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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313780
details
property
value
status
complete
benchmark
#3.8b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n099.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.688 seconds
cpu usage
1107.91
user time
1091.79
system time
16.121
max virtual memory
5.6805712E7
max residence set size
1.5121388E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
1106.94/291.47 WORST_CASE(Omega(n^1), O(n^3)) 1107.44/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1107.44/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1107.44/291.54 1107.44/291.54 1107.44/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1107.44/291.54 1107.44/291.54 (0) CpxTRS 1107.44/291.54 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.44/291.54 (2) CpxWeightedTrs 1107.44/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.44/291.54 (4) CpxTypedWeightedTrs 1107.44/291.54 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1107.44/291.54 (6) CpxTypedWeightedCompleteTrs 1107.44/291.54 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.44/291.54 (8) CpxTypedWeightedCompleteTrs 1107.44/291.54 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1107.44/291.54 (10) CpxRNTS 1107.44/291.54 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.44/291.54 (12) CpxRNTS 1107.44/291.54 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.44/291.54 (14) CpxRNTS 1107.44/291.54 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1107.44/291.54 (16) CpxRNTS 1107.44/291.54 (17) IntTrsBoundProof [UPPER BOUND(ID), 353 ms] 1107.44/291.54 (18) CpxRNTS 1107.44/291.54 (19) IntTrsBoundProof [UPPER BOUND(ID), 139 ms] 1107.44/291.54 (20) CpxRNTS 1107.44/291.54 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1107.44/291.54 (22) CpxRNTS 1107.44/291.54 (23) IntTrsBoundProof [UPPER BOUND(ID), 844 ms] 1107.44/291.54 (24) CpxRNTS 1107.44/291.54 (25) IntTrsBoundProof [UPPER BOUND(ID), 309 ms] 1107.44/291.54 (26) CpxRNTS 1107.44/291.54 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1107.44/291.54 (28) CpxRNTS 1107.44/291.54 (29) IntTrsBoundProof [UPPER BOUND(ID), 413 ms] 1107.44/291.54 (30) CpxRNTS 1107.44/291.54 (31) IntTrsBoundProof [UPPER BOUND(ID), 44 ms] 1107.44/291.54 (32) CpxRNTS 1107.44/291.54 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1107.44/291.54 (34) CpxRNTS 1107.44/291.54 (35) IntTrsBoundProof [UPPER BOUND(ID), 330 ms] 1107.44/291.54 (36) CpxRNTS 1107.44/291.54 (37) IntTrsBoundProof [UPPER BOUND(ID), 3 ms] 1107.44/291.54 (38) CpxRNTS 1107.44/291.54 (39) FinalProof [FINISHED, 0 ms] 1107.44/291.54 (40) BOUNDS(1, n^3) 1107.44/291.54 (41) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.44/291.54 (42) CpxTRS 1107.44/291.54 (43) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.44/291.54 (44) typed CpxTrs 1107.44/291.54 (45) OrderProof [LOWER BOUND(ID), 0 ms] 1107.44/291.54 (46) typed CpxTrs 1107.44/291.54 (47) RewriteLemmaProof [LOWER BOUND(ID), 323 ms] 1107.44/291.54 (48) BEST 1107.44/291.54 (49) proven lower bound 1107.44/291.54 (50) LowerBoundPropagationProof [FINISHED, 0 ms] 1107.44/291.54 (51) BOUNDS(n^1, INF) 1107.44/291.54 (52) typed CpxTrs 1107.44/291.54 1107.44/291.54 1107.44/291.54 ---------------------------------------- 1107.44/291.54 1107.44/291.54 (0) 1107.44/291.54 Obligation: 1107.44/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1107.44/291.54 1107.44/291.54 1107.44/291.54 The TRS R consists of the following rules: 1107.44/291.54 1107.44/291.54 le(0, y) -> true 1107.44/291.54 le(s(x), 0) -> false 1107.44/291.54 le(s(x), s(y)) -> le(x, y) 1107.44/291.54 minus(0, y) -> 0 1107.44/291.54 minus(s(x), y) -> if_minus(le(s(x), y), s(x), y) 1107.44/291.54 if_minus(true, s(x), y) -> 0 1107.44/291.54 if_minus(false, s(x), y) -> s(minus(x, y)) 1107.44/291.54 quot(0, s(y)) -> 0 1107.44/291.54 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1107.44/291.54 log(s(0)) -> 0 1107.44/291.54 log(s(s(x))) -> s(log(s(quot(x, s(s(0)))))) 1107.44/291.54 1107.44/291.54 S is empty. 1107.44/291.54 Rewrite Strategy: INNERMOST 1107.44/291.54 ---------------------------------------- 1107.44/291.54 1107.44/291.54 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1107.44/291.54 Transformed relative TRS to weighted TRS 1107.44/291.54 ---------------------------------------- 1107.44/291.54 1107.44/291.54 (2) 1107.44/291.54 Obligation: 1107.44/291.54 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 1107.44/291.54 1107.44/291.54 1107.44/291.54 The TRS R consists of the following rules: 1107.44/291.54 1107.44/291.54 le(0, y) -> true [1] 1107.44/291.54 le(s(x), 0) -> false [1]
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