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Runti Compl Full Rewri 10127 pair #381902605
details
property
value
status
complete
benchmark
22.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
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.73258209229 seconds
cpu usage
21.518734394
max memory
4.067282944E9
stage attributes
key
value
output-size
11434
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 2 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 13 ms] (10) CdtProblem (11) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (18) CdtProblem (19) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] (22) CdtProblem (23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (24) BOUNDS(1, 1) (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (26) TRS for Loop Detection (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (28) BEST (29) proven lower bound (30) LowerBoundPropagationProof [FINISHED, 0 ms] (31) BOUNDS(n^1, INF) (32) 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(x, 0) -> s(0) f(s(x), s(y)) -> s(f(x, y)) g(0, x) -> g(f(x, x), x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: g(0, []) The defined contexts are: g([], x1) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, 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: f(x, 0) -> s(0) f(s(x), s(y)) -> s(f(x, y)) g(0, x) -> g(f(x, x), x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation:
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