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Runti Compl Full Rewri 10127 pair #381903138
details
property
value
status
complete
benchmark
2.20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n034.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.26881098747 seconds
cpu usage
20.539443883
max memory
3.90674432E9
stage attributes
key
value
output-size
14803
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) InliningProof [UPPER BOUND(ID), 55 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 514 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 80 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 207 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 2 ms] (30) CpxRNTS (31) FinalProof [FINISHED, 0 ms] (32) BOUNDS(1, n^1) (33) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (34) TRS for Loop Detection (35) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (36) BEST (37) proven lower bound (38) LowerBoundPropagationProof [FINISHED, 0 ms] (39) BOUNDS(n^1, INF) (40) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: sum(0) -> 0 sum(s(x)) -> +(sqr(s(x)), sum(x)) sqr(x) -> *(x, x) sum(s(x)) -> +(*(s(x), s(x)), sum(x)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS does not nest defined symbols, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: sum(0) -> 0 sum(s(x)) -> +(sqr(s(x)), sum(x)) sqr(x) -> *(x, x) sum(s(x)) -> +(*(s(x), s(x)), sum(x)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ----------------------------------------
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