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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307658
details
property
value
status
complete
benchmark
11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n097.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.587 seconds
cpu usage
301.617
user time
299.687
system time
1.92948
max virtual memory
1.8279384E7
max residence set size
5159156.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
301.41/291.50 WORST_CASE(Omega(n^1), ?) 301.54/291.55 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 301.54/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 301.54/291.55 301.54/291.55 301.54/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 301.54/291.55 301.54/291.55 (0) CpxTRS 301.54/291.55 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 301.54/291.55 (2) CpxTRS 301.54/291.55 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 301.54/291.55 (4) typed CpxTrs 301.54/291.55 (5) OrderProof [LOWER BOUND(ID), 0 ms] 301.54/291.55 (6) typed CpxTrs 301.54/291.55 (7) RewriteLemmaProof [LOWER BOUND(ID), 234 ms] 301.54/291.55 (8) BEST 301.54/291.55 (9) proven lower bound 301.54/291.55 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 301.54/291.55 (11) BOUNDS(n^1, INF) 301.54/291.55 (12) typed CpxTrs 301.54/291.55 (13) RewriteLemmaProof [LOWER BOUND(ID), 85 ms] 301.54/291.55 (14) typed CpxTrs 301.54/291.55 301.54/291.55 301.54/291.55 ---------------------------------------- 301.54/291.55 301.54/291.55 (0) 301.54/291.55 Obligation: 301.54/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 301.54/291.55 301.54/291.55 301.54/291.55 The TRS R consists of the following rules: 301.54/291.55 301.54/291.55 cond1(true, x, y) -> cond2(gr(x, y), x, y) 301.54/291.55 cond2(true, x, y) -> cond1(neq(x, 0), y, y) 301.54/291.55 cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) 301.54/291.55 gr(0, x) -> false 301.54/291.55 gr(s(x), 0) -> true 301.54/291.55 gr(s(x), s(y)) -> gr(x, y) 301.54/291.55 neq(0, 0) -> false 301.54/291.55 neq(0, s(x)) -> true 301.54/291.55 neq(s(x), 0) -> true 301.54/291.55 neq(s(x), s(y)) -> neq(x, y) 301.54/291.55 p(0) -> 0 301.54/291.55 p(s(x)) -> x 301.54/291.55 301.54/291.55 S is empty. 301.54/291.55 Rewrite Strategy: FULL 301.54/291.55 ---------------------------------------- 301.54/291.55 301.54/291.55 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 301.54/291.55 Renamed function symbols to avoid clashes with predefined symbol. 301.54/291.55 ---------------------------------------- 301.54/291.55 301.54/291.55 (2) 301.54/291.55 Obligation: 301.54/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 301.54/291.55 301.54/291.55 301.54/291.55 The TRS R consists of the following rules: 301.54/291.55 301.54/291.55 cond1(true, x, y) -> cond2(gr(x, y), x, y) 301.54/291.55 cond2(true, x, y) -> cond1(neq(x, 0'), y, y) 301.54/291.55 cond2(false, x, y) -> cond1(neq(x, 0'), p(x), y) 301.54/291.55 gr(0', x) -> false 301.54/291.55 gr(s(x), 0') -> true 301.54/291.55 gr(s(x), s(y)) -> gr(x, y) 301.54/291.55 neq(0', 0') -> false 301.54/291.55 neq(0', s(x)) -> true 301.54/291.55 neq(s(x), 0') -> true 301.54/291.55 neq(s(x), s(y)) -> neq(x, y) 301.54/291.55 p(0') -> 0' 301.54/291.55 p(s(x)) -> x 301.54/291.55 301.54/291.55 S is empty. 301.54/291.55 Rewrite Strategy: FULL 301.54/291.55 ---------------------------------------- 301.54/291.55 301.54/291.55 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 301.54/291.55 Infered types. 301.54/291.55 ---------------------------------------- 301.54/291.55 301.54/291.55 (4) 301.54/291.55 Obligation: 301.54/291.55 TRS: 301.54/291.55 Rules: 301.54/291.55 cond1(true, x, y) -> cond2(gr(x, y), x, y) 301.54/291.55 cond2(true, x, y) -> cond1(neq(x, 0'), y, y) 301.54/291.55 cond2(false, x, y) -> cond1(neq(x, 0'), p(x), y) 301.54/291.55 gr(0', x) -> false 301.54/291.55 gr(s(x), 0') -> true 301.54/291.55 gr(s(x), s(y)) -> gr(x, y) 301.54/291.55 neq(0', 0') -> false 301.54/291.55 neq(0', s(x)) -> true 301.54/291.55 neq(s(x), 0') -> true 301.54/291.55 neq(s(x), s(y)) -> neq(x, y) 301.54/291.55 p(0') -> 0' 301.54/291.55 p(s(x)) -> x 301.54/291.55 301.54/291.55 Types:
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