MAYBE 1090.57/297.40 MAYBE 1090.57/297.40 1090.57/297.40 We are left with following problem, upon which TcT provides the 1090.57/297.40 certificate MAYBE. 1090.57/297.40 1090.57/297.40 Strict Trs: 1090.57/297.40 { a__filter(X1, X2, X3) -> filter(X1, X2, X3) 1090.57/297.40 , a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)) 1090.57/297.40 , a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)) 1090.57/297.40 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1090.57/297.40 , mark(0()) -> 0() 1090.57/297.40 , mark(filter(X1, X2, X3)) -> 1090.57/297.40 a__filter(mark(X1), mark(X2), mark(X3)) 1090.57/297.40 , mark(s(X)) -> s(mark(X)) 1090.57/297.40 , mark(sieve(X)) -> a__sieve(mark(X)) 1090.57/297.40 , mark(nats(X)) -> a__nats(mark(X)) 1090.57/297.40 , mark(zprimes()) -> a__zprimes() 1090.57/297.40 , a__sieve(X) -> sieve(X) 1090.57/297.40 , a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)) 1090.57/297.40 , a__sieve(cons(s(N), Y)) -> 1090.57/297.40 cons(s(mark(N)), sieve(filter(Y, N, N))) 1090.57/297.40 , a__nats(N) -> cons(mark(N), nats(s(N))) 1090.57/297.40 , a__nats(X) -> nats(X) 1090.57/297.40 , a__zprimes() -> a__sieve(a__nats(s(s(0())))) 1090.57/297.40 , a__zprimes() -> zprimes() } 1090.57/297.40 Obligation: 1090.57/297.40 runtime complexity 1090.57/297.40 Answer: 1090.57/297.40 MAYBE 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1090.57/297.40 following reason: 1090.57/297.40 1090.57/297.40 Computation stopped due to timeout after 297.0 seconds. 1090.57/297.40 1090.57/297.40 2) 'Best' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1090.57/297.40 seconds)' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'empty' failed due to the following reason: 1090.57/297.40 1090.57/297.40 Empty strict component of the problem is NOT empty. 1090.57/297.40 1090.57/297.40 2) 'With Problem ...' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'empty' failed due to the following reason: 1090.57/297.40 1090.57/297.40 Empty strict component of the problem is NOT empty. 1090.57/297.40 1090.57/297.40 2) 'Fastest' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'With Problem ...' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'empty' failed due to the following reason: 1090.57/297.40 1090.57/297.40 Empty strict component of the problem is NOT empty. 1090.57/297.40 1090.57/297.40 2) 'With Problem ...' failed due to the following reason: 1090.57/297.40 1090.57/297.40 Empty strict component of the problem is NOT empty. 1090.57/297.40 1090.57/297.40 1090.57/297.40 2) 'With Problem ...' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'empty' failed due to the following reason: 1090.57/297.40 1090.57/297.40 Empty strict component of the problem is NOT empty. 1090.57/297.40 1090.57/297.40 2) 'With Problem ...' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'empty' failed due to the following reason: 1090.57/297.40 1090.57/297.40 Empty strict component of the problem is NOT empty. 1090.57/297.40 1090.57/297.40 2) 'With Problem ...' