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Complexity_ITS 2019-03-21 04.46 pair #429990906
details
property
value
status
complete
benchmark
polyrank1.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.15272 seconds
cpu usage
5.24903
user time
4.84071
system time
0.408324
max virtual memory
1.8665088E7
max residence set size
251568.0
stage attributes
key
value
starexec-result
MAYBE
output
5.12/3.12 MAYBE 5.12/3.13 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 5.12/3.13 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.12/3.13 5.12/3.13 5.12/3.13 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). 5.12/3.13 5.12/3.13 (0) CpxIntTrs 5.12/3.13 (1) Loat Proof [FINISHED, 114 ms] 5.12/3.13 (2) BOUNDS(1, INF) 5.12/3.13 5.12/3.13 5.12/3.13 ---------------------------------------- 5.12/3.13 5.12/3.13 (0) 5.12/3.13 Obligation: 5.12/3.13 Complexity Int TRS consisting of the following rules: 5.12/3.13 f0(A, B) -> Com_1(f1(A, B)) :|: TRUE 5.12/3.13 f1(A, B) -> Com_1(f1(A - B, B + 1)) :|: A >= 1 5.12/3.13 5.12/3.13 The start-symbols are:[f0_2] 5.12/3.13 5.12/3.13 5.12/3.13 ---------------------------------------- 5.12/3.13 5.12/3.13 (1) Loat Proof (FINISHED) 5.12/3.13 5.12/3.13 5.12/3.13 ### Pre-processing the ITS problem ### 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 Initial linear ITS problem 5.12/3.13 5.12/3.13 Start location: f0 5.12/3.13 5.12/3.13 0: f0 -> f1 : [], cost: 1 5.12/3.13 5.12/3.13 1: f1 -> f1 : A'=A-B, B'=1+B, [ A>=1 ], cost: 1 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 ### Simplification by acceleration and chaining ### 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 Accelerating simple loops of location 1. 5.12/3.13 5.12/3.13 Accelerating the following rules: 5.12/3.13 5.12/3.13 1: f1 -> f1 : A'=A-B, B'=1+B, [ A>=1 ], cost: 1 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 Found no metering function for rule 1. 5.12/3.13 5.12/3.13 Removing the simple loops:. 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 Accelerated all simple loops using metering functions (where possible): 5.12/3.13 5.12/3.13 Start location: f0 5.12/3.13 5.12/3.13 0: f0 -> f1 : [], cost: 1 5.12/3.13 5.12/3.13 1: f1 -> f1 : A'=A-B, B'=1+B, [ A>=1 ], cost: 1 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 Chained accelerated rules (with incoming rules): 5.12/3.13 5.12/3.13 Start location: f0 5.12/3.13 5.12/3.13 0: f0 -> f1 : [], cost: 1 5.12/3.13 5.12/3.13 2: f0 -> f1 : A'=A-B, B'=1+B, [ A>=1 ], cost: 2 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 Removed unreachable locations (and leaf rules with constant cost): 5.12/3.13 5.12/3.13 Start location: f0 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 ### Computing asymptotic complexity ### 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 Fully simplified ITS problem 5.12/3.13 5.12/3.13 Start location: f0 5.12/3.13 5.12/3.13 5.12/3.13 5.12/3.13 Obtained the following overall complexity (w.r.t. the length of the input n): 5.12/3.13 5.12/3.13 Complexity: Unknown 5.12/3.13
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