(cons(X:S:S,Y:S:S)) -> Y:S:S 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 CleanTRS Processor: 0.002/0.002 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S Z:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (filter 1 2) 0.002/0.002 (from) 0.002/0.002 (head 1) 0.002/0.002 (if 1) 0.002/0.002 (primes) 0.002/0.002 (sieve 1) 0.002/0.002 (tail 1) 0.002/0.002 (cons) 0.002/0.002 (divides 1 2) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (ffalse) 0.002/0.002 (ftrue) 0.002/0.002 (num0) 0.002/0.002 (s 1) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)) -> if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S)))) 0.002/0.002 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.002/0.002 head(cons(X:S:S,Y:S:S)) -> X:S:S 0.002/0.002 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.002/0.002 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.002/0.002 primes -> sieve(from(s(s(num0)))) 0.002/0.002 sieve(cons(X:S:S,Y:S:S)) -> cons(X:S:S,filter(X:S:S,sieve(Y:S:S))) 0.002/0.002 tail(cons(X:S:S,Y:S:S)) -> Y:S:S 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 Modular Confluence Combinations Decomposition Processor: 0.002/0.002 It is a CTRS -> No modular confluence 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 CS-TRS Processor: 0.002/0.002 R is a CS-TRS 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S Z:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (filter 1 2) 0.002/0.002 (from) 0.002/0.002 (head 1) 0.002/0.002 (if 1) 0.002/0.002 (primes) 0.002/0.002 (sieve 1) 0.002/0.002 (tail 1) 0.002/0.002 (cons) 0.002/0.002 (divides 1 2) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (ffalse) 0.002/0.002 (ftrue) 0.002/0.002 (num0) 0.002/0.002 (s 1) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)) -> if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S)))) 0.002/0.002 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.002/0.002 head(cons(X:S:S,Y:S:S)) -> X:S:S 0.002/0.002 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.002/0.002 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.002/0.002 primes -> sieve(from(s(s(num0)))) 0.002/0.002 sieve(cons(X:S:S,Y:S:S)) -> cons(X:S:S,filter(X:S:S,sieve(Y:S:S))) 0.002/0.002 tail(cons(X:S:S,Y:S:S)) -> Y:S:S 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 Extended u-Critical Pairs NonLHRV Processor [JLAMP21]: 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))) 0.002/0.002 Rule 1 (l' :-> r') => filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)) -> if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S)))) 0.002/0.002 Var => x5:S 0.002/0.002 Pos x5:S in l => [1,1,1] 0.002/0.002 Sigma => {x5:S -> filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S))} 0.002/0.002 s => if(divides(s(s(filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)))),x6:S),filter(s(s(filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)))),x7:S),cons(x6:S,filter(filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)),sieve(x6:S)))) 0.002/0.002 t => filter(s(s(if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S)))))),cons(x6:S,x7:S)) 0.002/0.002 NW => 0 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))) 