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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313779
details
property
value
status
complete
benchmark
#4.30c.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
26.5635 seconds
cpu usage
100.471
user time
97.3191
system time
3.15236
max virtual memory
3.7578144E7
max residence set size
4907892.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
100.29/26.48 WORST_CASE(Omega(n^1), O(n^1)) 100.29/26.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 100.29/26.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 100.29/26.49 100.29/26.49 100.29/26.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 100.29/26.49 100.29/26.49 (0) CpxTRS 100.29/26.49 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 100.29/26.49 (2) CpxWeightedTrs 100.29/26.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 100.29/26.49 (4) CpxTypedWeightedTrs 100.29/26.49 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 100.29/26.49 (6) CpxTypedWeightedCompleteTrs 100.29/26.49 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 100.29/26.49 (8) CpxRNTS 100.29/26.49 (9) CompleteCoflocoProof [FINISHED, 1366 ms] 100.29/26.49 (10) BOUNDS(1, n^1) 100.29/26.49 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 100.29/26.49 (12) CpxTRS 100.29/26.49 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 100.29/26.49 (14) typed CpxTrs 100.29/26.49 (15) OrderProof [LOWER BOUND(ID), 0 ms] 100.29/26.49 (16) typed CpxTrs 100.29/26.49 (17) RewriteLemmaProof [LOWER BOUND(ID), 316 ms] 100.29/26.49 (18) BEST 100.29/26.49 (19) proven lower bound 100.29/26.49 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 100.29/26.49 (21) BOUNDS(n^1, INF) 100.29/26.49 (22) typed CpxTrs 100.29/26.49 (23) RewriteLemmaProof [LOWER BOUND(ID), 835 ms] 100.29/26.49 (24) typed CpxTrs 100.29/26.49 100.29/26.49 100.29/26.49 ---------------------------------------- 100.29/26.49 100.29/26.49 (0) 100.29/26.49 Obligation: 100.29/26.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 100.29/26.49 100.29/26.49 100.29/26.49 The TRS R consists of the following rules: 100.29/26.49 100.29/26.49 le(0, y) -> true 100.29/26.49 le(s(x), 0) -> false 100.29/26.49 le(s(x), s(y)) -> le(x, y) 100.29/26.49 pred(s(x)) -> x 100.29/26.49 minus(x, 0) -> x 100.29/26.49 minus(x, s(y)) -> pred(minus(x, y)) 100.29/26.49 gcd(0, y) -> y 100.29/26.49 gcd(s(x), 0) -> s(x) 100.29/26.49 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 100.29/26.49 if_gcd(true, x, y) -> gcd(minus(x, y), y) 100.29/26.49 if_gcd(false, x, y) -> gcd(minus(y, x), x) 100.29/26.49 100.29/26.49 S is empty. 100.29/26.49 Rewrite Strategy: INNERMOST 100.29/26.49 ---------------------------------------- 100.29/26.49 100.29/26.49 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 100.29/26.49 Transformed relative TRS to weighted TRS 100.29/26.49 ---------------------------------------- 100.29/26.49 100.29/26.49 (2) 100.29/26.49 Obligation: 100.29/26.49 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 100.29/26.49 100.29/26.49 100.29/26.49 The TRS R consists of the following rules: 100.29/26.49 100.29/26.49 le(0, y) -> true [1] 100.29/26.49 le(s(x), 0) -> false [1] 100.29/26.49 le(s(x), s(y)) -> le(x, y) [1] 100.29/26.49 pred(s(x)) -> x [1] 100.29/26.49 minus(x, 0) -> x [1] 100.29/26.49 minus(x, s(y)) -> pred(minus(x, y)) [1] 100.29/26.49 gcd(0, y) -> y [1] 100.29/26.49 gcd(s(x), 0) -> s(x) [1] 100.29/26.49 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) [1] 100.29/26.49 if_gcd(true, x, y) -> gcd(minus(x, y), y) [1] 100.29/26.49 if_gcd(false, x, y) -> gcd(minus(y, x), x) [1] 100.29/26.49 100.29/26.49 Rewrite Strategy: INNERMOST 100.29/26.49 ---------------------------------------- 100.29/26.49 100.29/26.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 100.29/26.49 Infered types. 100.29/26.49 ---------------------------------------- 100.29/26.49 100.29/26.49 (4) 100.29/26.49 Obligation: 100.29/26.49 Runtime Complexity Weighted TRS with Types. 100.29/26.49 The TRS R consists of the following rules: 100.29/26.49 100.29/26.49 le(0, y) -> true [1] 100.29/26.49 le(s(x), 0) -> false [1] 100.29/26.49 le(s(x), s(y)) -> le(x, y) [1] 100.29/26.49 pred(s(x)) -> x [1] 100.29/26.49 minus(x, 0) -> x [1] 100.29/26.49 minus(x, s(y)) -> pred(minus(x, y)) [1]
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