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'empty' failed due to the following reason: 1090.57/297.40 1090.57/297.40 Empty strict component of the problem is NOT empty. 1090.57/297.40 1090.57/297.40 2) 'With Problem ...' failed due to the following reason: 1090.57/297.40 1090.57/297.40 Empty strict component of the problem is NOT empty. 1090.57/297.40 1090.57/297.40 1090.57/297.40 1090.57/297.40 1090.57/297.40 1090.57/297.40 1090.57/297.40 1090.57/297.40 2) 'Best' failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1090.57/297.40 to the following reason: 1090.57/297.40 1090.57/297.40 The processor is inapplicable, reason: 1090.57/297.40 Processor only applicable for innermost runtime complexity analysis 1090.57/297.40 1090.57/297.40 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1090.57/297.40 following reason: 1090.57/297.40 1090.57/297.40 The processor is inapplicable, reason: 1090.57/297.40 Processor only applicable for innermost runtime complexity analysis 1090.57/297.40 1090.57/297.40 1090.57/297.40 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1090.57/297.40 failed due to the following reason: 1090.57/297.40 1090.57/297.40 None of the processors succeeded. 1090.57/297.40 1090.57/297.40 Details of failed attempt(s): 1090.57/297.40 ----------------------------- 1090.57/297.40 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1090.57/297.40 failed due to the following reason: 1090.57/297.40 1090.57/297.40 match-boundness of the problem could not be verified. 1090.57/297.40 1090.57/297.40 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1090.57/297.40 failed due to the following reason: 1090.57/297.40 1090.57/297.40 match-boundness of the problem could not be verified. 1090.57/297.40 1090.57/297.40 1090.57/297.40 1090.57/297.40 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1090.57/297.40 the following reason: 1090.57/297.40 1090.57/297.40 We add the following weak dependency pairs: 1090.57/297.40 1090.57/297.40 Strict DPs: 1090.57/297.40 { a__filter^#(X1, X2, X3) -> c_1(X1, X2, X3) 1090.57/297.40 , a__filter^#(cons(X, Y), 0(), M) -> c_2(Y, M, M) 1090.57/297.40 , a__filter^#(cons(X, Y), s(N), M) -> c_3(mark^#(X), Y, N, M) 1090.57/297.40 , mark^#(cons(X1, X2)) -> c_4(mark^#(X1), X2) 1090.57/297.40 , mark^#(0()) -> c_5() 1090.57/297.40 , mark^#(filter(X1, X2, X3)) -> 1090.57/297.40 c_6(a__filter^#(mark(X1), mark(X2), mark(X3))) 1090.57/297.40 , mark^#(s(X)) -> c_7(mark^#(X)) 1090.57/297.40 , mark^#(sieve(X)) -> c_8(a__sieve^#(mark(X))) 1090.57/297.40 , mark^#(nats(X)) -> c_9(a__nats^#(mark(X))) 1090.57/297.40 , mark^#(zprimes()) -> c_10(a__zprimes^#()) 1090.57/297.40 , a__sieve^#(X) -> c_11(X) 1090.57/297.40 , a__sieve^#(cons(0(), Y)) -> c_12(Y) 1090.57/297.40 , a__sieve^#(cons(s(N), Y)) -> c_13(mark^#(N), Y, N, N) 1090.57/297.40 , a__nats^#(N) -> c_14(mark^#(N), N) 1090.57/297.40 , a__nats^#(X) -> c_15(X) 1090.57/297.40 , a__zprimes^#() -> c_16(a__sieve^#(a__nats(s(s(0()))))) 1090.57/297.40 , a__zprimes^#() -> c_17() } 1090.57/297.40 1090.57/297.40 and mark the set of starting terms. 