0.002/0.002 Rule 2 (l' :-> r') => from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.002/0.002 Var => x5:S 0.002/0.002 Pos x5:S in l => [1,1,1] 0.002/0.002 Sigma => {x5:S -> from(X:S:S)} 0.002/0.002 s => if(divides(s(s(from(X:S:S))),x6:S),filter(s(s(from(X:S:S))),x7:S),cons(x6:S,filter(from(X:S:S),sieve(x6:S)))) 0.002/0.002 t => filter(s(s(cons(X:S:S,from(s(X:S:S))))),cons(x6:S,x7:S)) 0.002/0.002 NW => 0 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))) 0.002/0.002 Rule 3 (l' :-> r') => head(cons(X:S:S,Y:S:S)) -> X:S:S 0.002/0.002 Var => x5:S 0.002/0.002 Pos x5:S in l => [1,1,1] 0.002/0.002 Sigma => {x5:S -> head(cons(X:S:S,Y:S:S))} 0.002/0.002 s => if(divides(s(s(head(cons(X:S:S,Y:S:S)))),x6:S),filter(s(s(head(cons(X:S:S,Y:S:S)))),x7:S),cons(x6:S,filter(head(cons(X:S:S,Y:S:S)),sieve(x6:S)))) 0.002/0.002 t => filter(s(s(X:S:S)),cons(x6:S,x7:S)) 0.002/0.002 NW => 0 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))) 0.002/0.002 Rule 4 (l' :-> r') => if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.002/0.002 Var => x5:S 0.002/0.002 Pos x5:S in l => [1,1,1] 0.002/0.002 Sigma => {x5:S -> if(ffalse,X:S:S,Y:S:S)} 0.002/0.002 s => if(divides(s(s(if(ffalse,X:S:S,Y:S:S))),x6:S),filter(s(s(if(ffalse,X:S:S,Y:S:S))),x7:S),cons(x6:S,filter(if(ffalse,X:S:S,Y:S:S),sieve(x6:S)))) 0.002/0.002 t => filter(s(s(Y:S:S)),cons(x6:S,x7:S)) 0.002/0.002 NW => 0 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))) 0.002/0.002 Rule 5 (l' :-> r') => if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.002/0.002 Var => x5:S 0.002/0.002 Pos x5:S in l => [1,1,1] 0.002/0.002 Sigma => {x5:S -> if(ftrue,X:S:S,Y:S:S)} 0.002/0.002 s => if(divides(s(s(if(ftrue,X:S:S,Y:S:S))),x6:S),filter(s(s(if(ftrue,X:S:S,Y:S:S))),x7:S),cons(x6:S,filter(if(ftrue,X:S:S,Y:S:S),sieve(x6:S)))) 0.002/0.002 t => filter(s(s(X:S:S)),cons(x6:S,x7:S)) 0.002/0.002 NW => 0 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))) 0.002/0.002 Rule 6 (l' :-> r') => primes -> sieve(from(s(s(num0)))) 0.002/0.002 Var => x5:S 0.002/0.002 Pos x5:S in l => [1,1,1] 0.002/0.002 Sigma => {x5:S -> primes} 0.002/0.002 s => if(divides(s(s(primes)),x6:S),filter(s(s(primes)),x7:S),cons(x6:S,filter(primes,sieve(x6:S)))) 0.002/0.002 t => filter(s(s(sieve(from(s(s(num0)))))),cons(x6:S,x7:S)) 0.002/0.002 NW => 0 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))) 0.002/0.002 Rule 7 (l' :-> r') => sieve(cons(X:S:S,Y:S:S)) -> cons(X:S:S,filter(X:S:S,sieve(Y:S:S))) 0.002/0.002 Var => x5:S 0.002/0.002 Pos x5:S in l => [1,1,1] 0.002/0.002 Sigma => {x5:S -> sieve(cons(X:S:S,Y:S:S))} 0.002/0.002 s => if(divides(s(s(sieve(cons(X:S:S,Y:S:S)))),x6:S),filter(s(s(sieve(cons(X:S:S,Y:S:S)))),x7:S),cons(x6:S,filter(sieve(cons(X:S:S,Y:S:S)),sieve(x6:S)))) 0.002/0.002 t => filter(s(s(cons(X:S:S,filter(X:S:S,sieve(Y:S:S))))),cons(x6:S,x7:S)) 0.002/0.002 NW => 0 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))) 0.002/0.002 Rule 8 (l' :-> r') => tail(cons(X:S:S,Y:S:S)) -> Y:S:S 0.002/0.002 Var => x5:S 0.002/0.002 Pos x5:S in l => [1,1,1] 0.002/0.002 Sigma => {x5:S -> tail(cons(X:S:S,Y:S:S))} 0.002/0.002 s => if(divides(s(s(tail(cons(X:S:S,Y:S:S)))),x6:S),filter(s(s(tail(cons(X:S:S,Y:S:S)))),x7:S),cons(x6:S,filter(tail(cons(X:S:S,Y:S:S)),sieve(x6:S)))) 0.002/0.002 t => filter(s(s(Y:S:S)),cons(x6:S,x7:S)) 0.002/0.002 NW => 0 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S X:S:S Y:S:S Z:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (filter 1 2) 0.002/0.002 (from) 0.002/0.002 (head 1) 0.002/0.002 (if 1) 0.002/0.002 (primes) 0.002/0.002 (sieve 1) 0.002/0.002 (tail 1) 0.002/0.002 (cons) 0.002/0.002 (divides 1 2) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (ffalse) 0.002/0.002 (ftrue) 0.002/0.002 (num0) 0.002/0.002 (s 1) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)) -> if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S)))) 0.002/0.002 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.002/0.002 head(cons(X:S:S,Y:S:S)) -> X:S:S 0.002/0.002 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.002/0.002 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.002/0.002 primes -> sieve(from(s(s(num0)))) 0.002/0.002 sieve(cons(X:S:S,Y:S:S)) -> cons(X:S:S,filter(X:S:S,sieve(Y:S:S))) 0.002/0.002 tail(cons(X:S:S,Y:S:S)) -> Y:S:S 0.002/0.002 ) 0.002/0.002 Critical Pairs: 0.002/0.002 => Not trivial, Not overlay, NW0, N1 0.002/0.002 => Not trivial, Not overlay, NW0, N2 0.002/0.002 => Not trivial, Not overlay, NW0, N3 0.002/0.002 => Not trivial, Not overlay, NW0, N4 0.002/0.002 => Not trivial, Not overlay, NW0, N5 0.002/0.002 => Not trivial, Not overlay, NW0, N6 0.002/0.002 => Not trivial, Not overlay, NW0, N7 0.002/0.002 => Not trivial, Not overlay, NW0, N8 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 Huet Levy Processor: 0.002/0.002 -> Rules: 0.002/0.002 filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)) -> if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S)))) 0.002/0.002 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.002/0.002 head(cons(X:S:S,Y:S:S)) -> X:S:S 0.002/0.002 if(ffalse,X:S:S,Y:S:S) -> Y:S:S 0.002/0.002 if(ftrue,X:S:S,Y:S:S) -> X:S:S 0.002/0.002 primes -> sieve(from(s(s(num0)))) 0.002/0.002 sieve(cons(X:S:S,Y:S:S)) -> cons(X:S:S,filter(X:S:S,sieve(Y:S:S))) 0.002/0.002 tail(cons(X:S:S,Y:S:S)) -> Y:S:S 0.002/0.002 -> Vars: 0.002/0.002 X:S, Y:S, Z:S, X:S, X:S, Y:S, X:S, Y:S, X:S, Y:S, X:S, Y:S, X:S, Y:S 0.002/0.002 -> UVars: 0.002/0.002 (UV-RuleId: 1, UV-LActive: [X:S], UV-RActive: [X:S, Y:S], UV-LFrozen: [Y:S, Z:S], UV-RFrozen: [X:S, Y:S, Z:S]) 0.002/0.002 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 0.002/0.002 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.002/0.002 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: []) 0.002/0.002 -> FVars: 0.002/0.002 x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18 0.002/0.002 -> PVars: 0.002/0.002 X:S: [x5, x8, x9, x11, x13, x15, x17], Y:S: [x6, x10, x12, x14, x16, x18], Z:S: [x7] 0.002/0.002 0.002/0.002 -> Rlps: 0.002/0.002 (rule: filter(s(s(x5:S)),cons(x6:S,x7:S)) -> if(divides(s(s(x5:S)),x6:S),filter(s(s(x5:S)),x7:S),cons(x6:S,filter(x5:S,sieve(x6:S)))), id: 1, possubterms: filter(s(s(x5:S)),cons(x6:S,x7:S))->[], s(s(x5:S))->[1], s(x5:S)->[1, 1], cons(x6:S,x7:S)->[2]) 0.002/0.002 (rule: from(x8:S) -> cons(x8:S,from(s(x8:S))), id: 