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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313904
details
property
value
status
complete
benchmark
24.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)
20.7661 seconds
cpu usage
77.0823
user time
73.6733
system time
3.40899
max virtual memory
3.7509864E7
max residence set size
4643312.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
76.80/20.68 WORST_CASE(Omega(n^1), O(n^1)) 76.80/20.70 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 76.80/20.70 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 76.80/20.70 76.80/20.70 76.80/20.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 76.80/20.70 76.80/20.70 (0) CpxTRS 76.80/20.70 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 76.80/20.70 (2) CpxWeightedTrs 76.80/20.70 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 76.80/20.70 (4) CpxTypedWeightedTrs 76.80/20.70 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 76.80/20.70 (6) CpxTypedWeightedCompleteTrs 76.80/20.70 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 76.80/20.70 (8) CpxTypedWeightedCompleteTrs 76.80/20.70 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] 76.80/20.70 (10) CpxRNTS 76.80/20.70 (11) InliningProof [UPPER BOUND(ID), 421 ms] 76.80/20.70 (12) CpxRNTS 76.80/20.70 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 76.80/20.70 (14) CpxRNTS 76.80/20.70 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 76.80/20.70 (16) CpxRNTS 76.80/20.70 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 76.80/20.70 (18) CpxRNTS 76.80/20.70 (19) IntTrsBoundProof [UPPER BOUND(ID), 199 ms] 76.80/20.70 (20) CpxRNTS 76.80/20.70 (21) IntTrsBoundProof [UPPER BOUND(ID), 76 ms] 76.80/20.70 (22) CpxRNTS 76.80/20.70 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 76.80/20.70 (24) CpxRNTS 76.80/20.70 (25) IntTrsBoundProof [UPPER BOUND(ID), 202 ms] 76.80/20.70 (26) CpxRNTS 76.80/20.70 (27) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] 76.80/20.70 (28) CpxRNTS 76.80/20.70 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 76.80/20.70 (30) CpxRNTS 76.80/20.70 (31) IntTrsBoundProof [UPPER BOUND(ID), 291 ms] 76.80/20.70 (32) CpxRNTS 76.80/20.70 (33) IntTrsBoundProof [UPPER BOUND(ID), 130 ms] 76.80/20.70 (34) CpxRNTS 76.80/20.70 (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 76.80/20.70 (36) CpxRNTS 76.80/20.70 (37) IntTrsBoundProof [UPPER BOUND(ID), 3559 ms] 76.80/20.70 (38) CpxRNTS 76.80/20.70 (39) IntTrsBoundProof [UPPER BOUND(ID), 1515 ms] 76.80/20.70 (40) CpxRNTS 76.80/20.70 (41) FinalProof [FINISHED, 0 ms] 76.80/20.70 (42) BOUNDS(1, n^1) 76.80/20.70 (43) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 76.80/20.70 (44) CpxTRS 76.80/20.70 (45) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 76.80/20.70 (46) typed CpxTrs 76.80/20.70 (47) OrderProof [LOWER BOUND(ID), 0 ms] 76.80/20.70 (48) typed CpxTrs 76.80/20.70 (49) RewriteLemmaProof [LOWER BOUND(ID), 309 ms] 76.80/20.70 (50) BEST 76.80/20.70 (51) proven lower bound 76.80/20.70 (52) LowerBoundPropagationProof [FINISHED, 0 ms] 76.80/20.70 (53) BOUNDS(n^1, INF) 76.80/20.70 (54) typed CpxTrs 76.80/20.70 76.80/20.70 76.80/20.70 ---------------------------------------- 76.80/20.70 76.80/20.70 (0) 76.80/20.70 Obligation: 76.80/20.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 76.80/20.70 76.80/20.70 76.80/20.70 The TRS R consists of the following rules: 76.80/20.70 76.80/20.70 cond1(true, x, y) -> cond2(gr(x, y), x, y) 76.80/20.70 cond2(true, x, y) -> cond3(gr(x, 0), x, y) 76.80/20.70 cond2(false, x, y) -> cond4(gr(y, 0), x, y) 76.80/20.70 cond3(true, x, y) -> cond3(gr(x, 0), p(x), y) 76.80/20.70 cond3(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y) 76.80/20.70 cond4(true, x, y) -> cond4(gr(y, 0), x, p(y)) 76.80/20.70 cond4(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y) 76.80/20.70 gr(0, x) -> false 76.80/20.70 gr(s(x), 0) -> true 76.80/20.70 gr(s(x), s(y)) -> gr(x, y) 76.80/20.70 and(true, true) -> true 76.80/20.70 and(false, x) -> false 76.80/20.70 and(x, false) -> false 76.80/20.70 p(0) -> 0 76.80/20.70 p(s(x)) -> x 76.80/20.70 76.80/20.70 S is empty. 76.80/20.70 Rewrite Strategy: INNERMOST 76.80/20.70 ---------------------------------------- 76.80/20.70 76.80/20.70 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 76.80/20.70 Transformed relative TRS to weighted TRS 76.80/20.70 ---------------------------------------- 76.80/20.70 76.80/20.70 (2) 76.80/20.70 Obligation: 76.80/20.70 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
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