1090.57/297.40 1090.57/297.40 We are left with following problem, upon which TcT provides the 1090.57/297.40 certificate MAYBE. 1090.57/297.40 1090.57/297.40 Strict DPs: 1090.57/297.40 { a__filter^#(X1, X2, X3) -> c_1(X1, X2, X3) 1090.57/297.40 , a__filter^#(cons(X, Y), 0(), M) -> c_2(Y, M, M) 1090.57/297.40 , a__filter^#(cons(X, Y), s(N), M) -> c_3(mark^#(X), Y, N, M) 1090.57/297.40 , mark^#(cons(X1, X2)) -> c_4(mark^#(X1), X2) 1090.57/297.40 , mark^#(0()) -> c_5() 1090.57/297.40 , mark^#(filter(X1, X2, X3)) -> 1090.57/297.40 c_6(a__filter^#(mark(X1), mark(X2), mark(X3))) 1090.57/297.40 , mark^#(s(X)) -> c_7(mark^#(X)) 1090.57/297.40 , mark^#(sieve(X)) -> c_8(a__sieve^#(mark(X))) 1090.57/297.40 , mark^#(nats(X)) -> c_9(a__nats^#(mark(X))) 1090.57/297.40 , mark^#(zprimes()) -> c_10(a__zprimes^#()) 1090.57/297.40 , a__sieve^#(X) -> c_11(X) 1090.57/297.40 , a__sieve^#(cons(0(), Y)) -> c_12(Y) 1090.57/297.40 , a__sieve^#(cons(s(N), Y)) -> c_13(mark^#(N), Y, N, N) 1090.57/297.40 , a__nats^#(N) -> c_14(mark^#(N), N) 1090.57/297.40 , a__nats^#(X) -> c_15(X) 1090.57/297.40 , a__zprimes^#() -> c_16(a__sieve^#(a__nats(s(s(0()))))) 1090.57/297.40 , a__zprimes^#() -> c_17() } 1090.57/297.40 Strict Trs: 1090.57/297.40 { a__filter(X1, X2, X3) -> filter(X1, X2, X3) 1090.57/297.40 , a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)) 1090.57/297.40 , a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)) 1090.57/297.40 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1090.57/297.40 , mark(0()) -> 0() 1090.57/297.40 , mark(filter(X1, X2, X3)) -> 1090.57/297.40 a__filter(mark(X1), mark(X2), mark(X3)) 1090.57/297.42 , mark(s(X)) -> s(mark(X)) 1090.57/297.42 , mark(sieve(X)) -> a__sieve(mark(X)) 1090.57/297.42 , mark(nats(X)) -> a__nats(mark(X)) 1090.57/297.42 , mark(zprimes()) -> a__zprimes() 1090.57/297.42 , a__sieve(X) -> sieve(X) 1090.57/297.42 , a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)) 1090.57/297.42 , a__sieve(cons(s(N), Y)) -> 1090.57/297.42 cons(s(mark(N)), sieve(filter(Y, N, N))) 1090.57/297.42 , a__nats(N) -> cons(mark(N), nats(s(N))) 1090.57/297.42 , a__nats(X) -> nats(X) 1090.57/297.42 , a__zprimes() -> a__sieve(a__nats(s(s(0())))) 1090.57/297.42 , a__zprimes() -> zprimes() } 1090.57/297.42 Obligation: 1090.57/297.42 runtime complexity 1090.57/297.42 Answer: 1090.57/297.42 MAYBE 1090.57/297.42 1090.57/297.42 We estimate the number of application of {5,17} by applications of 1090.57/297.42 Pre({5,17}) = {1,2,3,4,7,10,11,12,13,14,15}. Here rules are labeled 1090.57/297.42 as follows: 1090.57/297.42 1090.57/297.42 DPs: 1090.57/297.42 { 1: a__filter^#(X1, X2, X3) -> c_1(X1, X2, X3) 1090.57/297.42 , 2: a__filter^#(cons(X, Y), 0(), M) -> c_2(Y, M, M) 1090.57/297.42 , 3: a__filter^#(cons(X, Y), s(N), M) -> c_3(mark^#(X), Y, N, M) 1090.57/297.42 , 4: mark^#(cons(X1, X2)) -> c_4(mark^#(X1), X2) 1090.57/297.42 , 5: mark^#(0()) -> c_5() 1090.57/297.42 , 6: mark^#(filter(X1, X2, X3)) -> 1090.57/297.42 c_6(a__filter^#(mark(X1), mark(X2), mark(X3))) 1090.57/297.42 , 7: mark^#(s(X)) -> c_7(mark^#(X)) 1090.57/297.42 , 8: mark^#(sieve(X)) -> c_8(a__sieve^#(mark(X))) 