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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313889
details
property
value
status
complete
benchmark
7.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n159.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.595 seconds
cpu usage
628.947
user time
622.057
system time
6.89104
max virtual memory
3.8236704E7
max residence set size
8532208.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
628.79/291.51 WORST_CASE(Omega(n^1), O(n^2)) 628.79/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 628.79/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 628.79/291.54 628.79/291.54 628.79/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 628.79/291.54 628.79/291.54 (0) CpxTRS 628.79/291.54 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 628.79/291.54 (2) CpxWeightedTrs 628.79/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 628.79/291.54 (4) CpxTypedWeightedTrs 628.79/291.54 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 628.79/291.54 (6) CpxTypedWeightedCompleteTrs 628.79/291.54 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 628.79/291.54 (8) CpxTypedWeightedCompleteTrs 628.79/291.54 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 628.79/291.54 (10) CpxRNTS 628.79/291.54 (11) InliningProof [UPPER BOUND(ID), 243 ms] 628.79/291.54 (12) CpxRNTS 628.79/291.54 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 628.79/291.54 (14) CpxRNTS 628.79/291.54 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 628.79/291.54 (16) CpxRNTS 628.79/291.54 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 628.79/291.54 (18) CpxRNTS 628.79/291.54 (19) IntTrsBoundProof [UPPER BOUND(ID), 280 ms] 628.79/291.54 (20) CpxRNTS 628.79/291.54 (21) IntTrsBoundProof [UPPER BOUND(ID), 89 ms] 628.79/291.54 (22) CpxRNTS 628.79/291.54 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 628.79/291.54 (24) CpxRNTS 628.79/291.54 (25) IntTrsBoundProof [UPPER BOUND(ID), 139 ms] 628.79/291.54 (26) CpxRNTS 628.79/291.54 (27) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] 628.79/291.54 (28) CpxRNTS 628.79/291.54 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 628.79/291.54 (30) CpxRNTS 628.79/291.54 (31) IntTrsBoundProof [UPPER BOUND(ID), 528 ms] 628.79/291.54 (32) CpxRNTS 628.79/291.54 (33) IntTrsBoundProof [UPPER BOUND(ID), 289 ms] 628.79/291.54 (34) CpxRNTS 628.79/291.54 (35) FinalProof [FINISHED, 0 ms] 628.79/291.54 (36) BOUNDS(1, n^2) 628.79/291.54 (37) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 628.79/291.54 (38) TRS for Loop Detection 628.79/291.54 (39) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 628.79/291.54 (40) BEST 628.79/291.54 (41) proven lower bound 628.79/291.54 (42) LowerBoundPropagationProof [FINISHED, 0 ms] 628.79/291.54 (43) BOUNDS(n^1, INF) 628.79/291.54 (44) TRS for Loop Detection 628.79/291.54 628.79/291.54 628.79/291.54 ---------------------------------------- 628.79/291.54 628.79/291.54 (0) 628.79/291.54 Obligation: 628.79/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 628.79/291.54 628.79/291.54 628.79/291.54 The TRS R consists of the following rules: 628.79/291.54 628.79/291.54 cond(true, x) -> cond(odd(x), p(p(p(x)))) 628.79/291.54 odd(0) -> false 628.79/291.54 odd(s(0)) -> true 628.79/291.54 odd(s(s(x))) -> odd(x) 628.79/291.54 p(0) -> 0 628.79/291.54 p(s(x)) -> x 628.79/291.54 628.79/291.54 S is empty. 628.79/291.54 Rewrite Strategy: INNERMOST 628.79/291.54 ---------------------------------------- 628.79/291.54 628.79/291.54 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 628.79/291.54 Transformed relative TRS to weighted TRS 628.79/291.54 ---------------------------------------- 628.79/291.54 628.79/291.54 (2) 628.79/291.54 Obligation: 628.79/291.54 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 628.79/291.54 628.79/291.54 628.79/291.54 The TRS R consists of the following rules: 628.79/291.54 628.79/291.54 cond(true, x) -> cond(odd(x), p(p(p(x)))) [1] 628.79/291.54 odd(0) -> false [1] 628.79/291.54 odd(s(0)) -> true [1] 628.79/291.54 odd(s(s(x))) -> odd(x) [1] 628.79/291.54 p(0) -> 0 [1] 628.79/291.54 p(s(x)) -> x [1] 628.79/291.54 628.79/291.54 Rewrite Strategy: INNERMOST 628.79/291.54 ---------------------------------------- 628.79/291.54 628.79/291.54 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 628.79/291.54 Infered types. 628.79/291.54 ---------------------------------------- 628.79/291.54 628.79/291.54 (4)
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