details

property	value
status	complete
benchmark	intSqRoot.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n018.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.00208 seconds
cpu usage	3.87263
user time	3.63346
system time	0.239168
max virtual memory	1.840722E7
max residence set size	217476.0

stage attributes

key	value
starexec-result	MAYBE

output

3.57/1.97 MAYBE 3.57/1.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 3.57/1.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.57/1.98 3.57/1.98 3.57/1.98 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). 3.57/1.98 3.57/1.98 (0) CpxIntTrs 3.57/1.98 (1) Loat Proof [FINISHED, 208 ms] 3.57/1.98 (2) BOUNDS(1, INF) 3.57/1.98 3.57/1.98 3.57/1.98 ---------------------------------------- 3.57/1.98 3.57/1.98 (0) 3.57/1.98 Obligation: 3.57/1.98 Complexity Int TRS consisting of the following rules: 3.57/1.98 f0(A, B, C, D) -> Com_1(f6(1, C, C, D)) :|: TRUE 3.57/1.98 f6(A, B, C, D) -> Com_1(f6(A, E, C, E)) :|: B >= A + 2 && E * E >= C + 1 3.57/1.98 f6(A, B, C, D) -> Com_1(f6(E, B, C, E)) :|: B >= A + 2 && C >= E * E 3.57/1.98 f6(A, B, C, D) -> Com_1(f16(A, B, C, D)) :|: A + 1 >= B 3.57/1.98 3.57/1.98 The start-symbols are:[f0_4] 3.57/1.98 3.57/1.98 3.57/1.98 ---------------------------------------- 3.57/1.98 3.57/1.98 (1) Loat Proof (FINISHED) 3.57/1.98 3.57/1.98 3.57/1.98 ### Pre-processing the ITS problem ### 3.57/1.98 3.57/1.98 3.57/1.98 3.57/1.98 Initial linear ITS problem 3.57/1.98 3.57/1.98 Start location: f0 3.57/1.98 3.57/1.98 0: f0 -> f6 : A'=1, B'=C, [], cost: 1 3.57/1.98 3.57/1.98 1: f6 -> f6 : B'=free, D'=free, [ B>=2+A && free^2>=1+C ], cost: 1 3.57/1.98 3.57/1.98 2: f6 -> f6 : A'=free_1, D'=free_1, [ B>=2+A && C>=free_1^2 ], cost: 1 3.57/1.98 3.57/1.98 3: f6 -> f16 : [ 1+A>=B ], cost: 1 3.57/1.98 3.57/1.98 3.57/1.98 3.57/1.98 Removed unreachable and leaf rules: 3.57/1.98 3.57/1.98 Start location: f0 3.57/1.98 3.57/1.98 0: f0 -> f6 : A'=1, B'=C, [], cost: 1 3.57/1.98 3.57/1.98 1: f6 -> f6 : B'=free, D'=free, [ B>=2+A && free^2>=1+C ], cost: 1 3.57/1.98 3.57/1.98 2: f6 -> f6 : A'=free_1, D'=free_1, [ B>=2+A && C>=free_1^2 ], cost: 1 3.57/1.98 3.57/1.98 3.57/1.98 3.57/1.98 ### Simplification by acceleration and chaining ### 3.57/1.98 3.57/1.98 3.57/1.98 3.57/1.98 Accelerating simple loops of location 1. 3.57/1.98 3.57/1.98 Accelerating the following rules: 3.57/1.98 3.57/1.98 1: f6 -> f6 : B'=free, D'=free, [ B>=2+A && free^2>=1+C ], cost: 1 3.57/1.98 3.57/1.98 2: f6 -> f6 : A'=free_1, D'=free_1, [ B>=2+A && C>=free_1^2 ], cost: 1 3.57/1.98 3.57/1.98 3.57/1.98 3.57/1.98 Found no metering function for rule 1 (rule is too complicated). 3.57/1.98 3.57/1.98 Found no metering function for rule 2 (rule is too complicated). 3.57/1.98 3.57/1.98 Removing the simple loops:. 3.57/1.98 3.57/1.98 3.57/1.98 3.57/1.98 Accelerated all simple loops using metering functions (where possible): 3.57/1.98 3.57/1.98 Start location: f0 3.57/1.98 3.57/1.98 0: f0 -> f6 : A'=1, B'=C, [], cost: 1 3.57/1.98 3.57/1.98 1: f6 -> f6 : B'=free, D'=free, [ B>=2+A && free^2>=1+C ], cost: 1 3.57/1.98 3.57/1.98 2: f6 -> f6 : A'=free_1, D'=free_1, [ B>=2+A && C>=free_1^2 ], cost: 1 3.57/1.98 3.57/1.98 3.57/1.98 3.57/1.98 Chained accelerated rules (with incoming rules): 3.57/1.98 3.57/1.98 Start location: f0 3.57/1.98 3.57/1.98 0: f0 -> f6 : A'=1, B'=C, [], cost: 1 3.57/1.98 popout

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all output return to Complexity_ITS 2019-03-21 04.46