1090.57/297.42 , 9: mark^#(nats(X)) -> c_9(a__nats^#(mark(X))) 1090.57/297.42 , 10: mark^#(zprimes()) -> c_10(a__zprimes^#()) 1090.57/297.42 , 11: a__sieve^#(X) -> c_11(X) 1090.57/297.42 , 12: a__sieve^#(cons(0(), Y)) -> c_12(Y) 1090.57/297.42 , 13: a__sieve^#(cons(s(N), Y)) -> c_13(mark^#(N), Y, N, N) 1090.57/297.42 , 14: a__nats^#(N) -> c_14(mark^#(N), N) 1090.57/297.42 , 15: a__nats^#(X) -> c_15(X) 1090.57/297.42 , 16: a__zprimes^#() -> c_16(a__sieve^#(a__nats(s(s(0()))))) 1090.57/297.42 , 17: a__zprimes^#() -> c_17() } 1090.57/297.42 1090.57/297.42 We are left with following problem, upon which TcT provides the 1090.57/297.42 certificate MAYBE. 1090.57/297.42 1090.57/297.42 Strict DPs: 1090.57/297.42 { a__filter^#(X1, X2, X3) -> c_1(X1, X2, X3) 1090.57/297.42 , a__filter^#(cons(X, Y), 0(), M) -> c_2(Y, M, M) 1090.57/297.42 , a__filter^#(cons(X, Y), s(N), M) -> c_3(mark^#(X), Y, N, M) 1090.57/297.42 , mark^#(cons(X1, X2)) -> c_4(mark^#(X1), X2) 1090.57/297.42 , mark^#(filter(X1, X2, X3)) -> 1090.57/297.42 c_6(a__filter^#(mark(X1), mark(X2), mark(X3))) 1090.57/297.42 , mark^#(s(X)) -> c_7(mark^#(X)) 1090.57/297.42 , mark^#(sieve(X)) -> c_8(a__sieve^#(mark(X))) 1090.57/297.42 , mark^#(nats(X)) -> c_9(a__nats^#(mark(X))) 1090.57/297.42 , mark^#(zprimes()) -> c_10(a__zprimes^#()) 1090.57/297.42 , a__sieve^#(X) -> c_11(X) 1090.57/297.42 , a__sieve^#(cons(0(), Y)) -> c_12(Y) 1090.57/297.42 , a__sieve^#(cons(s(N), Y)) -> c_13(mark^#(N), Y, N, N) 1090.57/297.42 , a__nats^#(N) -> c_14(mark^#(N), N) 1090.57/297.42 , a__nats^#(X) -> c_15(X) 1090.57/297.42 , a__zprimes^#() -> c_16(a__sieve^#(a__nats(s(s(0()))))) } 1090.57/297.42 Strict Trs: 1090.57/297.42 { a__filter(X1, X2, X3) -> filter(X1, X2, X3) 1090.57/297.42 , a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)) 1090.57/297.42 , a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)) 1090.57/297.42 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1090.57/297.42 , mark(0()) -> 0() 1090.57/297.42 , mark(filter(X1, X2, X3)) -> 1090.57/297.42 a__filter(mark(X1), mark(X2), mark(X3)) 1090.57/297.42 , mark(s(X)) -> s(mark(X)) 1090.57/297.42 , mark(sieve(X)) -> a__sieve(mark(X)) 1090.57/297.42 , mark(nats(X)) -> a__nats(mark(X)) 1090.57/297.42 , mark(zprimes()) -> a__zprimes() 1090.57/297.42 , a__sieve(X) -> sieve(X) 1090.57/297.42 , a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)) 1090.57/297.42 , a__sieve(cons(s(N), Y)) -> 1090.57/297.42 cons(s(mark(N)), sieve(filter(Y, N, N))) 1090.57/297.42 , a__nats(N) -> cons(mark(N), nats(s(N))) 1090.57/297.42 , a__nats(X) -> nats(X) 1090.57/297.42 , a__zprimes() -> a__sieve(a__nats(s(s(0())))) 1090.57/297.42 , a__zprimes() -> zprimes() } 1090.57/297.42 Weak DPs: 1090.57/297.42 { mark^#(0()) -> c_5() 1090.57/297.42 , a__zprimes^#() -> c_17() } 1090.57/297.42 Obligation: 1090.57/297.42 runtime complexity 1090.57/297.42 Answer: 1090.57/297.42 MAYBE 1090.57/297.42 1090.57/297.42 Empty strict component of the problem is NOT empty. 1090.57/297.42 1090.57/297.42 1090.57/297.42 Arrrr.. 1090.73/297.59 EOF