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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307697
details
property
value
status
complete
benchmark
#3.52.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.41183 seconds
cpu usage
16.9559
user time
15.7723
system time
1.18358
max virtual memory
1.8742636E7
max residence set size
3881732.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
16.78/5.24 WORST_CASE(Omega(n^1), O(n^1)) 16.78/5.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 16.78/5.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.78/5.25 16.78/5.25 16.78/5.25 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 16.78/5.25 16.78/5.25 (0) CpxTRS 16.78/5.25 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 16.78/5.25 (2) CpxTRS 16.78/5.25 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 16.78/5.25 (4) CdtProblem 16.78/5.25 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 16.78/5.25 (6) CdtProblem 16.78/5.25 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 32 ms] 16.78/5.25 (8) CdtProblem 16.78/5.25 (9) CdtKnowledgeProof [FINISHED, 0 ms] 16.78/5.25 (10) BOUNDS(1, 1) 16.78/5.25 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 16.78/5.25 (12) TRS for Loop Detection 16.78/5.25 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 16.78/5.25 (14) BEST 16.78/5.25 (15) proven lower bound 16.78/5.25 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 16.78/5.25 (17) BOUNDS(n^1, INF) 16.78/5.25 (18) TRS for Loop Detection 16.78/5.25 16.78/5.25 16.78/5.25 ---------------------------------------- 16.78/5.25 16.78/5.25 (0) 16.78/5.25 Obligation: 16.78/5.25 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 16.78/5.25 16.78/5.25 16.78/5.25 The TRS R consists of the following rules: 16.78/5.25 16.78/5.25 f(0, 1, x) -> f(s(x), x, x) 16.78/5.25 f(x, y, s(z)) -> s(f(0, 1, z)) 16.78/5.25 16.78/5.25 S is empty. 16.78/5.25 Rewrite Strategy: FULL 16.78/5.25 ---------------------------------------- 16.78/5.25 16.78/5.25 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 16.78/5.25 Converted rc-obligation to irc-obligation. 16.78/5.25 16.78/5.25 As the TRS does not nest defined symbols, we have rc = irc. 16.78/5.25 ---------------------------------------- 16.78/5.25 16.78/5.25 (2) 16.78/5.25 Obligation: 16.78/5.25 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 16.78/5.25 16.78/5.25 16.78/5.25 The TRS R consists of the following rules: 16.78/5.25 16.78/5.25 f(0, 1, x) -> f(s(x), x, x) 16.78/5.25 f(x, y, s(z)) -> s(f(0, 1, z)) 16.78/5.25 16.78/5.25 S is empty. 16.78/5.25 Rewrite Strategy: INNERMOST 16.78/5.25 ---------------------------------------- 16.78/5.25 16.78/5.25 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 16.78/5.25 Converted Cpx (relative) TRS to CDT 16.78/5.25 ---------------------------------------- 16.78/5.25 16.78/5.25 (4) 16.78/5.25 Obligation: 16.78/5.25 Complexity Dependency Tuples Problem 16.78/5.25 16.78/5.25 Rules: 16.78/5.25 f(0, 1, z0) -> f(s(z0), z0, z0) 16.78/5.25 f(z0, z1, s(z2)) -> s(f(0, 1, z2)) 16.78/5.25 Tuples: 16.78/5.25 F(0, 1, z0) -> c(F(s(z0), z0, z0)) 16.78/5.25 F(z0, z1, s(z2)) -> c1(F(0, 1, z2)) 16.78/5.25 S tuples: 16.78/5.25 F(0, 1, z0) -> c(F(s(z0), z0, z0)) 16.78/5.25 F(z0, z1, s(z2)) -> c1(F(0, 1, z2)) 16.78/5.25 K tuples:none 16.78/5.25 Defined Rule Symbols: f_3 16.78/5.25 16.78/5.25 Defined Pair Symbols: F_3 16.78/5.25 16.78/5.25 Compound Symbols: c_1, c1_1 16.78/5.25 16.78/5.25 16.78/5.25 ---------------------------------------- 16.78/5.25 16.78/5.25 (5) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) 16.78/5.25 The following rules are not usable and were removed: 16.78/5.25 f(0, 1, z0) -> f(s(z0), z0, z0) 16.78/5.25 f(z0, z1, s(z2)) -> s(f(0, 1, z2)) 16.78/5.25 16.78/5.25 ---------------------------------------- 16.78/5.25 16.78/5.25 (6) 16.78/5.25 Obligation:
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