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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308417
details
property
value
status
complete
benchmark
2.29.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.93082 seconds
cpu usage
23.6001
user time
22.1694
system time
1.43075
max virtual memory
1.8815016E7
max residence set size
3927376.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
23.31/6.84 WORST_CASE(Omega(n^1), O(n^1)) 23.31/6.85 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 23.31/6.85 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 23.31/6.85 23.31/6.85 23.31/6.85 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 23.31/6.85 23.31/6.85 (0) CpxTRS 23.31/6.85 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 23.31/6.85 (2) CpxTRS 23.31/6.85 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 23.31/6.85 (4) CdtProblem 23.31/6.85 (5) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 23.31/6.85 (6) CdtProblem 23.31/6.85 (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 23.31/6.85 (8) CdtProblem 23.31/6.85 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 23.31/6.85 (10) CdtProblem 23.31/6.85 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 15 ms] 23.31/6.85 (12) CdtProblem 23.31/6.85 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 23.31/6.85 (14) BOUNDS(1, 1) 23.31/6.85 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 23.31/6.85 (16) TRS for Loop Detection 23.31/6.85 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 23.31/6.85 (18) BEST 23.31/6.85 (19) proven lower bound 23.31/6.85 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 23.31/6.85 (21) BOUNDS(n^1, INF) 23.31/6.85 (22) TRS for Loop Detection 23.31/6.85 23.31/6.85 23.31/6.85 ---------------------------------------- 23.31/6.85 23.31/6.85 (0) 23.31/6.85 Obligation: 23.31/6.85 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 23.31/6.85 23.31/6.85 23.31/6.85 The TRS R consists of the following rules: 23.31/6.85 23.31/6.85 prime(0) -> false 23.31/6.85 prime(s(0)) -> false 23.31/6.85 prime(s(s(x))) -> prime1(s(s(x)), s(x)) 23.31/6.85 prime1(x, 0) -> false 23.31/6.85 prime1(x, s(0)) -> true 23.31/6.85 prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) 23.31/6.85 divp(x, y) -> =(rem(x, y), 0) 23.31/6.85 23.31/6.85 S is empty. 23.31/6.85 Rewrite Strategy: FULL 23.31/6.85 ---------------------------------------- 23.31/6.85 23.31/6.85 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 23.31/6.85 Converted rc-obligation to irc-obligation. 23.31/6.85 23.31/6.85 As the TRS does not nest defined symbols, we have rc = irc. 23.31/6.85 ---------------------------------------- 23.31/6.85 23.31/6.85 (2) 23.31/6.85 Obligation: 23.31/6.85 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 23.31/6.85 23.31/6.85 23.31/6.85 The TRS R consists of the following rules: 23.31/6.85 23.31/6.85 prime(0) -> false 23.31/6.85 prime(s(0)) -> false 23.31/6.85 prime(s(s(x))) -> prime1(s(s(x)), s(x)) 23.31/6.85 prime1(x, 0) -> false 23.31/6.85 prime1(x, s(0)) -> true 23.31/6.85 prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) 23.31/6.85 divp(x, y) -> =(rem(x, y), 0) 23.31/6.85 23.31/6.85 S is empty. 23.31/6.85 Rewrite Strategy: INNERMOST 23.31/6.85 ---------------------------------------- 23.31/6.85 23.31/6.85 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 23.31/6.85 Converted Cpx (relative) TRS to CDT 23.31/6.85 ---------------------------------------- 23.31/6.85 23.31/6.85 (4) 23.31/6.85 Obligation: 23.31/6.85 Complexity Dependency Tuples Problem 23.31/6.85 23.31/6.85 Rules: 23.31/6.85 prime(0) -> false 23.31/6.85 prime(s(0)) -> false 23.31/6.85 prime(s(s(z0))) -> prime1(s(s(z0)), s(z0)) 23.31/6.85 prime1(z0, 0) -> false 23.31/6.85 prime1(z0, s(0)) -> true 23.31/6.85 prime1(z0, s(s(z1))) -> and(not(divp(s(s(z1)), z0)), prime1(z0, s(z1))) 23.31/6.85 divp(z0, z1) -> =(rem(z0, z1), 0) 23.31/6.85 Tuples: 23.31/6.85 PRIME(0) -> c 23.31/6.85 PRIME(s(0)) -> c1 23.31/6.85 PRIME(s(s(z0))) -> c2(PRIME1(s(s(z0)), s(z0))) 23.31/6.85 PRIME1(z0, 0) -> c3 23.31/6.85 PRIME1(z0, s(0)) -> c4
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