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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313539
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
n105.star.cs.uiowa.edu
space
TCT_12
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.576 seconds
cpu usage
1014.48
user time
1007.6
system time
6.87827
max virtual memory
5.6792368E7
max residence set size
6177240.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^5))
output
1014.17/291.50 WORST_CASE(Omega(n^1), O(n^5)) 1014.17/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1014.17/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1014.17/291.52 1014.17/291.52 1014.17/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). 1014.17/291.52 1014.17/291.52 (0) CpxTRS 1014.17/291.52 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1014.17/291.52 (2) CpxWeightedTrs 1014.17/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1014.17/291.52 (4) CpxTypedWeightedTrs 1014.17/291.52 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1014.17/291.52 (6) CpxTypedWeightedCompleteTrs 1014.17/291.52 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1014.17/291.52 (8) CpxTypedWeightedCompleteTrs 1014.17/291.52 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1014.17/291.52 (10) CpxRNTS 1014.17/291.52 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1014.17/291.52 (12) CpxRNTS 1014.17/291.52 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 1014.17/291.52 (14) CpxRNTS 1014.17/291.52 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1014.17/291.52 (16) CpxRNTS 1014.17/291.52 (17) IntTrsBoundProof [UPPER BOUND(ID), 3592 ms] 1014.17/291.52 (18) CpxRNTS 1014.17/291.52 (19) IntTrsBoundProof [UPPER BOUND(ID), 3555 ms] 1014.17/291.52 (20) CpxRNTS 1014.17/291.52 (21) FinalProof [FINISHED, 0 ms] 1014.17/291.52 (22) BOUNDS(1, n^5) 1014.17/291.52 (23) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1014.17/291.52 (24) TRS for Loop Detection 1014.17/291.52 (25) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1014.17/291.52 (26) BEST 1014.17/291.52 (27) proven lower bound 1014.17/291.52 (28) LowerBoundPropagationProof [FINISHED, 0 ms] 1014.17/291.52 (29) BOUNDS(n^1, INF) 1014.17/291.52 (30) TRS for Loop Detection 1014.17/291.52 1014.17/291.52 1014.17/291.52 ---------------------------------------- 1014.17/291.52 1014.17/291.52 (0) 1014.17/291.52 Obligation: 1014.17/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^5). 1014.17/291.52 1014.17/291.52 1014.17/291.52 The TRS R consists of the following rules: 1014.17/291.52 1014.17/291.52 f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) 1014.17/291.52 f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) 1014.17/291.52 f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) 1014.17/291.52 f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) 1014.17/291.52 f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) 1014.17/291.52 f(0, 0, 0, 0, 0) -> 0 1014.17/291.52 1014.17/291.52 S is empty. 1014.17/291.52 Rewrite Strategy: INNERMOST 1014.17/291.52 ---------------------------------------- 1014.17/291.52 1014.17/291.52 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1014.17/291.52 Transformed relative TRS to weighted TRS 1014.17/291.52 ---------------------------------------- 1014.17/291.52 1014.17/291.52 (2) 1014.17/291.52 Obligation: 1014.17/291.52 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^5). 1014.17/291.52 1014.17/291.52 1014.17/291.52 The TRS R consists of the following rules: 1014.17/291.52 1014.17/291.52 f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) [1] 1014.17/291.52 f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) [1] 1014.17/291.52 f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) [1] 1014.17/291.52 f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) [1] 1014.17/291.52 f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) [1] 1014.17/291.52 f(0, 0, 0, 0, 0) -> 0 [1] 1014.17/291.52 1014.17/291.52 Rewrite Strategy: INNERMOST 1014.17/291.52 ---------------------------------------- 1014.17/291.52 1014.17/291.52 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1014.17/291.52 Infered types. 1014.17/291.52 ---------------------------------------- 1014.17/291.52 1014.17/291.52 (4) 1014.17/291.52 Obligation: 1014.17/291.52 Runtime Complexity Weighted TRS with Types. 1014.17/291.52 The TRS R consists of the following rules: 1014.17/291.52 1014.17/291.52 f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) [1] 1014.17/291.52 f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) [1] 1014.17/291.52 f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) [1] 1014.17/291.52 f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) [1] 1014.17/291.52 f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) [1] 1014.17/291.52 f(0, 0, 0, 0, 0) -> 0 [1] 1014.17/291.52 1014.17/291.52 The TRS has the following type information: 1014.17/291.52 f :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 1014.17/291.52 s :: s:0 -> s:0
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