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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313906
details
property
value
status
complete
benchmark
22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n157.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
12.1136 seconds
cpu usage
32.1735
user time
30.3932
system time
1.78027
max virtual memory
1.9030828E7
max residence set size
3884412.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
32.04/9.47 WORST_CASE(Omega(n^1), O(n^1)) 32.04/9.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 32.04/9.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 32.04/9.49 32.04/9.49 32.04/9.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 32.04/9.49 32.04/9.49 (0) CpxTRS 32.04/9.49 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 32.04/9.49 (2) CpxWeightedTrs 32.04/9.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 32.04/9.49 (4) CpxTypedWeightedTrs 32.04/9.49 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 32.04/9.49 (6) CpxTypedWeightedCompleteTrs 32.04/9.49 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 32.04/9.49 (8) CpxTypedWeightedCompleteTrs 32.04/9.49 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 32.04/9.49 (10) CpxRNTS 32.04/9.49 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 32.04/9.49 (12) CpxRNTS 32.04/9.49 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 1 ms] 32.04/9.49 (14) CpxRNTS 32.04/9.49 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 32.04/9.49 (16) CpxRNTS 32.04/9.49 (17) IntTrsBoundProof [UPPER BOUND(ID), 1165 ms] 32.04/9.49 (18) CpxRNTS 32.04/9.49 (19) IntTrsBoundProof [UPPER BOUND(ID), 609 ms] 32.04/9.49 (20) CpxRNTS 32.04/9.49 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 32.04/9.49 (22) CpxRNTS 32.04/9.49 (23) IntTrsBoundProof [UPPER BOUND(ID), 101 ms] 32.04/9.49 (24) CpxRNTS 32.04/9.49 (25) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 32.04/9.49 (26) CpxRNTS 32.04/9.49 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 32.04/9.49 (28) CpxRNTS 32.04/9.49 (29) IntTrsBoundProof [UPPER BOUND(ID), 280 ms] 32.04/9.49 (30) CpxRNTS 32.04/9.49 (31) IntTrsBoundProof [UPPER BOUND(ID), 115 ms] 32.04/9.49 (32) CpxRNTS 32.04/9.49 (33) FinalProof [FINISHED, 0 ms] 32.04/9.49 (34) BOUNDS(1, n^1) 32.04/9.49 (35) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 32.04/9.49 (36) CpxTRS 32.04/9.49 (37) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 32.04/9.49 (38) typed CpxTrs 32.04/9.49 (39) OrderProof [LOWER BOUND(ID), 0 ms] 32.04/9.49 (40) typed CpxTrs 32.04/9.49 (41) RewriteLemmaProof [LOWER BOUND(ID), 309 ms] 32.04/9.49 (42) BEST 32.04/9.49 (43) proven lower bound 32.04/9.49 (44) LowerBoundPropagationProof [FINISHED, 0 ms] 32.04/9.49 (45) BOUNDS(n^1, INF) 32.04/9.49 (46) typed CpxTrs 32.04/9.49 32.04/9.49 32.04/9.49 ---------------------------------------- 32.04/9.49 32.04/9.49 (0) 32.04/9.49 Obligation: 32.04/9.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 32.04/9.49 32.04/9.49 32.04/9.49 The TRS R consists of the following rules: 32.04/9.49 32.04/9.49 cond1(true, x, y) -> cond2(gr(y, 0), x, y) 32.04/9.49 cond2(true, x, y) -> cond2(gr(y, 0), x, p(y)) 32.04/9.49 cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) 32.04/9.49 gr(0, x) -> false 32.04/9.49 gr(s(x), 0) -> true 32.04/9.49 gr(s(x), s(y)) -> gr(x, y) 32.04/9.49 p(0) -> 0 32.04/9.49 p(s(x)) -> x 32.04/9.49 32.04/9.49 S is empty. 32.04/9.49 Rewrite Strategy: INNERMOST 32.04/9.49 ---------------------------------------- 32.04/9.49 32.04/9.49 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 32.04/9.49 Transformed relative TRS to weighted TRS 32.04/9.49 ---------------------------------------- 32.04/9.49 32.04/9.49 (2) 32.04/9.49 Obligation: 32.04/9.49 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 32.04/9.49 32.04/9.49 32.04/9.49 The TRS R consists of the following rules: 32.04/9.49 32.04/9.49 cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1] 32.04/9.49 cond2(true, x, y) -> cond2(gr(y, 0), x, p(y)) [1] 32.04/9.49 cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) [1] 32.04/9.49 gr(0, x) -> false [1] 32.04/9.49 gr(s(x), 0) -> true [1] 32.04/9.49 gr(s(x), s(y)) -> gr(x, y) [1] 32.04/9.49 p(0) -> 0 [1] 32.04/9.49 p(s(x)) -> x [1] 32.04/9.49 32.04/9.49 Rewrite Strategy: INNERMOST 32.04/9.49 ----------------------------------------
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