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Runti Compl Full Rewri 10127 pair #381902963
details
property
value
status
complete
benchmark
2.07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.23792910576 seconds
cpu usage
19.053586544
max memory
3.452203008E9
stage attributes
key
value
output-size
13528
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 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), 1030 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 230 ms] (24) CpxRNTS (25) FinalProof [FINISHED, 0 ms] (26) BOUNDS(1, n^1) (27) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (28) TRS for Loop Detection (29) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (30) BEST (31) proven lower bound (32) LowerBoundPropagationProof [FINISHED, 0 ms] (33) BOUNDS(n^1, INF) (34) 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: f(0, y) -> y f(x, 0) -> x f(i(x), y) -> i(x) f(f(x, y), z) -> f(x, f(y, z)) f(g(x, y), z) -> g(f(x, z), f(y, z)) f(1, g(x, y)) -> x f(2, g(x, y)) -> y S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The TRS does not nest defined symbols. Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: f(f(x, y), z) -> f(x, f(y, z)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(0, y) -> y f(x, 0) -> x f(i(x), y) -> i(x) f(g(x, y), z) -> g(f(x, z), f(y, z)) f(1, g(x, y)) -> x f(2, g(x, y)) -> y S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS does not nest defined symbols, we have rc = irc.
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