details

property	value
status	complete
benchmark	polyrank6.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n164.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.44417 seconds
cpu usage	7.09573
user time	6.6901
system time	0.405624
max virtual memory	1.8680504E7
max residence set size	213836.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

6.92/4.40 WORST_CASE(Omega(n^1), ?) 6.92/4.41 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 6.92/4.41 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.92/4.41 6.92/4.41 6.92/4.41 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). 6.92/4.41 6.92/4.41 (0) CpxIntTrs 6.92/4.41 (1) Loat Proof [FINISHED, 417 ms] 6.92/4.41 (2) BOUNDS(n^1, INF) 6.92/4.41 6.92/4.41 6.92/4.41 ---------------------------------------- 6.92/4.41 6.92/4.41 (0) 6.92/4.41 Obligation: 6.92/4.41 Complexity Int TRS consisting of the following rules: 6.92/4.41 f0(A, B, C) -> Com_1(f2(A, B, C)) :|: A >= 0 && B >= C 6.92/4.41 f2(A, B, C) -> Com_1(f2(A - 1, B, C - 1)) :|: A >= 1 && B + 1 >= C 6.92/4.41 f2(A, B, C) -> Com_1(f2(A, B + C - 1, C - 1)) :|: A >= 0 && B >= 0 6.92/4.41 6.92/4.41 The start-symbols are:[f0_3] 6.92/4.41 6.92/4.41 6.92/4.41 ---------------------------------------- 6.92/4.41 6.92/4.41 (1) Loat Proof (FINISHED) 6.92/4.41 6.92/4.41 6.92/4.41 ### Pre-processing the ITS problem ### 6.92/4.41 6.92/4.41 6.92/4.41 6.92/4.41 Initial linear ITS problem 6.92/4.41 6.92/4.41 Start location: f0 6.92/4.41 6.92/4.41 0: f0 -> f2 : [ A>=0 && B>=C ], cost: 1 6.92/4.41 6.92/4.41 1: f2 -> f2 : A'=-1+A, C'=-1+C, [ A>=1 && 1+B>=C ], cost: 1 6.92/4.41 6.92/4.41 2: f2 -> f2 : B'=-1+C+B, C'=-1+C, [ A>=0 && B>=0 ], cost: 1 6.92/4.41 6.92/4.41 6.92/4.41 6.92/4.41 ### Simplification by acceleration and chaining ### 6.92/4.41 6.92/4.41 6.92/4.41 6.92/4.41 Accelerating simple loops of location 1. 6.92/4.41 6.92/4.41 Accelerating the following rules: 6.92/4.41 6.92/4.41 1: f2 -> f2 : A'=-1+A, C'=-1+C, [ A>=1 && 1+B>=C ], cost: 1 6.92/4.41 6.92/4.41 2: f2 -> f2 : B'=-1+C+B, C'=-1+C, [ A>=0 && B>=0 ], cost: 1 6.92/4.41 6.92/4.41 6.92/4.41 6.92/4.41 Accelerated rule 1 with metering function A, yielding the new rule 3. 6.92/4.41 6.92/4.41 Found no metering function for rule 2. 6.92/4.41 6.92/4.41 Removing the simple loops: 1. 6.92/4.41 6.92/4.41 6.92/4.41 6.92/4.41 Accelerated all simple loops using metering functions (where possible): 6.92/4.41 6.92/4.41 Start location: f0 6.92/4.41 6.92/4.41 0: f0 -> f2 : [ A>=0 && B>=C ], cost: 1 6.92/4.41 6.92/4.41 2: f2 -> f2 : B'=-1+C+B, C'=-1+C, [ A>=0 && B>=0 ], cost: 1 6.92/4.41 6.92/4.41 3: f2 -> f2 : A'=0, C'=C-A, [ A>=1 && 1+B>=C ], cost: A 6.92/4.41 6.92/4.41 6.92/4.41 6.92/4.41 Chained accelerated rules (with incoming rules): 6.92/4.41 6.92/4.41 Start location: f0 6.92/4.41 6.92/4.41 0: f0 -> f2 : [ A>=0 && B>=C ], cost: 1 6.92/4.41 6.92/4.41 4: f0 -> f2 : B'=-1+C+B, C'=-1+C, [ A>=0 && B>=C && B>=0 ], cost: 2 6.92/4.41 6.92/4.41 5: f0 -> f2 : A'=0, C'=C-A, [ B>=C && A>=1 ], cost: 1+A 6.92/4.41 6.92/4.41 6.92/4.41 6.92/4.41 Removed unreachable locations (and leaf rules with constant cost): 6.92/4.41 6.92/4.41 Start location: f0 6.92/4.41 6.92/4.41 5: f0 -> f2 : A'=0, C'=C-A, [ B>=C && A>=1 ], cost: 1+A 6.92/4.41 6.92/4.41 6.92/4.41 6.92/4.41 ### Computing asymptotic complexity ### popout

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all output return to Complexity_ITS 2019-03-21 04.46