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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308432
details
property
value
status
complete
benchmark
4.05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n002.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.534 seconds
cpu usage
344.218
user time
338.736
system time
5.4827
max virtual memory
1.8943264E7
max residence set size
8577196.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
344.05/291.47 WORST_CASE(Omega(n^1), O(n^2)) 344.13/291.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 344.13/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 344.13/291.48 344.13/291.48 344.13/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 344.13/291.48 344.13/291.48 (0) CpxTRS 344.13/291.48 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 344.13/291.48 (2) CpxTRS 344.13/291.48 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 10 ms] 344.13/291.48 (4) CdtProblem 344.13/291.48 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 344.13/291.48 (6) CdtProblem 344.13/291.48 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 344.13/291.48 (8) CdtProblem 344.13/291.48 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 38 ms] 344.13/291.48 (10) CdtProblem 344.13/291.48 (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 344.13/291.48 (12) BOUNDS(1, 1) 344.13/291.48 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 344.13/291.48 (14) TRS for Loop Detection 344.13/291.48 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 344.13/291.48 (16) BEST 344.13/291.48 (17) proven lower bound 344.13/291.48 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 344.13/291.48 (19) BOUNDS(n^1, INF) 344.13/291.48 (20) TRS for Loop Detection 344.13/291.48 344.13/291.48 344.13/291.48 ---------------------------------------- 344.13/291.48 344.13/291.48 (0) 344.13/291.48 Obligation: 344.13/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 344.13/291.48 344.13/291.48 344.13/291.48 The TRS R consists of the following rules: 344.13/291.48 344.13/291.48 *(x, +(y, z)) -> +(*(x, y), *(x, z)) 344.13/291.48 *(+(x, y), z) -> +(*(x, z), *(y, z)) 344.13/291.48 *(x, 1) -> x 344.13/291.48 *(1, y) -> y 344.13/291.48 344.13/291.48 S is empty. 344.13/291.48 Rewrite Strategy: FULL 344.13/291.48 ---------------------------------------- 344.13/291.48 344.13/291.48 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 344.13/291.48 Converted rc-obligation to irc-obligation. 344.13/291.48 344.13/291.48 As the TRS does not nest defined symbols, we have rc = irc. 344.13/291.48 ---------------------------------------- 344.13/291.48 344.13/291.48 (2) 344.13/291.48 Obligation: 344.13/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 344.13/291.48 344.13/291.48 344.13/291.48 The TRS R consists of the following rules: 344.13/291.48 344.13/291.48 *(x, +(y, z)) -> +(*(x, y), *(x, z)) 344.13/291.48 *(+(x, y), z) -> +(*(x, z), *(y, z)) 344.13/291.48 *(x, 1) -> x 344.13/291.48 *(1, y) -> y 344.13/291.48 344.13/291.48 S is empty. 344.13/291.48 Rewrite Strategy: INNERMOST 344.13/291.48 ---------------------------------------- 344.13/291.48 344.13/291.48 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 344.13/291.48 Converted Cpx (relative) TRS to CDT 344.13/291.48 ---------------------------------------- 344.13/291.48 344.13/291.48 (4) 344.13/291.48 Obligation: 344.13/291.48 Complexity Dependency Tuples Problem 344.13/291.48 344.13/291.48 Rules: 344.13/291.48 *(z0, +(z1, z2)) -> +(*(z0, z1), *(z0, z2)) 344.13/291.48 *(+(z0, z1), z2) -> +(*(z0, z2), *(z1, z2)) 344.13/291.48 *(z0, 1) -> z0 344.13/291.48 *(1, z0) -> z0 344.13/291.48 Tuples: 344.13/291.48 *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) 344.13/291.48 *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) 344.13/291.48 *'(z0, 1) -> c2 344.13/291.48 *'(1, z0) -> c3 344.13/291.48 S tuples: 344.13/291.48 *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) 344.13/291.48 *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) 344.13/291.48 *'(z0, 1) -> c2 344.13/291.48 *'(1, z0) -> c3 344.13/291.48 K tuples:none 344.13/291.48 Defined Rule Symbols: *_2 344.13/291.48 344.13/291.48 Defined Pair Symbols: *'_2 344.13/291.48 344.13/291.48 Compound Symbols: c_2, c1_2, c2, c3 344.13/291.48
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