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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307937
details
property
value
status
complete
benchmark
cade08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n154.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
296.226 seconds
cpu usage
1136.77
user time
1123.75
system time
13.0193
max virtual memory
5.7366336E7
max residence set size
1.5167992E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1118.23/291.51 WORST_CASE(Omega(n^1), O(n^2)) 1136.50/296.13 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1136.50/296.13 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1136.50/296.13 1136.50/296.13 1136.50/296.13 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1136.50/296.13 1136.50/296.13 (0) CpxTRS 1136.50/296.13 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1136.50/296.13 (2) CpxTRS 1136.50/296.13 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1136.50/296.13 (4) CpxWeightedTrs 1136.50/296.13 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1136.50/296.13 (6) CpxTypedWeightedTrs 1136.50/296.13 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1136.50/296.13 (8) CpxTypedWeightedCompleteTrs 1136.50/296.13 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] 1136.50/296.13 (10) CpxRNTS 1136.50/296.13 (11) CompleteCoflocoProof [FINISHED, 1991 ms] 1136.50/296.13 (12) BOUNDS(1, n^2) 1136.50/296.13 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1136.50/296.13 (14) TRS for Loop Detection 1136.50/296.13 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1136.50/296.13 (16) BEST 1136.50/296.13 (17) proven lower bound 1136.50/296.13 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1136.50/296.13 (19) BOUNDS(n^1, INF) 1136.50/296.13 (20) TRS for Loop Detection 1136.50/296.13 1136.50/296.13 1136.50/296.13 ---------------------------------------- 1136.50/296.13 1136.50/296.13 (0) 1136.50/296.13 Obligation: 1136.50/296.13 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1136.50/296.13 1136.50/296.13 1136.50/296.13 The TRS R consists of the following rules: 1136.50/296.13 1136.50/296.13 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) 1136.50/296.13 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) 1136.50/296.13 gt(0, v) -> false 1136.50/296.13 gt(s(u), 0) -> true 1136.50/296.13 gt(s(u), s(v)) -> gt(u, v) 1136.50/296.13 and(x, true) -> x 1136.50/296.13 and(x, false) -> false 1136.50/296.13 1136.50/296.13 S is empty. 1136.50/296.13 Rewrite Strategy: FULL 1136.50/296.13 ---------------------------------------- 1136.50/296.13 1136.50/296.13 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1136.50/296.13 Converted rc-obligation to irc-obligation. 1136.50/296.13 1136.50/296.13 The duplicating contexts are: 1136.50/296.13 f(true, [], y, z) 1136.50/296.13 f(true, x, [], z) 1136.50/296.13 f(true, x, y, []) 1136.50/296.13 1136.50/296.13 1136.50/296.13 The defined contexts are: 1136.50/296.13 f([], x1, s(x2), x3) 1136.50/296.13 and([], x1) 1136.50/296.13 and(x0, []) 1136.50/296.13 f([], x1, x2, s(x3)) 1136.50/296.13 1136.50/296.13 1136.50/296.13 [] just represents basic- or constructor-terms in the following defined contexts: 1136.50/296.13 and([], x1) 1136.50/296.13 and(x0, []) 1136.50/296.13 1136.50/296.13 1136.50/296.13 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 1136.50/296.13 ---------------------------------------- 1136.50/296.13 1136.50/296.13 (2) 1136.50/296.13 Obligation: 1136.50/296.13 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 1136.50/296.13 1136.50/296.13 1136.50/296.13 The TRS R consists of the following rules: 1136.50/296.13 1136.50/296.13 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) 1136.50/296.13 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) 1136.50/296.13 gt(0, v) -> false 1136.50/296.13 gt(s(u), 0) -> true 1136.50/296.13 gt(s(u), s(v)) -> gt(u, v) 1136.50/296.13 and(x, true) -> x 1136.50/296.13 and(x, false) -> false 1136.50/296.13 1136.50/296.13 S is empty. 1136.50/296.13 Rewrite Strategy: INNERMOST 1136.50/296.13 ---------------------------------------- 1136.50/296.13 1136.50/296.13 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1136.50/296.13 Transformed relative TRS to weighted TRS 1136.50/296.13 ---------------------------------------- 1136.50/296.13 1136.50/296.13 (4) 1136.50/296.13 Obligation:
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