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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313747
details
property
value
status
complete
benchmark
#3.6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
13.0813 seconds
cpu usage
39.4963
user time
36.9741
system time
2.52213
max virtual memory
3.7526576E7
max residence set size
4530700.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
39.38/13.01 WORST_CASE(Omega(n^1), O(n^1)) 39.38/13.02 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 39.38/13.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 39.38/13.02 39.38/13.02 39.38/13.02 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 39.38/13.02 39.38/13.02 (0) CpxTRS 39.38/13.02 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 39.38/13.02 (2) CpxWeightedTrs 39.38/13.02 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 39.38/13.02 (4) CpxTypedWeightedTrs 39.38/13.02 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 39.38/13.02 (6) CpxTypedWeightedCompleteTrs 39.38/13.02 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 39.38/13.02 (8) CpxRNTS 39.38/13.02 (9) CompleteCoflocoProof [FINISHED, 1455 ms] 39.38/13.02 (10) BOUNDS(1, n^1) 39.38/13.02 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 39.38/13.02 (12) CpxTRS 39.38/13.02 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 39.38/13.02 (14) typed CpxTrs 39.38/13.02 (15) OrderProof [LOWER BOUND(ID), 0 ms] 39.38/13.02 (16) typed CpxTrs 39.38/13.02 (17) RewriteLemmaProof [LOWER BOUND(ID), 305 ms] 39.38/13.02 (18) BEST 39.38/13.02 (19) proven lower bound 39.38/13.02 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 39.38/13.02 (21) BOUNDS(n^1, INF) 39.38/13.02 (22) typed CpxTrs 39.38/13.02 (23) RewriteLemmaProof [LOWER BOUND(ID), 850 ms] 39.38/13.02 (24) typed CpxTrs 39.38/13.02 39.38/13.02 39.38/13.02 ---------------------------------------- 39.38/13.02 39.38/13.02 (0) 39.38/13.02 Obligation: 39.38/13.02 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 39.38/13.02 39.38/13.02 39.38/13.02 The TRS R consists of the following rules: 39.38/13.02 39.38/13.02 le(0, y) -> true 39.38/13.02 le(s(x), 0) -> false 39.38/13.02 le(s(x), s(y)) -> le(x, y) 39.38/13.02 pred(s(x)) -> x 39.38/13.02 minus(x, 0) -> x 39.38/13.02 minus(x, s(y)) -> pred(minus(x, y)) 39.38/13.02 gcd(0, y) -> y 39.38/13.02 gcd(s(x), 0) -> s(x) 39.38/13.02 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 39.38/13.02 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) 39.38/13.02 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) 39.38/13.02 39.38/13.02 S is empty. 39.38/13.02 Rewrite Strategy: INNERMOST 39.38/13.02 ---------------------------------------- 39.38/13.02 39.38/13.02 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 39.38/13.02 Transformed relative TRS to weighted TRS 39.38/13.02 ---------------------------------------- 39.38/13.02 39.38/13.02 (2) 39.38/13.02 Obligation: 39.38/13.02 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 39.38/13.02 39.38/13.02 39.38/13.02 The TRS R consists of the following rules: 39.38/13.02 39.38/13.02 le(0, y) -> true [1] 39.38/13.02 le(s(x), 0) -> false [1] 39.38/13.02 le(s(x), s(y)) -> le(x, y) [1] 39.38/13.02 pred(s(x)) -> x [1] 39.38/13.02 minus(x, 0) -> x [1] 39.38/13.02 minus(x, s(y)) -> pred(minus(x, y)) [1] 39.38/13.02 gcd(0, y) -> y [1] 39.38/13.02 gcd(s(x), 0) -> s(x) [1] 39.38/13.02 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) [1] 39.38/13.02 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) [1] 39.38/13.02 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) [1] 39.38/13.02 39.38/13.02 Rewrite Strategy: INNERMOST 39.38/13.02 ---------------------------------------- 39.38/13.02 39.38/13.02 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 39.38/13.02 Infered types. 39.38/13.02 ---------------------------------------- 39.38/13.02 39.38/13.02 (4) 39.38/13.02 Obligation: 39.38/13.02 Runtime Complexity Weighted TRS with Types. 39.38/13.02 The TRS R consists of the following rules: 39.38/13.02 39.38/13.02 le(0, y) -> true [1] 39.38/13.02 le(s(x), 0) -> false [1] 39.38/13.02 le(s(x), s(y)) -> le(x, y) [1] 39.38/13.02 pred(s(x)) -> x [1] 39.38/13.02 minus(x, 0) -> x [1] 39.38/13.02 minus(x, s(y)) -> pred(minus(x, y)) [1]
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