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TRS_Contextsensitive 2019-03-21 05.07 pair #429997001
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
n074.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.52853 seconds
cpu usage
3.50445
user time
3.34473
system time
0.159714
max virtual memory
1.8341304E7
max residence set size
223260.0
stage attributes
key
value
starexec-result
YES
output
3.26/1.49 YES 3.26/1.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.26/1.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.26/1.50 3.26/1.50 3.26/1.50 Termination of the given CSR could be proven: 3.26/1.50 3.26/1.50 (0) CSR 3.26/1.50 (1) CSRRRRProof [EQUIVALENT, 22 ms] 3.26/1.50 (2) CSR 3.26/1.50 (3) CSRRRRProof [EQUIVALENT, 5 ms] 3.26/1.50 (4) CSR 3.26/1.50 (5) CSRRRRProof [EQUIVALENT, 0 ms] 3.26/1.50 (6) CSR 3.26/1.50 (7) CSRRRRProof [EQUIVALENT, 0 ms] 3.26/1.50 (8) CSR 3.26/1.50 (9) RisEmptyProof [EQUIVALENT, 0 ms] 3.26/1.50 (10) YES 3.26/1.50 3.26/1.50 3.26/1.50 ---------------------------------------- 3.26/1.50 3.26/1.50 (0) 3.26/1.50 Obligation: 3.26/1.50 Context-sensitive rewrite system: 3.26/1.50 The TRS R consists of the following rules: 3.26/1.50 3.26/1.50 filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) 3.26/1.50 filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M)) 3.26/1.50 sieve(cons(0, Y)) -> cons(0, sieve(Y)) 3.26/1.50 sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N))) 3.26/1.50 nats(N) -> cons(N, nats(s(N))) 3.26/1.50 zprimes -> sieve(nats(s(s(0)))) 3.26/1.50 3.26/1.50 The replacement map contains the following entries: 3.26/1.50 3.26/1.50 filter: {1, 2, 3} 3.26/1.50 cons: {1} 3.26/1.50 0: empty set 3.26/1.50 s: {1} 3.26/1.50 sieve: {1} 3.26/1.50 nats: {1} 3.26/1.50 zprimes: empty set 3.26/1.50 3.26/1.50 ---------------------------------------- 3.26/1.50 3.26/1.50 (1) CSRRRRProof (EQUIVALENT) 3.26/1.50 The following CSR is given: Context-sensitive rewrite system: 3.26/1.50 The TRS R consists of the following rules: 3.26/1.50 3.26/1.50 filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) 3.26/1.50 filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M)) 3.26/1.50 sieve(cons(0, Y)) -> cons(0, sieve(Y)) 3.26/1.50 sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N))) 3.26/1.50 nats(N) -> cons(N, nats(s(N))) 3.26/1.50 zprimes -> sieve(nats(s(s(0)))) 3.26/1.50 3.26/1.50 The replacement map contains the following entries: 3.26/1.50 3.26/1.50 filter: {1, 2, 3} 3.26/1.50 cons: {1} 3.26/1.50 0: empty set 3.26/1.50 s: {1} 3.26/1.50 sieve: {1} 3.26/1.50 nats: {1} 3.26/1.50 zprimes: empty set 3.26/1.50 Used ordering: 3.26/1.50 Polynomial interpretation [POLO]: 3.26/1.50 3.26/1.50 POL(0) = 0 3.26/1.50 POL(cons(x_1, x_2)) = x_1 3.26/1.50 POL(filter(x_1, x_2, x_3)) = x_1 + x_2 + x_3 3.26/1.50 POL(nats(x_1)) = x_1 3.26/1.50 POL(s(x_1)) = x_1 3.26/1.50 POL(sieve(x_1)) = 1 + x_1 3.26/1.50 POL(zprimes) = 1 3.26/1.50 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 3.26/1.50 3.26/1.50 sieve(cons(0, Y)) -> cons(0, sieve(Y)) 3.26/1.50 sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N))) 3.26/1.50 3.26/1.50 3.26/1.50 3.26/1.50 3.26/1.50 ---------------------------------------- 3.26/1.50 3.26/1.50 (2) 3.26/1.50 Obligation: 3.26/1.50 Context-sensitive rewrite system: 3.26/1.50 The TRS R consists of the following rules: 3.26/1.50 3.26/1.50 filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) 3.26/1.50 filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M)) 3.26/1.50 nats(N) -> cons(N, nats(s(N))) 3.26/1.50 zprimes -> sieve(nats(s(s(0)))) 3.26/1.50 3.26/1.50 The replacement map contains the following entries: 3.26/1.50 3.26/1.50 filter: {1, 2, 3} 3.26/1.50 cons: {1}
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