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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313561
details
property
value
status
complete
benchmark
#4.30.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.6392 seconds
cpu usage
31.6129
user time
29.4597
system time
2.15318
max virtual memory
5.6006944E7
max residence set size
4251548.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
31.44/10.58 WORST_CASE(Omega(n^1), O(n^1)) 31.44/10.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 31.44/10.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.44/10.59 31.44/10.59 31.44/10.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 31.44/10.59 31.44/10.59 (0) CpxTRS 31.44/10.59 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 31.44/10.59 (2) CpxWeightedTrs 31.44/10.59 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 31.44/10.59 (4) CpxTypedWeightedTrs 31.44/10.59 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 31.44/10.59 (6) CpxTypedWeightedCompleteTrs 31.44/10.59 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms] 31.44/10.59 (8) CpxRNTS 31.44/10.59 (9) CompleteCoflocoProof [FINISHED, 354 ms] 31.44/10.59 (10) BOUNDS(1, n^1) 31.44/10.59 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 31.44/10.59 (12) CpxTRS 31.44/10.59 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 31.44/10.59 (14) typed CpxTrs 31.44/10.59 (15) OrderProof [LOWER BOUND(ID), 0 ms] 31.44/10.59 (16) typed CpxTrs 31.44/10.59 (17) RewriteLemmaProof [LOWER BOUND(ID), 248 ms] 31.44/10.59 (18) BEST 31.44/10.59 (19) proven lower bound 31.44/10.59 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 31.44/10.59 (21) BOUNDS(n^1, INF) 31.44/10.59 (22) typed CpxTrs 31.44/10.59 (23) RewriteLemmaProof [LOWER BOUND(ID), 59 ms] 31.44/10.59 (24) typed CpxTrs 31.44/10.59 31.44/10.59 31.44/10.59 ---------------------------------------- 31.44/10.59 31.44/10.59 (0) 31.44/10.59 Obligation: 31.44/10.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 31.44/10.59 31.44/10.59 31.44/10.59 The TRS R consists of the following rules: 31.44/10.59 31.44/10.59 minus(x, 0) -> x 31.44/10.59 minus(s(x), s(y)) -> minus(x, y) 31.44/10.59 le(0, y) -> true 31.44/10.59 le(s(x), 0) -> false 31.44/10.59 le(s(x), s(y)) -> le(x, y) 31.44/10.59 quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) 31.44/10.59 if_quot(true, x, y) -> s(quot(minus(x, y), y)) 31.44/10.59 if_quot(false, x, y) -> 0 31.44/10.59 31.44/10.59 S is empty. 31.44/10.59 Rewrite Strategy: INNERMOST 31.44/10.59 ---------------------------------------- 31.44/10.59 31.44/10.59 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 31.44/10.59 Transformed relative TRS to weighted TRS 31.44/10.59 ---------------------------------------- 31.44/10.59 31.44/10.59 (2) 31.44/10.59 Obligation: 31.44/10.59 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 31.44/10.59 31.44/10.59 31.44/10.59 The TRS R consists of the following rules: 31.44/10.59 31.44/10.59 minus(x, 0) -> x [1] 31.44/10.59 minus(s(x), s(y)) -> minus(x, y) [1] 31.44/10.59 le(0, y) -> true [1] 31.44/10.59 le(s(x), 0) -> false [1] 31.44/10.59 le(s(x), s(y)) -> le(x, y) [1] 31.44/10.59 quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) [1] 31.44/10.59 if_quot(true, x, y) -> s(quot(minus(x, y), y)) [1] 31.44/10.59 if_quot(false, x, y) -> 0 [1] 31.44/10.59 31.44/10.59 Rewrite Strategy: INNERMOST 31.44/10.59 ---------------------------------------- 31.44/10.59 31.44/10.59 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 31.44/10.59 Infered types. 31.44/10.59 ---------------------------------------- 31.44/10.59 31.44/10.59 (4) 31.44/10.59 Obligation: 31.44/10.59 Runtime Complexity Weighted TRS with Types. 31.44/10.59 The TRS R consists of the following rules: 31.44/10.59 31.44/10.59 minus(x, 0) -> x [1] 31.44/10.59 minus(s(x), s(y)) -> minus(x, y) [1] 31.44/10.59 le(0, y) -> true [1] 31.44/10.59 le(s(x), 0) -> false [1] 31.44/10.59 le(s(x), s(y)) -> le(x, y) [1] 31.44/10.59 quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) [1] 31.44/10.59 if_quot(true, x, y) -> s(quot(minus(x, y), y)) [1] 31.44/10.59 if_quot(false, x, y) -> 0 [1] 31.44/10.59 31.44/10.59 The TRS has the following type information: 31.44/10.59 minus :: 0:s -> 0:s -> 0:s 31.44/10.59 0 :: 0:s
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