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Runti Compl Inner Rewri 22807 pair #381904727
details
property
value
status
complete
benchmark
gexgcd2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.002389193 seconds
cpu usage
330.241977069
max memory
5.307826176E9
stage attributes
key
value
output-size
35225
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
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^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 245 ms] (2) CpxRelTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 84 ms] (14) CdtProblem (15) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 202 ms] (20) CdtProblem (21) CdtKnowledgeProof [FINISHED, 0 ms] (22) BOUNDS(1, 1) (23) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxRelTRS (25) SlicingProof [LOWER BOUND(ID), 0 ms] (26) CpxRelTRS (27) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (28) typed CpxTrs (29) OrderProof [LOWER BOUND(ID), 0 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 530 ms] (32) BEST (33) proven lower bound (34) LowerBoundPropagationProof [FINISHED, 0 ms] (35) BOUNDS(n^1, INF) (36) typed CpxTrs (37) RewriteLemmaProof [LOWER BOUND(ID), 58 ms] (38) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: monus(S(x'), S(x)) -> monus(x', x) gcd(x, y) -> gcd[Ite](equal0(x, y), x, y) equal0(a, b) -> equal0[Ite](<(a, b), a, b) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False gcd[Ite](False, x, y) -> gcd[False][Ite](<(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(y, monus(y, x)) gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y) equal0[Ite](False, a, b) -> False equal0[Ite](True, a, b) -> equal0[True][Ite](<(b, a), a, b) equal0[True][Ite](False, a, b) -> False equal0[True][Ite](True, a, b) -> True Rewrite Strategy: INNERMOST ---------------------------------------- (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: monus(S(x'), S(x)) -> monus(x', x) gcd(x, y) -> gcd[Ite](equal0(x, y), x, y) equal0(a, b) -> equal0[Ite](<(a, b), a, b) The (relative) TRS S consists of the following rules:
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