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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313899
details
property
value
status
complete
benchmark
18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n061.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
20.6174 seconds
cpu usage
76.4216
user time
73.4787
system time
2.94289
max virtual memory
3.7781128E7
max residence set size
4653360.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
75.73/20.44 WORST_CASE(Omega(n^1), O(n^1)) 75.95/20.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 75.95/20.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 75.95/20.48 75.95/20.48 75.95/20.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 75.95/20.48 75.95/20.48 (0) CpxTRS 75.95/20.48 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 75.95/20.48 (2) CpxWeightedTrs 75.95/20.48 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 75.95/20.48 (4) CpxTypedWeightedTrs 75.95/20.48 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 75.95/20.48 (6) CpxTypedWeightedCompleteTrs 75.95/20.48 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 75.95/20.48 (8) CpxTypedWeightedCompleteTrs 75.95/20.48 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 75.95/20.48 (10) CpxRNTS 75.95/20.48 (11) InliningProof [UPPER BOUND(ID), 639 ms] 75.95/20.48 (12) CpxRNTS 75.95/20.48 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 75.95/20.48 (14) CpxRNTS 75.95/20.48 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 75.95/20.48 (16) CpxRNTS 75.95/20.48 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 75.95/20.48 (18) CpxRNTS 75.95/20.48 (19) IntTrsBoundProof [UPPER BOUND(ID), 3925 ms] 75.95/20.48 (20) CpxRNTS 75.95/20.48 (21) IntTrsBoundProof [UPPER BOUND(ID), 1898 ms] 75.95/20.48 (22) CpxRNTS 75.95/20.48 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 75.95/20.48 (24) CpxRNTS 75.95/20.48 (25) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] 75.95/20.48 (26) CpxRNTS 75.95/20.48 (27) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] 75.95/20.48 (28) CpxRNTS 75.95/20.48 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 75.95/20.48 (30) CpxRNTS 75.95/20.48 (31) IntTrsBoundProof [UPPER BOUND(ID), 388 ms] 75.95/20.48 (32) CpxRNTS 75.95/20.48 (33) IntTrsBoundProof [UPPER BOUND(ID), 114 ms] 75.95/20.48 (34) CpxRNTS 75.95/20.48 (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 75.95/20.48 (36) CpxRNTS 75.95/20.48 (37) IntTrsBoundProof [UPPER BOUND(ID), 118 ms] 75.95/20.48 (38) CpxRNTS 75.95/20.48 (39) IntTrsBoundProof [UPPER BOUND(ID), 72 ms] 75.95/20.48 (40) CpxRNTS 75.95/20.48 (41) FinalProof [FINISHED, 0 ms] 75.95/20.48 (42) BOUNDS(1, n^1) 75.95/20.48 (43) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 75.95/20.48 (44) CpxTRS 75.95/20.48 (45) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 75.95/20.48 (46) typed CpxTrs 75.95/20.48 (47) OrderProof [LOWER BOUND(ID), 0 ms] 75.95/20.48 (48) typed CpxTrs 75.95/20.48 (49) RewriteLemmaProof [LOWER BOUND(ID), 293 ms] 75.95/20.48 (50) BEST 75.95/20.48 (51) proven lower bound 75.95/20.48 (52) LowerBoundPropagationProof [FINISHED, 0 ms] 75.95/20.48 (53) BOUNDS(n^1, INF) 75.95/20.48 (54) typed CpxTrs 75.95/20.48 75.95/20.48 75.95/20.48 ---------------------------------------- 75.95/20.48 75.95/20.48 (0) 75.95/20.48 Obligation: 75.95/20.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 75.95/20.48 75.95/20.48 75.95/20.48 The TRS R consists of the following rules: 75.95/20.48 75.95/20.48 cond1(true, x, y) -> cond2(gr(x, 0), x, y) 75.95/20.48 cond2(true, x, y) -> cond1(or(gr(x, 0), gr(y, 0)), p(x), y) 75.95/20.48 cond2(false, x, y) -> cond3(gr(y, 0), x, y) 75.95/20.48 cond3(true, x, y) -> cond1(or(gr(x, 0), gr(y, 0)), x, p(y)) 75.95/20.48 cond3(false, x, y) -> cond1(or(gr(x, 0), gr(y, 0)), x, y) 75.95/20.48 gr(0, x) -> false 75.95/20.48 gr(s(x), 0) -> true 75.95/20.48 gr(s(x), s(y)) -> gr(x, y) 75.95/20.48 or(false, false) -> false 75.95/20.48 or(true, x) -> true 75.95/20.48 or(x, true) -> true 75.95/20.48 p(0) -> 0 75.95/20.48 p(s(x)) -> x 75.95/20.48 75.95/20.48 S is empty. 75.95/20.48 Rewrite Strategy: INNERMOST 75.95/20.48 ---------------------------------------- 75.95/20.48 75.95/20.48 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 75.95/20.48 Transformed relative TRS to weighted TRS 75.95/20.48 ---------------------------------------- 75.95/20.48 75.95/20.48 (2) 75.95/20.48 Obligation: 75.95/20.48 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 75.95/20.48 75.95/20.48
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