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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307947
details
property
value
status
complete
benchmark
test77.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n102.star.cs.uiowa.edu
space
Strategy_removed_mixed_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.80798 seconds
cpu usage
21.5577
user time
19.9106
system time
1.64708
max virtual memory
1.9207756E7
max residence set size
3943200.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
21.46/7.73 WORST_CASE(Omega(n^1), O(n^1)) 21.47/7.74 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 21.47/7.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.47/7.74 21.47/7.74 21.47/7.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.47/7.74 21.47/7.74 (0) CpxTRS 21.47/7.74 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 21.47/7.74 (2) CpxTRS 21.47/7.74 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 21.47/7.74 (4) CdtProblem 21.47/7.74 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 21.47/7.74 (6) CdtProblem 21.47/7.74 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 21.47/7.74 (8) CdtProblem 21.47/7.74 (9) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 21.47/7.74 (10) CdtProblem 21.47/7.74 (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 21.47/7.74 (12) CdtProblem 21.47/7.74 (13) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] 21.47/7.74 (14) CdtProblem 21.47/7.74 (15) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 21.47/7.74 (16) CdtProblem 21.47/7.74 (17) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 21.47/7.74 (18) CdtProblem 21.47/7.74 (19) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 21.47/7.74 (20) CdtProblem 21.47/7.74 (21) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 21.47/7.74 (22) CdtProblem 21.47/7.74 (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] 21.47/7.74 (24) CdtProblem 21.47/7.74 (25) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 21.47/7.74 (26) BOUNDS(1, 1) 21.47/7.74 (27) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 21.47/7.74 (28) TRS for Loop Detection 21.47/7.74 (29) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 21.47/7.74 (30) BEST 21.47/7.74 (31) proven lower bound 21.47/7.74 (32) LowerBoundPropagationProof [FINISHED, 0 ms] 21.47/7.74 (33) BOUNDS(n^1, INF) 21.47/7.74 (34) TRS for Loop Detection 21.47/7.74 21.47/7.74 21.47/7.74 ---------------------------------------- 21.47/7.74 21.47/7.74 (0) 21.47/7.74 Obligation: 21.47/7.74 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.47/7.74 21.47/7.74 21.47/7.74 The TRS R consists of the following rules: 21.47/7.74 21.47/7.74 +(X, 0) -> X 21.47/7.74 +(X, s(Y)) -> s(+(X, Y)) 21.47/7.74 double(X) -> +(X, X) 21.47/7.74 f(0, s(0), X) -> f(X, double(X), X) 21.47/7.74 g(X, Y) -> X 21.47/7.74 g(X, Y) -> Y 21.47/7.74 21.47/7.74 S is empty. 21.47/7.74 Rewrite Strategy: FULL 21.47/7.74 ---------------------------------------- 21.47/7.74 21.47/7.74 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 21.47/7.74 Converted rc-obligation to irc-obligation. 21.47/7.74 21.47/7.74 The duplicating contexts are: 21.47/7.74 double([]) 21.47/7.74 f(0, s(0), []) 21.47/7.74 21.47/7.74 21.47/7.74 The defined contexts are: 21.47/7.74 f(x0, [], x2) 21.47/7.74 21.47/7.74 21.47/7.74 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 21.47/7.74 ---------------------------------------- 21.47/7.74 21.47/7.74 (2) 21.47/7.74 Obligation: 21.47/7.74 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 21.47/7.74 21.47/7.74 21.47/7.74 The TRS R consists of the following rules: 21.47/7.74 21.47/7.74 +(X, 0) -> X 21.47/7.74 +(X, s(Y)) -> s(+(X, Y)) 21.47/7.74 double(X) -> +(X, X) 21.47/7.74 f(0, s(0), X) -> f(X, double(X), X) 21.47/7.74 g(X, Y) -> X 21.47/7.74 g(X, Y) -> Y 21.47/7.74 21.47/7.74 S is empty. 21.47/7.74 Rewrite Strategy: INNERMOST 21.47/7.74 ---------------------------------------- 21.47/7.74 21.47/7.74 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 21.47/7.74 Converted Cpx (relative) TRS to CDT 21.47/7.74 ----------------------------------------
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