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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308143
details
property
value
status
complete
benchmark
Ex9_BLR02_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n068.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.621 seconds
cpu usage
329.43
user time
324.196
system time
5.2334
max virtual memory
1.8281476E7
max residence set size
8393776.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
329.28/291.55 WORST_CASE(Omega(n^1), ?) 329.28/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 329.28/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 329.28/291.56 329.28/291.56 329.28/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 329.28/291.56 329.28/291.56 (0) CpxTRS 329.28/291.56 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 329.28/291.56 (2) CpxTRS 329.28/291.56 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 329.28/291.56 (4) typed CpxTrs 329.28/291.56 (5) OrderProof [LOWER BOUND(ID), 0 ms] 329.28/291.56 (6) typed CpxTrs 329.28/291.56 (7) RewriteLemmaProof [LOWER BOUND(ID), 478 ms] 329.28/291.56 (8) BEST 329.28/291.56 (9) proven lower bound 329.28/291.56 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 329.28/291.56 (11) BOUNDS(n^1, INF) 329.28/291.56 (12) typed CpxTrs 329.28/291.56 (13) RewriteLemmaProof [LOWER BOUND(ID), 173 ms] 329.28/291.56 (14) typed CpxTrs 329.28/291.56 (15) RewriteLemmaProof [LOWER BOUND(ID), 79 ms] 329.28/291.56 (16) typed CpxTrs 329.28/291.56 (17) RewriteLemmaProof [LOWER BOUND(ID), 56 ms] 329.28/291.56 (18) typed CpxTrs 329.28/291.56 (19) RewriteLemmaProof [LOWER BOUND(ID), 37 ms] 329.28/291.56 (20) typed CpxTrs 329.28/291.56 329.28/291.56 329.28/291.56 ---------------------------------------- 329.28/291.56 329.28/291.56 (0) 329.28/291.56 Obligation: 329.28/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 329.28/291.56 329.28/291.56 329.28/291.56 The TRS R consists of the following rules: 329.28/291.56 329.28/291.56 active(filter(cons(X, Y), 0, M)) -> mark(cons(0, filter(Y, M, M))) 329.28/291.56 active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M))) 329.28/291.56 active(sieve(cons(0, Y))) -> mark(cons(0, sieve(Y))) 329.28/291.56 active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N)))) 329.28/291.56 active(nats(N)) -> mark(cons(N, nats(s(N)))) 329.28/291.56 active(zprimes) -> mark(sieve(nats(s(s(0))))) 329.28/291.56 active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3) 329.28/291.56 active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3) 329.28/291.56 active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3)) 329.28/291.56 active(cons(X1, X2)) -> cons(active(X1), X2) 329.28/291.56 active(s(X)) -> s(active(X)) 329.28/291.56 active(sieve(X)) -> sieve(active(X)) 329.28/291.56 active(nats(X)) -> nats(active(X)) 329.28/291.56 filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3)) 329.28/291.56 filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3)) 329.28/291.56 filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3)) 329.28/291.56 cons(mark(X1), X2) -> mark(cons(X1, X2)) 329.28/291.56 s(mark(X)) -> mark(s(X)) 329.28/291.56 sieve(mark(X)) -> mark(sieve(X)) 329.28/291.56 nats(mark(X)) -> mark(nats(X)) 329.28/291.56 proper(filter(X1, X2, X3)) -> filter(proper(X1), proper(X2), proper(X3)) 329.28/291.56 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 329.28/291.56 proper(0) -> ok(0) 329.28/291.56 proper(s(X)) -> s(proper(X)) 329.28/291.56 proper(sieve(X)) -> sieve(proper(X)) 329.28/291.56 proper(nats(X)) -> nats(proper(X)) 329.28/291.56 proper(zprimes) -> ok(zprimes) 329.28/291.56 filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3)) 329.28/291.56 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 329.28/291.56 s(ok(X)) -> ok(s(X)) 329.28/291.56 sieve(ok(X)) -> ok(sieve(X)) 329.28/291.56 nats(ok(X)) -> ok(nats(X)) 329.28/291.56 top(mark(X)) -> top(proper(X)) 329.28/291.56 top(ok(X)) -> top(active(X)) 329.28/291.56 329.28/291.56 S is empty. 329.28/291.56 Rewrite Strategy: FULL 329.28/291.56 ---------------------------------------- 329.28/291.56 329.28/291.56 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 329.28/291.56 Renamed function symbols to avoid clashes with predefined symbol. 329.28/291.56 ---------------------------------------- 329.28/291.56 329.28/291.56 (2) 329.28/291.56 Obligation: 329.28/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 329.28/291.56 329.28/291.56 329.28/291.56 The TRS R consists of the following rules: 329.28/291.56 329.28/291.56 active(filter(cons(X, Y), 0', M)) -> mark(cons(0', filter(Y, M, M))) 329.28/291.56 active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M))) 329.28/291.56 active(sieve(cons(0', Y))) -> mark(cons(0', sieve(Y))) 329.28/291.56 active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N)))) 329.28/291.56 active(nats(N)) -> mark(cons(N, nats(s(N)))) 329.28/291.56 active(zprimes) -> mark(sieve(nats(s(s(0'))))) 329.28/291.56 active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3) 329.28/291.56 active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3) 329.28/291.56 active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3)) 329.28/291.56 active(cons(X1, X2)) -> cons(active(X1), X2) 329.28/291.56 active(s(X)) -> s(active(X))
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