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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313896
details
property
value
status
complete
benchmark
11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n084.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.531 seconds
cpu usage
1073.1
user time
1066.9
system time
6.19759
max virtual memory
3.8059568E7
max residence set size
5784132.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1072.75/291.48 WORST_CASE(Omega(n^1), O(n^2)) 1072.98/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1072.98/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1072.98/291.49 1072.98/291.49 1072.98/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1072.98/291.49 1072.98/291.49 (0) CpxTRS 1072.98/291.49 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1072.98/291.49 (2) CpxWeightedTrs 1072.98/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1072.98/291.49 (4) CpxTypedWeightedTrs 1072.98/291.49 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1072.98/291.49 (6) CpxTypedWeightedCompleteTrs 1072.98/291.49 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1072.98/291.49 (8) CpxRNTS 1072.98/291.49 (9) CompleteCoflocoProof [FINISHED, 422 ms] 1072.98/291.49 (10) BOUNDS(1, n^2) 1072.98/291.49 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1072.98/291.49 (12) TRS for Loop Detection 1072.98/291.49 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1072.98/291.49 (14) BEST 1072.98/291.49 (15) proven lower bound 1072.98/291.49 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1072.98/291.49 (17) BOUNDS(n^1, INF) 1072.98/291.49 (18) TRS for Loop Detection 1072.98/291.49 1072.98/291.49 1072.98/291.49 ---------------------------------------- 1072.98/291.49 1072.98/291.49 (0) 1072.98/291.49 Obligation: 1072.98/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1072.98/291.49 1072.98/291.49 1072.98/291.49 The TRS R consists of the following rules: 1072.98/291.49 1072.98/291.49 cond1(true, x, y) -> cond2(gr(x, y), x, y) 1072.98/291.49 cond2(true, x, y) -> cond1(neq(x, 0), y, y) 1072.98/291.49 cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) 1072.98/291.49 gr(0, x) -> false 1072.98/291.49 gr(s(x), 0) -> true 1072.98/291.49 gr(s(x), s(y)) -> gr(x, y) 1072.98/291.49 neq(0, 0) -> false 1072.98/291.49 neq(0, s(x)) -> true 1072.98/291.49 neq(s(x), 0) -> true 1072.98/291.49 neq(s(x), s(y)) -> neq(x, y) 1072.98/291.49 p(0) -> 0 1072.98/291.49 p(s(x)) -> x 1072.98/291.49 1072.98/291.49 S is empty. 1072.98/291.49 Rewrite Strategy: INNERMOST 1072.98/291.49 ---------------------------------------- 1072.98/291.49 1072.98/291.49 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1072.98/291.49 Transformed relative TRS to weighted TRS 1072.98/291.49 ---------------------------------------- 1072.98/291.49 1072.98/291.49 (2) 1072.98/291.49 Obligation: 1072.98/291.49 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1072.98/291.49 1072.98/291.49 1072.98/291.49 The TRS R consists of the following rules: 1072.98/291.49 1072.98/291.49 cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] 1072.98/291.49 cond2(true, x, y) -> cond1(neq(x, 0), y, y) [1] 1072.98/291.49 cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) [1] 1072.98/291.49 gr(0, x) -> false [1] 1072.98/291.49 gr(s(x), 0) -> true [1] 1072.98/291.49 gr(s(x), s(y)) -> gr(x, y) [1] 1072.98/291.49 neq(0, 0) -> false [1] 1072.98/291.49 neq(0, s(x)) -> true [1] 1072.98/291.49 neq(s(x), 0) -> true [1] 1072.98/291.49 neq(s(x), s(y)) -> neq(x, y) [1] 1072.98/291.49 p(0) -> 0 [1] 1072.98/291.49 p(s(x)) -> x [1] 1072.98/291.49 1072.98/291.49 Rewrite Strategy: INNERMOST 1072.98/291.49 ---------------------------------------- 1072.98/291.49 1072.98/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1072.98/291.49 Infered types. 1072.98/291.49 ---------------------------------------- 1072.98/291.49 1072.98/291.49 (4) 1072.98/291.49 Obligation: 1072.98/291.49 Runtime Complexity Weighted TRS with Types. 1072.98/291.49 The TRS R consists of the following rules: 1072.98/291.49 1072.98/291.49 cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] 1072.98/291.49 cond2(true, x, y) -> cond1(neq(x, 0), y, y) [1] 1072.98/291.49 cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) [1] 1072.98/291.49 gr(0, x) -> false [1] 1072.98/291.49 gr(s(x), 0) -> true [1] 1072.98/291.49 gr(s(x), s(y)) -> gr(x, y) [1] 1072.98/291.49 neq(0, 0) -> false [1] 1072.98/291.49 neq(0, s(x)) -> true [1] 1072.98/291.49 neq(s(x), 0) -> true [1] 1072.98/291.49 neq(s(x), s(y)) -> neq(x, y) [1]
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