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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313867
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
n133.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.58 seconds
cpu usage
332.891
user time
329.254
system time
3.63696
max virtual memory
3.7573568E7
max residence set size
5236300.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
332.74/291.50 WORST_CASE(Omega(n^1), O(n^2)) 332.75/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 332.75/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 332.75/291.52 332.75/291.52 332.75/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 332.75/291.52 332.75/291.52 (0) CpxRelTRS 332.75/291.52 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 250 ms] 332.75/291.52 (2) CpxRelTRS 332.75/291.52 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 332.75/291.52 (4) CdtProblem 332.75/291.52 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 332.75/291.52 (6) CdtProblem 332.75/291.52 (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 332.75/291.52 (8) CdtProblem 332.75/291.52 (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] 332.75/291.52 (10) CdtProblem 332.75/291.52 (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 332.75/291.52 (12) CdtProblem 332.75/291.52 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 68 ms] 332.75/291.52 (14) CdtProblem 332.75/291.52 (15) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 332.75/291.52 (16) CdtProblem 332.75/291.52 (17) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 332.75/291.52 (18) CdtProblem 332.75/291.52 (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 221 ms] 332.75/291.52 (20) CdtProblem 332.75/291.52 (21) CdtKnowledgeProof [FINISHED, 0 ms] 332.75/291.52 (22) BOUNDS(1, 1) 332.75/291.52 (23) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 332.75/291.52 (24) CpxRelTRS 332.75/291.52 (25) SlicingProof [LOWER BOUND(ID), 0 ms] 332.75/291.52 (26) CpxRelTRS 332.75/291.52 (27) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 332.75/291.52 (28) typed CpxTrs 332.75/291.52 (29) OrderProof [LOWER BOUND(ID), 0 ms] 332.75/291.52 (30) typed CpxTrs 332.75/291.52 (31) RewriteLemmaProof [LOWER BOUND(ID), 504 ms] 332.75/291.52 (32) BEST 332.75/291.52 (33) proven lower bound 332.75/291.52 (34) LowerBoundPropagationProof [FINISHED, 0 ms] 332.75/291.52 (35) BOUNDS(n^1, INF) 332.75/291.52 (36) typed CpxTrs 332.75/291.52 (37) RewriteLemmaProof [LOWER BOUND(ID), 53 ms] 332.75/291.52 (38) typed CpxTrs 332.75/291.52 332.75/291.52 332.75/291.52 ---------------------------------------- 332.75/291.52 332.75/291.52 (0) 332.75/291.52 Obligation: 332.75/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 332.75/291.52 332.75/291.52 332.75/291.52 The TRS R consists of the following rules: 332.75/291.52 332.75/291.52 monus(S(x'), S(x)) -> monus(x', x) 332.75/291.52 gcd(x, y) -> gcd[Ite](equal0(x, y), x, y) 332.75/291.52 equal0(a, b) -> equal0[Ite](<(a, b), a, b) 332.75/291.52 332.75/291.52 The (relative) TRS S consists of the following rules: 332.75/291.52 332.75/291.52 <(S(x), S(y)) -> <(x, y) 332.75/291.52 <(0, S(y)) -> True 332.75/291.52 <(x, 0) -> False 332.75/291.52 gcd[Ite](False, x, y) -> gcd[False][Ite](<(x, y), x, y) 332.75/291.52 gcd[Ite](True, x, y) -> x 332.75/291.52 gcd[False][Ite](False, x, y) -> gcd(y, monus(y, x)) 332.75/291.52 gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y) 332.75/291.52 equal0[Ite](False, a, b) -> False 332.75/291.52 equal0[Ite](True, a, b) -> equal0[True][Ite](<(b, a), a, b) 332.75/291.52 equal0[True][Ite](False, a, b) -> False 332.75/291.52 equal0[True][Ite](True, a, b) -> True 332.75/291.52 332.75/291.52 Rewrite Strategy: INNERMOST 332.75/291.52 ---------------------------------------- 332.75/291.52 332.75/291.52 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 332.75/291.52 proved termination of relative rules 332.75/291.52 ---------------------------------------- 332.75/291.52 332.75/291.52 (2) 332.75/291.52 Obligation: 332.75/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 332.75/291.52 332.75/291.52 332.75/291.52 The TRS R consists of the following rules: 332.75/291.52 332.75/291.52 monus(S(x'), S(x)) -> monus(x', x) 332.75/291.52 gcd(x, y) -> gcd[Ite](equal0(x, y), x, y) 332.75/291.52 equal0(a, b) -> equal0[Ite](<(a, b), a, b) 332.75/291.52 332.75/291.52 The (relative) TRS S consists of the following rules: 332.75/291.52 332.75/291.52 <(S(x), S(y)) -> <(x, y) 332.75/291.52 <(0, S(y)) -> True 332.75/291.52 <(x, 0) -> False 332.75/291.52 gcd[Ite](False, x, y) -> gcd[False][Ite](<(x, y), x, y) 332.75/291.52 gcd[Ite](True, x, y) -> x
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