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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313850
details
property
value
status
complete
benchmark
gexgcd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n112.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.90985 seconds
cpu usage
25.9489
user time
24.6826
system time
1.2663
max virtual memory
1.9315944E7
max residence set size
3755064.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
24.94/7.24 WORST_CASE(Omega(n^1), O(n^1)) 24.94/7.25 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 24.94/7.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 24.94/7.25 24.94/7.25 24.94/7.25 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 24.94/7.25 24.94/7.25 (0) CpxRelTRS 24.94/7.25 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 148 ms] 24.94/7.25 (2) CpxRelTRS 24.94/7.25 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 24.94/7.25 (4) CdtProblem 24.94/7.25 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 24.94/7.25 (6) CdtProblem 24.94/7.25 (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 24.94/7.25 (8) CdtProblem 24.94/7.25 (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] 24.94/7.25 (10) CdtProblem 24.94/7.25 (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 24.94/7.25 (12) CdtProblem 24.94/7.25 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 179 ms] 24.94/7.25 (14) CdtProblem 24.94/7.25 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 91 ms] 24.94/7.25 (16) CdtProblem 24.94/7.25 (17) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 24.94/7.25 (18) CdtProblem 24.94/7.25 (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 78 ms] 24.94/7.25 (20) CdtProblem 24.94/7.25 (21) CdtKnowledgeProof [FINISHED, 0 ms] 24.94/7.25 (22) BOUNDS(1, 1) 24.94/7.25 (23) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 24.94/7.25 (24) TRS for Loop Detection 24.94/7.25 (25) DecreasingLoopProof [LOWER BOUND(ID), 408 ms] 24.94/7.25 (26) BEST 24.94/7.25 (27) proven lower bound 24.94/7.25 (28) LowerBoundPropagationProof [FINISHED, 0 ms] 24.94/7.25 (29) BOUNDS(n^1, INF) 24.94/7.25 (30) TRS for Loop Detection 24.94/7.25 24.94/7.25 24.94/7.25 ---------------------------------------- 24.94/7.25 24.94/7.25 (0) 24.94/7.25 Obligation: 24.94/7.25 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 24.94/7.25 24.94/7.25 24.94/7.25 The TRS R consists of the following rules: 24.94/7.25 24.94/7.25 m2(S(0), b, res, True) -> False 24.94/7.25 m2(S(S(x)), b, res, True) -> True 24.94/7.25 m2(0, b, res, True) -> False 24.94/7.25 m3(S(0), b, res, t) -> False 24.94/7.25 m3(S(S(x)), b, res, t) -> True 24.94/7.25 m3(0, b, res, t) -> False 24.94/7.25 l8(res, y, res', True, mtmp, t) -> res 24.94/7.25 l5(x, y, res, tmp, mtmp, True) -> 0 24.94/7.25 help1(S(0)) -> False 24.94/7.25 help1(S(S(x))) -> True 24.94/7.25 e4(a, b, res, False) -> False 24.94/7.25 e4(a, b, res, True) -> True 24.94/7.25 e2(a, b, res, False) -> False 24.94/7.25 l15(x, y, res, tmp, False, t) -> l16(x, y, gcd(y, 0), tmp, False, t) 24.94/7.25 l15(x, y, res, tmp, True, t) -> l16(x, y, gcd(y, S(0)), tmp, True, t) 24.94/7.25 l13(x, y, res, tmp, False, t) -> l16(x, y, gcd(0, y), tmp, False, t) 24.94/7.25 l13(x, y, res, tmp, True, t) -> l16(x, y, gcd(S(0), y), tmp, True, t) 24.94/7.25 m4(S(x'), S(x), res, t) -> m5(S(x'), S(x), monus(x', x), t) 24.94/7.25 m2(a, b, res, False) -> m4(a, b, res, False) 24.94/7.25 l8(x, y, res, False, mtmp, t) -> l10(x, y, res, False, mtmp, t) 24.94/7.25 l5(x, y, res, tmp, mtmp, False) -> l7(x, y, res, tmp, mtmp, False) 24.94/7.25 l2(x, y, res, tmp, mtmp, False) -> l3(x, y, res, tmp, mtmp, False) 24.94/7.25 l2(x, y, res, tmp, mtmp, True) -> res 24.94/7.25 l11(x, y, res, tmp, mtmp, False) -> l14(x, y, res, tmp, mtmp, False) 24.94/7.25 l11(x, y, res, tmp, mtmp, True) -> l12(x, y, res, tmp, mtmp, True) 24.94/7.25 help1(0) -> False 24.94/7.25 e2(a, b, res, True) -> e3(a, b, res, True) 24.94/7.25 bool2Nat(False) -> 0 24.94/7.25 bool2Nat(True) -> S(0) 24.94/7.25 m1(a, x, res, t) -> m2(a, x, res, False) 24.94/7.25 l9(res, y, res', tmp, mtmp, t) -> res 24.94/7.25 l6(x, y, res, tmp, mtmp, t) -> 0 24.94/7.25 l4(x', x, res, tmp, mtmp, t) -> l5(x', x, res, tmp, mtmp, False) 24.94/7.25 l1(x, y, res, tmp, mtmp, t) -> l2(x, y, res, tmp, mtmp, False) 24.94/7.25 e7(a, b, res, t) -> False 24.94/7.25 e6(a, b, res, t) -> False 24.94/7.25 e5(a, b, res, t) -> True 24.94/7.25 monus(a, b) -> m1(a, b, False, False) 24.94/7.25 m5(a, b, res, t) -> res 24.94/7.25 l7(x, y, res, tmp, mtmp, t) -> l8(x, y, res, equal0(x, y), mtmp, t) 24.94/7.25 l3(x, y, res, tmp, mtmp, t) -> l4(x, y, 0, tmp, mtmp, t) 24.94/7.25 l16(x, y, res, tmp, mtmp, t) -> res 24.94/7.25 l14(x, y, res, tmp, mtmp, t) -> l15(x, y, res, tmp, monus(x, y), t) 24.94/7.25 l12(x, y, res, tmp, mtmp, t) -> l13(x, y, res, tmp, monus(x, y), t) 24.94/7.25 l10(x, y, res, tmp, mtmp, t) -> l11(x, y, res, tmp, mtmp, <(x, y)) 24.94/7.25 gcd(x, y) -> l1(x, y, 0, False, False, False) 24.94/7.25 equal0(a, b) -> e1(a, b, False, False) 24.94/7.25 e8(a, b, res, t) -> res 24.94/7.25 e3(a, b, res, t) -> e4(a, b, res, <(b, a)) 24.94/7.25 e1(a, b, res, t) -> e2(a, b, res, <(a, b)) 24.94/7.25
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40