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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307943
details
property
value
status
complete
benchmark
polycounter-5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n167.star.cs.uiowa.edu
space
TCT_12
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.589 seconds
cpu usage
1023.82
user time
1017.17
system time
6.65352
max virtual memory
3.8326904E7
max residence set size
6111304.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^5))
output
1023.44/291.52 WORST_CASE(Omega(n^1), O(n^5)) 1023.44/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1023.44/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1023.44/291.54 1023.44/291.54 1023.44/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). 1023.44/291.54 1023.44/291.54 (0) CpxTRS 1023.44/291.54 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1023.44/291.54 (2) CpxTRS 1023.44/291.54 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1023.44/291.54 (4) CpxWeightedTrs 1023.44/291.54 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1023.44/291.54 (6) CpxTypedWeightedTrs 1023.44/291.54 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1023.44/291.54 (8) CpxTypedWeightedCompleteTrs 1023.44/291.54 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1023.44/291.54 (10) CpxTypedWeightedCompleteTrs 1023.44/291.54 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1023.44/291.54 (12) CpxRNTS 1023.44/291.54 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1023.44/291.54 (14) CpxRNTS 1023.44/291.54 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 1023.44/291.54 (16) CpxRNTS 1023.44/291.54 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1023.44/291.54 (18) CpxRNTS 1023.44/291.54 (19) IntTrsBoundProof [UPPER BOUND(ID), 3575 ms] 1023.44/291.54 (20) CpxRNTS 1023.44/291.54 (21) IntTrsBoundProof [UPPER BOUND(ID), 3633 ms] 1023.44/291.54 (22) CpxRNTS 1023.44/291.54 (23) FinalProof [FINISHED, 0 ms] 1023.44/291.54 (24) BOUNDS(1, n^5) 1023.44/291.54 (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1023.44/291.54 (26) TRS for Loop Detection 1023.44/291.54 (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1023.44/291.54 (28) BEST 1023.44/291.54 (29) proven lower bound 1023.44/291.54 (30) LowerBoundPropagationProof [FINISHED, 0 ms] 1023.44/291.54 (31) BOUNDS(n^1, INF) 1023.44/291.54 (32) TRS for Loop Detection 1023.44/291.54 1023.44/291.54 1023.44/291.54 ---------------------------------------- 1023.44/291.54 1023.44/291.54 (0) 1023.44/291.54 Obligation: 1023.44/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). 1023.44/291.54 1023.44/291.54 1023.44/291.54 The TRS R consists of the following rules: 1023.44/291.54 1023.44/291.54 f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) 1023.44/291.54 f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) 1023.44/291.54 f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) 1023.44/291.54 f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) 1023.44/291.54 f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) 1023.44/291.54 f(0, 0, 0, 0, 0) -> 0 1023.44/291.54 1023.44/291.54 S is empty. 1023.44/291.54 Rewrite Strategy: FULL 1023.44/291.54 ---------------------------------------- 1023.44/291.54 1023.44/291.54 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1023.44/291.54 Converted rc-obligation to irc-obligation. 1023.44/291.54 1023.44/291.54 As the TRS does not nest defined symbols, we have rc = irc. 1023.44/291.54 ---------------------------------------- 1023.44/291.54 1023.44/291.54 (2) 1023.44/291.54 Obligation: 1023.44/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^5). 1023.44/291.54 1023.44/291.54 1023.44/291.54 The TRS R consists of the following rules: 1023.44/291.54 1023.44/291.54 f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) 1023.44/291.54 f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) 1023.44/291.54 f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) 1023.44/291.54 f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) 1023.44/291.54 f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) 1023.44/291.54 f(0, 0, 0, 0, 0) -> 0 1023.44/291.54 1023.44/291.54 S is empty. 1023.44/291.54 Rewrite Strategy: INNERMOST 1023.44/291.54 ---------------------------------------- 1023.44/291.54 1023.44/291.54 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1023.44/291.54 Transformed relative TRS to weighted TRS 1023.44/291.54 ---------------------------------------- 1023.44/291.54 1023.44/291.54 (4) 1023.44/291.54 Obligation: 1023.44/291.54 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^5). 1023.44/291.54 1023.44/291.54 1023.44/291.54 The TRS R consists of the following rules: 1023.44/291.54 1023.44/291.54 f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) [1] 1023.44/291.54 f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) [1] 1023.44/291.54 f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) [1]
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