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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313350
details
property
value
status
complete
benchmark
t002.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.615 seconds
cpu usage
318.497
user time
315.603
system time
2.89455
max virtual memory
1.9277344E7
max residence set size
5250704.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
318.34/291.56 WORST_CASE(Omega(n^1), O(n^2)) 318.34/291.58 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 318.34/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 318.34/291.58 318.34/291.58 318.34/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 318.34/291.58 318.34/291.58 (0) CpxTRS 318.34/291.58 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 318.34/291.58 (2) CpxWeightedTrs 318.34/291.58 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 318.34/291.58 (4) CpxWeightedTrs 318.34/291.58 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 318.34/291.58 (6) CpxTypedWeightedTrs 318.34/291.58 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 318.34/291.58 (8) CpxTypedWeightedCompleteTrs 318.34/291.58 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 318.34/291.58 (10) CpxTypedWeightedCompleteTrs 318.34/291.58 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 318.34/291.58 (12) CpxRNTS 318.34/291.58 (13) InliningProof [UPPER BOUND(ID), 0 ms] 318.34/291.58 (14) CpxRNTS 318.34/291.58 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 318.34/291.58 (16) CpxRNTS 318.34/291.58 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 4 ms] 318.34/291.58 (18) CpxRNTS 318.34/291.58 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 318.34/291.58 (20) CpxRNTS 318.34/291.58 (21) IntTrsBoundProof [UPPER BOUND(ID), 375 ms] 318.34/291.58 (22) CpxRNTS 318.34/291.58 (23) IntTrsBoundProof [UPPER BOUND(ID), 99 ms] 318.34/291.58 (24) CpxRNTS 318.34/291.58 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 318.34/291.58 (26) CpxRNTS 318.34/291.58 (27) IntTrsBoundProof [UPPER BOUND(ID), 332 ms] 318.34/291.58 (28) CpxRNTS 318.34/291.58 (29) IntTrsBoundProof [UPPER BOUND(ID), 156 ms] 318.34/291.58 (30) CpxRNTS 318.34/291.58 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 318.34/291.58 (32) CpxRNTS 318.34/291.58 (33) IntTrsBoundProof [UPPER BOUND(ID), 331 ms] 318.34/291.58 (34) CpxRNTS 318.34/291.58 (35) IntTrsBoundProof [UPPER BOUND(ID), 73 ms] 318.34/291.58 (36) CpxRNTS 318.34/291.58 (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 318.34/291.58 (38) CpxRNTS 318.34/291.58 (39) IntTrsBoundProof [UPPER BOUND(ID), 1030 ms] 318.34/291.58 (40) CpxRNTS 318.34/291.58 (41) IntTrsBoundProof [UPPER BOUND(ID), 551 ms] 318.34/291.58 (42) CpxRNTS 318.34/291.58 (43) FinalProof [FINISHED, 0 ms] 318.34/291.58 (44) BOUNDS(1, n^2) 318.34/291.58 (45) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 318.34/291.58 (46) CpxTRS 318.34/291.58 (47) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 318.34/291.58 (48) typed CpxTrs 318.34/291.58 (49) OrderProof [LOWER BOUND(ID), 0 ms] 318.34/291.58 (50) typed CpxTrs 318.34/291.58 (51) RewriteLemmaProof [LOWER BOUND(ID), 271 ms] 318.34/291.58 (52) BEST 318.34/291.58 (53) proven lower bound 318.34/291.58 (54) LowerBoundPropagationProof [FINISHED, 0 ms] 318.34/291.58 (55) BOUNDS(n^1, INF) 318.34/291.58 (56) typed CpxTrs 318.34/291.58 (57) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] 318.34/291.58 (58) typed CpxTrs 318.34/291.58 318.34/291.58 318.34/291.58 ---------------------------------------- 318.34/291.58 318.34/291.58 (0) 318.34/291.58 Obligation: 318.34/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 318.34/291.58 318.34/291.58 318.34/291.58 The TRS R consists of the following rules: 318.34/291.58 318.34/291.58 leq(0, y) -> true 318.34/291.58 leq(s(x), 0) -> false 318.34/291.58 leq(s(x), s(y)) -> leq(x, y) 318.34/291.58 if(true, x, y) -> x 318.34/291.58 if(false, x, y) -> y 318.34/291.58 -(x, 0) -> x 318.34/291.58 -(s(x), s(y)) -> -(x, y) 318.34/291.58 mod(0, y) -> 0 318.34/291.58 mod(s(x), 0) -> 0 318.34/291.58 mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) 318.34/291.58 318.34/291.58 S is empty. 318.34/291.58 Rewrite Strategy: INNERMOST 318.34/291.58 ---------------------------------------- 318.34/291.58 318.34/291.58 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 318.34/291.58 Transformed relative TRS to weighted TRS 318.34/291.58 ---------------------------------------- 318.34/291.58 318.34/291.58 (2) 318.34/291.58 Obligation: 318.34/291.58 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 318.34/291.58
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