details

property	value
status	complete
benchmark	Ex9_BLR02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.48356 seconds
cpu usage	3.20966
user time	3.03998
system time	0.169679
max virtual memory	1.8275768E7
max residence set size	212032.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 61 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M)) sieve(cons(0, Y)) -> cons(0, sieve(Y)) sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N))) nats(N) -> cons(N, nats(s(N))) zprimes -> sieve(nats(s(s(0)))) The replacement map contains the following entries: filter: {1, 2, 3} cons: {1} 0: empty set s: {1} sieve: {1} nats: {1} zprimes: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M)) sieve(cons(0, Y)) -> cons(0, sieve(Y)) sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N))) nats(N) -> cons(N, nats(s(N))) zprimes -> sieve(nats(s(s(0)))) The replacement map contains the following entries: filter: {1, 2, 3} cons: {1} 0: empty set s: {1} sieve: {1} nats: {1} zprimes: empty set Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(cons(x_1, x_2)) = x_1 POL(filter(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(nats(x_1)) = x_1 POL(s(x_1)) = x_1 POL(sieve(x_1)) = 1 + x_1 POL(zprimes) = 1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: sieve(cons(0, Y)) -> cons(0, sieve(Y)) sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N))) ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M)) nats(N) -> cons(N, nats(s(N))) zprimes -> sieve(nats(s(s(0)))) The replacement map contains the following entries: filter: {1, 2, 3} cons: {1} 0: empty set s: {1} sieve: {1} nats: {1} popout

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job log

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actions

all output return to TRS Contextsensitive