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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313313
details
property
value
status
complete
benchmark
division.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.645 seconds
cpu usage
1009.63
user time
998.086
system time
11.5484
max virtual memory
3.8043424E7
max residence set size
1.0981884E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1009.40/291.56 WORST_CASE(Omega(n^1), O(n^2)) 1009.50/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1009.50/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1009.50/291.57 1009.50/291.57 1009.50/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1009.50/291.57 1009.50/291.57 (0) CpxTRS 1009.50/291.57 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1009.50/291.57 (2) CpxWeightedTrs 1009.50/291.57 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1009.50/291.57 (4) CpxTypedWeightedTrs 1009.50/291.57 (5) CompletionProof [UPPER BOUND(ID), 3 ms] 1009.50/291.57 (6) CpxTypedWeightedCompleteTrs 1009.50/291.57 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1009.50/291.57 (8) CpxTypedWeightedCompleteTrs 1009.50/291.57 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1009.50/291.57 (10) CpxRNTS 1009.50/291.57 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 5 ms] 1009.50/291.57 (12) CpxRNTS 1009.50/291.57 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 1009.50/291.57 (14) CpxRNTS 1009.50/291.57 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1009.50/291.57 (16) CpxRNTS 1009.50/291.57 (17) IntTrsBoundProof [UPPER BOUND(ID), 448 ms] 1009.50/291.57 (18) CpxRNTS 1009.50/291.57 (19) IntTrsBoundProof [UPPER BOUND(ID), 139 ms] 1009.50/291.57 (20) CpxRNTS 1009.50/291.57 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1009.50/291.57 (22) CpxRNTS 1009.50/291.57 (23) IntTrsBoundProof [UPPER BOUND(ID), 334 ms] 1009.50/291.57 (24) CpxRNTS 1009.50/291.57 (25) IntTrsBoundProof [UPPER BOUND(ID), 96 ms] 1009.50/291.57 (26) CpxRNTS 1009.50/291.57 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1009.50/291.57 (28) CpxRNTS 1009.50/291.57 (29) IntTrsBoundProof [UPPER BOUND(ID), 251 ms] 1009.50/291.57 (30) CpxRNTS 1009.50/291.57 (31) IntTrsBoundProof [UPPER BOUND(ID), 114 ms] 1009.50/291.57 (32) CpxRNTS 1009.50/291.57 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1009.50/291.57 (34) CpxRNTS 1009.50/291.57 (35) IntTrsBoundProof [UPPER BOUND(ID), 2094 ms] 1009.50/291.57 (36) CpxRNTS 1009.50/291.57 (37) IntTrsBoundProof [UPPER BOUND(ID), 1501 ms] 1009.50/291.57 (38) CpxRNTS 1009.50/291.57 (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1009.50/291.57 (40) CpxRNTS 1009.50/291.57 (41) IntTrsBoundProof [UPPER BOUND(ID), 159 ms] 1009.50/291.57 (42) CpxRNTS 1009.50/291.57 (43) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 1009.50/291.57 (44) CpxRNTS 1009.50/291.57 (45) FinalProof [FINISHED, 0 ms] 1009.50/291.57 (46) BOUNDS(1, n^2) 1009.50/291.57 (47) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1009.50/291.57 (48) CpxTRS 1009.50/291.57 (49) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1009.50/291.57 (50) typed CpxTrs 1009.50/291.57 (51) OrderProof [LOWER BOUND(ID), 0 ms] 1009.50/291.57 (52) typed CpxTrs 1009.50/291.57 (53) RewriteLemmaProof [LOWER BOUND(ID), 282 ms] 1009.50/291.57 (54) BEST 1009.50/291.57 (55) proven lower bound 1009.50/291.57 (56) LowerBoundPropagationProof [FINISHED, 0 ms] 1009.50/291.57 (57) BOUNDS(n^1, INF) 1009.50/291.57 (58) typed CpxTrs 1009.50/291.57 (59) RewriteLemmaProof [LOWER BOUND(ID), 30 ms] 1009.50/291.57 (60) typed CpxTrs 1009.50/291.57 (61) RewriteLemmaProof [LOWER BOUND(ID), 81 ms] 1009.50/291.57 (62) typed CpxTrs 1009.50/291.57 1009.50/291.57 1009.50/291.57 ---------------------------------------- 1009.50/291.57 1009.50/291.57 (0) 1009.50/291.57 Obligation: 1009.50/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1009.50/291.57 1009.50/291.57 1009.50/291.57 The TRS R consists of the following rules: 1009.50/291.57 1009.50/291.57 division(x, y) -> div(x, y, 0) 1009.50/291.57 div(x, y, z) -> if(lt(x, y), x, y, inc(z)) 1009.50/291.57 if(true, x, y, z) -> z 1009.50/291.57 if(false, x, s(y), z) -> div(minus(x, s(y)), s(y), z) 1009.50/291.57 minus(x, 0) -> x 1009.50/291.57 minus(s(x), s(y)) -> minus(x, y) 1009.50/291.57 lt(x, 0) -> false 1009.50/291.57 lt(0, s(y)) -> true 1009.50/291.57 lt(s(x), s(y)) -> lt(x, y) 1009.50/291.57 inc(0) -> s(0) 1009.50/291.57 inc(s(x)) -> s(inc(x)) 1009.50/291.57 1009.50/291.57 S is empty. 1009.50/291.57 Rewrite Strategy: INNERMOST 1009.50/291.57 ---------------------------------------- 1009.50/291.57 1009.50/291.57 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1009.50/291.57 Transformed relative TRS to weighted TRS 1009.50/291.57 ----------------------------------------
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