2, possubterms: from(x8:S)->[]) 0.002/0.002 (rule: head(cons(x9:S,x10:S)) -> x9:S, id: 3, possubterms: head(cons(x9:S,x10:S))->[], cons(x9:S,x10:S)->[1]) 0.002/0.002 (rule: if(ffalse,x11:S,x12:S) -> x12:S, id: 4, possubterms: if(ffalse,x11:S,x12:S)->[], ffalse->[1]) 0.002/0.002 (rule: if(ftrue,x13:S,x14:S) -> x13:S, id: 5, possubterms: if(ftrue,x13:S,x14:S)->[], ftrue->[1]) 0.002/0.002 (rule: primes -> sieve(from(s(s(num0)))), id: 6, possubterms: primes->[]) 0.002/0.002 (rule: sieve(cons(x15:S,x16:S)) -> cons(x15:S,filter(x15:S,sieve(x16:S))), id: 7, possubterms: sieve(cons(x15:S,x16:S))->[], cons(x15:S,x16:S)->[1]) 0.002/0.002 (rule: tail(cons(x17:S,x18:S)) -> x18:S, id: 8, possubterms: tail(cons(x17:S,x18:S))->[], cons(x17:S,x18:S)->[1]) 0.002/0.002 0.002/0.002 -> Unifications: 0.002/0.002 0.002/0.002 0.002/0.002 -> Critical pairs info: 0.002/0.002 => Not trivial, Not overlay, NW0, N1 0.002/0.002 => Not trivial, Not overlay, NW0, N2 0.002/0.002 => Not trivial, Not overlay, NW0, N3 0.002/0.002 => Not trivial, Not overlay, NW0, N4 0.002/0.002 => Not trivial, Not overlay, NW0, N5 0.002/0.002 => Not trivial, Not overlay, NW0, N6 0.002/0.002 => Not trivial, Not overlay, NW0, N7 0.002/0.002 => Not trivial, Not overlay, NW0, N8 0.002/0.002 0.002/0.002 -> Problem conclusions: 0.002/0.002 Left linear, Not right linear, Not linear 0.002/0.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.002/0.002 Not Huet-Levy confluent, Not Newman confluent 0.002/0.002 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 No Convergence Brute Force Processor: 0.002/0.002 -> Rewritings: 0.002/0.002 s: if(divides(s(s(head(cons(X:S:S,Y:S:S)))),Y:S:S),filter(s(s(head(cons(X:S:S,Y:S:S)))),Z:S:S),cons(Y:S:S,filter(head(cons(X:S:S,Y:S:S)),sieve(Y:S:S)))) 0.002/0.002 Nodes: [0,1] 0.002/0.002 Edges: [(0,1)] 0.002/0.002 ID: 0 => ('if(divides(s(s(head(cons(X:S:S,Y:S:S)))),Y:S:S),filter(s(s(head(cons(X:S:S,Y:S:S)))),Z:S:S),cons(Y:S:S,filter(head(cons(X:S:S,Y:S:S)),sieve(Y:S:S))))', D0) 0.002/0.002 ID: 1 => ('if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(head(cons(X:S:S,Y:S:S)))),Z:S:S),cons(Y:S:S,filter(head(cons(X:S:S,Y:S:S)),sieve(Y:S:S))))', D1, R3, P[1, 1, 1, 1], S{x9:S -> X:S:S, x10:S -> Y:S:S}), NR: 'X:S:S' 0.002/0.002 t: filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)) 0.002/0.002 Nodes: [0,1] 0.002/0.002 Edges: [(0,1)] 0.002/0.002 ID: 0 => ('filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S))', D0) 0.002/0.002 ID: 1 => ('if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S))))', D1, R1, P[], S{x5:S -> X:S:S, x6:S -> Y:S:S, x7:S -> Z:S:S}), NR: 'if(divides(s(s(X:S:S)),Y:S:S),filter(s(s(X:S:S)),Z:S:S),cons(Y:S:S,filter(X:S:S,sieve(Y:S:S))))' 0.002/0.002 if(divides(s(s(head(cons(X:S:S,Y:S:S)))),Y:S:S),filter(s(s(head(cons(X:S:S,Y:S:S)))),Z:S:S),cons(Y:S:S,filter(head(cons(X:S:S,Y:S:S)),sieve(Y:S:S)))) ->* no union *<- filter(s(s(X:S:S)),cons(Y:S:S,Z:S:S)) 0.002/0.002 "Not joinable" 0.002/0.002 0.002/0.002 The problem is not joinable. 0.002/0.002 0.01user 0.00system 0:00.02elapsed 69%CPU (0avgtext+0avgdata 11452maxresident)k 0.002/0.002 8inputs+0outputs (0major+1164minor)pagefaults 0swaps