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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307647
details
property
value
status
complete
benchmark
14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n130.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.532 seconds
cpu usage
934.508
user time
927.564
system time
6.94324
max virtual memory
3.7832656E7
max residence set size
5473120.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
934.26/291.47 WORST_CASE(Omega(n^1), O(n^2)) 934.38/291.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 934.38/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 934.38/291.48 934.38/291.48 934.38/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 934.38/291.48 934.38/291.48 (0) CpxTRS 934.38/291.48 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 934.38/291.48 (2) CpxTRS 934.38/291.48 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 934.38/291.48 (4) CpxWeightedTrs 934.38/291.48 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 934.38/291.48 (6) CpxTypedWeightedTrs 934.38/291.48 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 934.38/291.48 (8) CpxTypedWeightedCompleteTrs 934.38/291.48 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 934.38/291.48 (10) CpxRNTS 934.38/291.48 (11) CompleteCoflocoProof [FINISHED, 333 ms] 934.38/291.48 (12) BOUNDS(1, n^2) 934.38/291.48 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 934.38/291.48 (14) CpxTRS 934.38/291.48 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 934.38/291.48 (16) typed CpxTrs 934.38/291.48 (17) OrderProof [LOWER BOUND(ID), 0 ms] 934.38/291.48 (18) typed CpxTrs 934.38/291.48 (19) RewriteLemmaProof [LOWER BOUND(ID), 269 ms] 934.38/291.48 (20) BEST 934.38/291.48 (21) proven lower bound 934.38/291.48 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 934.38/291.48 (23) BOUNDS(n^1, INF) 934.38/291.48 (24) typed CpxTrs 934.38/291.48 (25) RewriteLemmaProof [LOWER BOUND(ID), 1217 ms] 934.38/291.48 (26) BOUNDS(1, INF) 934.38/291.48 934.38/291.48 934.38/291.48 ---------------------------------------- 934.38/291.48 934.38/291.48 (0) 934.38/291.48 Obligation: 934.38/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 934.38/291.48 934.38/291.48 934.38/291.48 The TRS R consists of the following rules: 934.38/291.48 934.38/291.48 cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) 934.38/291.48 cond2(true, x, y) -> cond1(y, y) 934.38/291.48 cond2(false, x, y) -> cond1(p(x), y) 934.38/291.48 gr(0, x) -> false 934.38/291.48 gr(s(x), 0) -> true 934.38/291.48 gr(s(x), s(y)) -> gr(x, y) 934.38/291.48 neq(0, 0) -> false 934.38/291.48 neq(0, s(x)) -> true 934.38/291.48 neq(s(x), 0) -> true 934.38/291.48 neq(s(x), s(y)) -> neq(x, y) 934.38/291.48 p(0) -> 0 934.38/291.48 p(s(x)) -> x 934.38/291.48 934.38/291.48 S is empty. 934.38/291.48 Rewrite Strategy: FULL 934.38/291.48 ---------------------------------------- 934.38/291.48 934.38/291.48 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 934.38/291.48 Converted rc-obligation to irc-obligation. 934.38/291.48 934.38/291.48 The duplicating contexts are: 934.38/291.48 cond1(s([]), y) 934.38/291.48 cond1(s(x), []) 934.38/291.48 cond2(true, x, []) 934.38/291.48 934.38/291.48 934.38/291.48 The defined contexts are: 934.38/291.48 cond2([], s(x1), x2) 934.38/291.48 cond1([], x1) 934.38/291.48 gr(s([]), x1) 934.38/291.48 cond2(x0, s([]), x2) 934.38/291.48 p([]) 934.38/291.48 gr([], x1) 934.38/291.48 934.38/291.48 934.38/291.48 [] just represents basic- or constructor-terms in the following defined contexts: 934.38/291.48 cond2([], s(x1), x2) 934.38/291.48 cond1([], x1) 934.38/291.48 934.38/291.48 934.38/291.48 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 934.38/291.48 ---------------------------------------- 934.38/291.48 934.38/291.48 (2) 934.38/291.48 Obligation: 934.38/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 934.38/291.48 934.38/291.48 934.38/291.48 The TRS R consists of the following rules: 934.38/291.48 934.38/291.48 cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) 934.38/291.48 cond2(true, x, y) -> cond1(y, y) 934.38/291.48 cond2(false, x, y) -> cond1(p(x), y) 934.38/291.48 gr(0, x) -> false 934.38/291.48 gr(s(x), 0) -> true
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