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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308428
details
property
value
status
complete
benchmark
2.13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.28262 seconds
cpu usage
19.5307
user time
18.0453
system time
1.48543
max virtual memory
1.927436E7
max residence set size
3934932.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
19.27/7.22 WORST_CASE(Omega(n^1), O(n^1)) 19.43/7.24 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 19.43/7.24 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.43/7.24 19.43/7.24 19.43/7.24 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.43/7.24 19.43/7.24 (0) CpxTRS 19.43/7.24 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 19.43/7.24 (2) CpxTRS 19.43/7.24 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 19.43/7.24 (4) CpxWeightedTrs 19.43/7.24 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 19.43/7.24 (6) CpxWeightedTrs 19.43/7.24 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 19.43/7.24 (8) CpxTypedWeightedTrs 19.43/7.24 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 19.43/7.24 (10) CpxTypedWeightedCompleteTrs 19.43/7.24 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 19.43/7.24 (12) CpxTypedWeightedCompleteTrs 19.43/7.24 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 19.43/7.24 (14) CpxRNTS 19.43/7.24 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 19.43/7.24 (16) CpxRNTS 19.43/7.24 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 19.43/7.24 (18) CpxRNTS 19.43/7.24 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 19.43/7.24 (20) CpxRNTS 19.43/7.24 (21) IntTrsBoundProof [UPPER BOUND(ID), 433 ms] 19.43/7.24 (22) CpxRNTS 19.43/7.24 (23) IntTrsBoundProof [UPPER BOUND(ID), 116 ms] 19.43/7.24 (24) CpxRNTS 19.43/7.24 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 19.43/7.24 (26) CpxRNTS 19.43/7.24 (27) IntTrsBoundProof [UPPER BOUND(ID), 283 ms] 19.43/7.24 (28) CpxRNTS 19.43/7.24 (29) IntTrsBoundProof [UPPER BOUND(ID), 116 ms] 19.43/7.24 (30) CpxRNTS 19.43/7.24 (31) FinalProof [FINISHED, 0 ms] 19.43/7.24 (32) BOUNDS(1, n^1) 19.43/7.24 (33) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 19.43/7.24 (34) TRS for Loop Detection 19.43/7.24 (35) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 19.43/7.24 (36) BEST 19.43/7.24 (37) proven lower bound 19.43/7.24 (38) LowerBoundPropagationProof [FINISHED, 0 ms] 19.43/7.24 (39) BOUNDS(n^1, INF) 19.43/7.24 (40) TRS for Loop Detection 19.43/7.24 19.43/7.24 19.43/7.24 ---------------------------------------- 19.43/7.24 19.43/7.24 (0) 19.43/7.24 Obligation: 19.43/7.24 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.43/7.24 19.43/7.24 19.43/7.24 The TRS R consists of the following rules: 19.43/7.24 19.43/7.24 double(0) -> 0 19.43/7.24 double(s(x)) -> s(s(double(x))) 19.43/7.24 +(x, 0) -> x 19.43/7.24 +(x, s(y)) -> s(+(x, y)) 19.43/7.24 +(s(x), y) -> s(+(x, y)) 19.43/7.24 double(x) -> +(x, x) 19.43/7.24 19.43/7.24 S is empty. 19.43/7.24 Rewrite Strategy: FULL 19.43/7.24 ---------------------------------------- 19.43/7.24 19.43/7.24 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 19.43/7.24 Converted rc-obligation to irc-obligation. 19.43/7.24 19.43/7.24 As the TRS does not nest defined symbols, we have rc = irc. 19.43/7.24 ---------------------------------------- 19.43/7.24 19.43/7.24 (2) 19.43/7.24 Obligation: 19.43/7.24 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 19.43/7.24 19.43/7.24 19.43/7.24 The TRS R consists of the following rules: 19.43/7.24 19.43/7.24 double(0) -> 0 19.43/7.24 double(s(x)) -> s(s(double(x))) 19.43/7.24 +(x, 0) -> x 19.43/7.24 +(x, s(y)) -> s(+(x, y)) 19.43/7.24 +(s(x), y) -> s(+(x, y)) 19.43/7.24 double(x) -> +(x, x) 19.43/7.24 19.43/7.24 S is empty. 19.43/7.24 Rewrite Strategy: INNERMOST 19.43/7.24 ---------------------------------------- 19.43/7.24 19.43/7.24 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 19.43/7.24 Transformed relative TRS to weighted TRS 19.43/7.24 ---------------------------------------- 19.43/7.24 19.43/7.24 (4) 19.43/7.24 Obligation:
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