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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307702
details
property
value
status
complete
benchmark
#3.22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n080.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.78774 seconds
cpu usage
18.8388
user time
17.6231
system time
1.21567
max virtual memory
1.9010696E7
max residence set size
3445348.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
18.65/6.73 WORST_CASE(Omega(n^2), O(n^2)) 18.65/6.74 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 18.65/6.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.65/6.74 18.65/6.74 18.65/6.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 18.65/6.74 18.65/6.74 (0) CpxTRS 18.65/6.74 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 18.65/6.74 (2) CpxTRS 18.65/6.74 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 18.65/6.74 (4) CpxTRS 18.65/6.74 (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 18.65/6.74 (6) CpxWeightedTrs 18.65/6.74 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.65/6.74 (8) CpxTypedWeightedTrs 18.65/6.74 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 18.65/6.74 (10) CpxTypedWeightedCompleteTrs 18.65/6.74 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] 18.65/6.74 (12) CpxRNTS 18.65/6.74 (13) CompleteCoflocoProof [FINISHED, 175 ms] 18.65/6.74 (14) BOUNDS(1, n^2) 18.65/6.74 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 18.65/6.74 (16) CpxTRS 18.65/6.74 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.65/6.74 (18) typed CpxTrs 18.65/6.74 (19) OrderProof [LOWER BOUND(ID), 0 ms] 18.65/6.74 (20) typed CpxTrs 18.65/6.74 (21) RewriteLemmaProof [LOWER BOUND(ID), 268 ms] 18.65/6.74 (22) BEST 18.65/6.74 (23) proven lower bound 18.65/6.74 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 18.65/6.74 (25) BOUNDS(n^1, INF) 18.65/6.74 (26) typed CpxTrs 18.65/6.74 (27) RewriteLemmaProof [LOWER BOUND(ID), 82 ms] 18.65/6.74 (28) proven lower bound 18.65/6.74 (29) LowerBoundPropagationProof [FINISHED, 0 ms] 18.65/6.74 (30) BOUNDS(n^2, INF) 18.65/6.74 18.65/6.74 18.65/6.74 ---------------------------------------- 18.65/6.74 18.65/6.74 (0) 18.65/6.74 Obligation: 18.65/6.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 18.65/6.74 18.65/6.74 18.65/6.74 The TRS R consists of the following rules: 18.65/6.74 18.65/6.74 times(x, plus(y, s(z))) -> plus(times(x, plus(y, times(s(z), 0))), times(x, s(z))) 18.65/6.74 times(x, 0) -> 0 18.65/6.74 times(x, s(y)) -> plus(times(x, y), x) 18.65/6.74 plus(x, 0) -> x 18.65/6.74 plus(x, s(y)) -> s(plus(x, y)) 18.65/6.74 18.65/6.74 S is empty. 18.65/6.74 Rewrite Strategy: FULL 18.65/6.74 ---------------------------------------- 18.65/6.74 18.65/6.74 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 18.65/6.74 The following defined symbols can occur below the 0th argument of plus: plus, times 18.65/6.74 18.65/6.74 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 18.65/6.74 times(x, plus(y, s(z))) -> plus(times(x, plus(y, times(s(z), 0))), times(x, s(z))) 18.65/6.74 18.65/6.74 ---------------------------------------- 18.65/6.74 18.65/6.74 (2) 18.65/6.74 Obligation: 18.65/6.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 18.65/6.74 18.65/6.74 18.65/6.74 The TRS R consists of the following rules: 18.65/6.74 18.65/6.74 times(x, 0) -> 0 18.65/6.74 times(x, s(y)) -> plus(times(x, y), x) 18.65/6.74 plus(x, 0) -> x 18.65/6.74 plus(x, s(y)) -> s(plus(x, y)) 18.65/6.74 18.65/6.74 S is empty. 18.65/6.74 Rewrite Strategy: FULL 18.65/6.74 ---------------------------------------- 18.65/6.74 18.65/6.74 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 18.65/6.74 Converted rc-obligation to irc-obligation. 18.65/6.74 18.65/6.74 The duplicating contexts are: 18.65/6.74 times([], s(y)) 18.65/6.74 18.65/6.74 18.65/6.74 The defined contexts are: 18.65/6.74 plus([], x1) 18.65/6.74 18.65/6.74 18.65/6.74 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 18.65/6.74 ---------------------------------------- 18.65/6.74 18.65/6.74 (4) 18.65/6.74 Obligation: 18.65/6.74 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2).
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