details

property	value
status	complete
benchmark	ack.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n017.star.cs.uiowa.edu
space	misc

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.66908 seconds
cpu usage	5.28106
user time	4.9575
system time	0.323555
max virtual memory	1.865912E7
max residence set size	215152.0

stage attributes

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

output

5.19/2.62 WORST_CASE(Omega(n^1), ?) 5.23/2.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.23/2.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.23/2.63 5.23/2.63 5.23/2.63 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). 5.23/2.63 5.23/2.63 (0) CpxIntTrs 5.23/2.63 (1) Loat Proof [FINISHED, 522 ms] 5.23/2.63 (2) BOUNDS(n^1, INF) 5.23/2.63 5.23/2.63 5.23/2.63 ---------------------------------------- 5.23/2.63 5.23/2.63 (0) 5.23/2.63 Obligation: 5.23/2.63 Complexity Int TRS consisting of the following rules: 5.23/2.63 ack(A, B) -> Com_1(ack(A - 1, C)) :|: A >= 1 && B >= 1 5.23/2.63 ack(A, B) -> Com_1(ack(A, B - 1)) :|: A >= 1 && B >= 1 5.23/2.63 start(A, B) -> Com_1(ack(A, B)) :|: TRUE 5.23/2.63 5.23/2.63 The start-symbols are:[start_2] 5.23/2.63 5.23/2.63 5.23/2.63 ---------------------------------------- 5.23/2.63 5.23/2.63 (1) Loat Proof (FINISHED) 5.23/2.63 5.23/2.63 5.23/2.63 ### Pre-processing the ITS problem ### 5.23/2.63 5.23/2.63 5.23/2.63 5.23/2.63 Initial linear ITS problem 5.23/2.63 5.23/2.63 Start location: start 5.23/2.63 5.23/2.63 0: ack -> ack : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 5.23/2.63 5.23/2.63 1: ack -> ack : B'=-1+B, [ A>=1 && B>=1 ], cost: 1 5.23/2.63 5.23/2.63 2: start -> ack : [], cost: 1 5.23/2.63 5.23/2.63 5.23/2.63 5.23/2.63 ### Simplification by acceleration and chaining ### 5.23/2.63 5.23/2.63 5.23/2.63 5.23/2.63 Accelerating simple loops of location 0. 5.23/2.63 5.23/2.63 Accelerating the following rules: 5.23/2.63 5.23/2.63 0: ack -> ack : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 5.23/2.63 5.23/2.63 1: ack -> ack : B'=-1+B, [ A>=1 && B>=1 ], cost: 1 5.23/2.63 5.23/2.63 5.23/2.63 5.23/2.63 Accelerated rule 0 with metering function A (after strengthening guard), yielding the new rule 3. 5.23/2.63 5.23/2.63 Accelerated rule 1 with metering function B, yielding the new rule 4. 5.23/2.63 5.23/2.63 Removing the simple loops: 1. 5.23/2.63 5.23/2.63 5.23/2.63 5.23/2.63 Accelerated all simple loops using metering functions (where possible): 5.23/2.63 5.23/2.63 Start location: start 5.23/2.63 5.23/2.63 0: ack -> ack : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 5.23/2.63 5.23/2.63 3: ack -> ack : A'=0, B'=free, [ A>=1 && B>=1 && free>=1 ], cost: A 5.23/2.63 5.23/2.63 4: ack -> ack : B'=0, [ A>=1 && B>=1 ], cost: B 5.23/2.63 5.23/2.63 2: start -> ack : [], cost: 1 5.23/2.63 5.23/2.63 5.23/2.63 5.23/2.63 Chained accelerated rules (with incoming rules): 5.23/2.63 5.23/2.63 Start location: start 5.23/2.63 5.23/2.63 2: start -> ack : [], cost: 1 5.23/2.63 5.23/2.63 5: start -> ack : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 2 5.23/2.63 5.23/2.63 6: start -> ack : A'=0, B'=free, [ A>=1 && B>=1 && free>=1 ], cost: 1+A 5.23/2.63 5.23/2.63 7: start -> ack : B'=0, [ A>=1 && B>=1 ], cost: 1+B 5.23/2.63 5.23/2.63 5.23/2.63 5.23/2.63 Removed unreachable locations (and leaf rules with constant cost): 5.23/2.63 5.23/2.63 Start location: start 5.23/2.63 5.23/2.63 6: start -> ack : A'=0, B'=free, [ A>=1 && B>=1 && free>=1 ], cost: 1+A popout

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all output return to Complexity_ITS 2019-03-21 04.46