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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313885
details
property
value
status
complete
benchmark
14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n105.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.574 seconds
cpu usage
938.714
user time
931.466
system time
7.2482
max virtual memory
3.7967384E7
max residence set size
5507324.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
938.43/291.50 WORST_CASE(Omega(n^1), O(n^2)) 938.59/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 938.59/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 938.59/291.52 938.59/291.52 938.59/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 938.59/291.52 938.59/291.52 (0) CpxTRS 938.59/291.52 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 938.59/291.52 (2) CpxWeightedTrs 938.59/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 938.59/291.52 (4) CpxTypedWeightedTrs 938.59/291.52 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 938.59/291.52 (6) CpxTypedWeightedCompleteTrs 938.59/291.52 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 938.59/291.52 (8) CpxRNTS 938.59/291.52 (9) CompleteCoflocoProof [FINISHED, 322 ms] 938.59/291.52 (10) BOUNDS(1, n^2) 938.59/291.52 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 938.59/291.52 (12) CpxTRS 938.59/291.52 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 938.59/291.52 (14) typed CpxTrs 938.59/291.52 (15) OrderProof [LOWER BOUND(ID), 0 ms] 938.59/291.52 (16) typed CpxTrs 938.59/291.52 (17) RewriteLemmaProof [LOWER BOUND(ID), 277 ms] 938.59/291.52 (18) BEST 938.59/291.52 (19) proven lower bound 938.59/291.52 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 938.59/291.52 (21) BOUNDS(n^1, INF) 938.59/291.52 (22) typed CpxTrs 938.59/291.52 (23) RewriteLemmaProof [LOWER BOUND(ID), 1298 ms] 938.59/291.52 (24) BOUNDS(1, INF) 938.59/291.52 938.59/291.52 938.59/291.52 ---------------------------------------- 938.59/291.52 938.59/291.52 (0) 938.59/291.52 Obligation: 938.59/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 938.59/291.52 938.59/291.52 938.59/291.52 The TRS R consists of the following rules: 938.59/291.52 938.59/291.52 cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) 938.59/291.52 cond2(true, x, y) -> cond1(y, y) 938.59/291.52 cond2(false, x, y) -> cond1(p(x), y) 938.59/291.52 gr(0, x) -> false 938.59/291.52 gr(s(x), 0) -> true 938.59/291.52 gr(s(x), s(y)) -> gr(x, y) 938.59/291.52 neq(0, 0) -> false 938.59/291.52 neq(0, s(x)) -> true 938.59/291.52 neq(s(x), 0) -> true 938.59/291.52 neq(s(x), s(y)) -> neq(x, y) 938.59/291.52 p(0) -> 0 938.59/291.52 p(s(x)) -> x 938.59/291.52 938.59/291.52 S is empty. 938.59/291.52 Rewrite Strategy: INNERMOST 938.59/291.52 ---------------------------------------- 938.59/291.52 938.59/291.52 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 938.59/291.52 Transformed relative TRS to weighted TRS 938.59/291.52 ---------------------------------------- 938.59/291.52 938.59/291.52 (2) 938.59/291.52 Obligation: 938.59/291.52 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 938.59/291.52 938.59/291.52 938.59/291.52 The TRS R consists of the following rules: 938.59/291.52 938.59/291.52 cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) [1] 938.59/291.52 cond2(true, x, y) -> cond1(y, y) [1] 938.59/291.52 cond2(false, x, y) -> cond1(p(x), y) [1] 938.59/291.52 gr(0, x) -> false [1] 938.59/291.52 gr(s(x), 0) -> true [1] 938.59/291.52 gr(s(x), s(y)) -> gr(x, y) [1] 938.59/291.52 neq(0, 0) -> false [1] 938.59/291.52 neq(0, s(x)) -> true [1] 938.59/291.52 neq(s(x), 0) -> true [1] 938.59/291.52 neq(s(x), s(y)) -> neq(x, y) [1] 938.59/291.52 p(0) -> 0 [1] 938.59/291.52 p(s(x)) -> x [1] 938.59/291.52 938.59/291.52 Rewrite Strategy: INNERMOST 938.59/291.52 ---------------------------------------- 938.59/291.52 938.59/291.52 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 938.59/291.52 Infered types. 938.59/291.52 ---------------------------------------- 938.59/291.52 938.59/291.52 (4) 938.59/291.52 Obligation: 938.59/291.52 Runtime Complexity Weighted TRS with Types. 938.59/291.52 The TRS R consists of the following rules: 938.59/291.52 938.59/291.52 cond1(s(x), y) -> cond2(gr(s(x), y), s(x), y) [1] 938.59/291.52 cond2(true, x, y) -> cond1(y, y) [1] 938.59/291.52 cond2(false, x, y) -> cond1(p(x), y) [1] 938.59/291.52 gr(0, x) -> false [1]
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