details

property	value
status	complete
benchmark	nested2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.98951 seconds
cpu usage	5.5415
user time	5.18683
system time	0.354669
max virtual memory	1.8505636E7
max residence set size	217600.0

stage attributes

key	value
starexec-result	MAYBE

output

5.41/2.95 MAYBE 5.41/2.96 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.41/2.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.41/2.96 5.41/2.96 5.41/2.96 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). 5.41/2.96 5.41/2.96 (0) CpxIntTrs 5.41/2.96 (1) Loat Proof [FINISHED, 299 ms] 5.41/2.96 (2) BOUNDS(1, INF) 5.41/2.96 5.41/2.96 5.41/2.96 ---------------------------------------- 5.41/2.96 5.41/2.96 (0) 5.41/2.96 Obligation: 5.41/2.96 Complexity Int TRS consisting of the following rules: 5.41/2.96 f0(A, B, C, D, E, F) -> Com_1(f0(-(1) + A, C, -(1) + C, A, E, F)) :|: A >= 1 5.41/2.96 f1(A, B, C, D, E, F) -> Com_1(f0(-(1) + A, B, -(1) + C, D, C, A)) :|: A >= 1 && C >= 1 5.41/2.96 f0(A, B, C, D, E, F) -> Com_1(f0(5000, B, C, D, E, F)) :|: 0 >= A && C >= 1 5.41/2.96 f3(A, B, C, D, E, F) -> Com_1(f0(5000, B, G, D, E, F)) :|: G >= 1 5.41/2.96 5.41/2.96 The start-symbols are:[f3_6] 5.41/2.96 5.41/2.96 5.41/2.96 ---------------------------------------- 5.41/2.96 5.41/2.96 (1) Loat Proof (FINISHED) 5.41/2.96 5.41/2.96 5.41/2.96 ### Pre-processing the ITS problem ### 5.41/2.96 5.41/2.96 5.41/2.96 5.41/2.96 Initial linear ITS problem 5.41/2.96 5.41/2.96 Start location: f3 5.41/2.96 5.41/2.96 0: f0 -> f0 : A'=-1+A, B'=C, C'=-1+C, D'=A, [ A>=1 ], cost: 1 5.41/2.96 5.41/2.96 2: f0 -> f0 : A'=5000, [ 0>=A && C>=1 ], cost: 1 5.41/2.96 5.41/2.96 1: f1 -> f0 : A'=-1+A, C'=-1+C, E'=C, F'=A, [ A>=1 && C>=1 ], cost: 1 5.41/2.96 5.41/2.96 3: f3 -> f0 : A'=5000, C'=free, [ free>=1 ], cost: 1 5.41/2.96 5.41/2.96 5.41/2.96 5.41/2.96 Removed unreachable and leaf rules: 5.41/2.96 5.41/2.96 Start location: f3 5.41/2.96 5.41/2.96 0: f0 -> f0 : A'=-1+A, B'=C, C'=-1+C, D'=A, [ A>=1 ], cost: 1 5.41/2.96 5.41/2.96 2: f0 -> f0 : A'=5000, [ 0>=A && C>=1 ], cost: 1 5.41/2.96 5.41/2.96 3: f3 -> f0 : A'=5000, C'=free, [ free>=1 ], cost: 1 5.41/2.96 5.41/2.96 5.41/2.96 5.41/2.96 ### Simplification by acceleration and chaining ### 5.41/2.96 5.41/2.96 5.41/2.96 5.41/2.96 Accelerating simple loops of location 0. 5.41/2.96 5.41/2.96 Accelerating the following rules: 5.41/2.96 5.41/2.96 0: f0 -> f0 : A'=-1+A, B'=C, C'=-1+C, D'=A, [ A>=1 ], cost: 1 5.41/2.96 5.41/2.96 2: f0 -> f0 : A'=5000, [ 0>=A && C>=1 ], cost: 1 5.41/2.96 5.41/2.96 5.41/2.96 5.41/2.96 Accelerated rule 0 with metering function A, yielding the new rule 4. 5.41/2.96 5.41/2.96 Found no metering function for rule 2. 5.41/2.96 5.41/2.96 Removing the simple loops: 0. 5.41/2.96 5.41/2.96 5.41/2.96 5.41/2.96 Accelerated all simple loops using metering functions (where possible): 5.41/2.96 5.41/2.96 Start location: f3 5.41/2.96 5.41/2.96 2: f0 -> f0 : A'=5000, [ 0>=A && C>=1 ], cost: 1 5.41/2.96 5.41/2.96 4: f0 -> f0 : A'=0, B'=1+C-A, C'=C-A, D'=1, [ A>=1 ], cost: A 5.41/2.96 5.41/2.96 3: f3 -> f0 : A'=5000, C'=free, [ free>=1 ], cost: 1 5.41/2.96 5.41/2.96 5.41/2.96 5.41/2.96 Chained accelerated rules (with incoming rules): 5.41/2.96 5.41/2.96 Start location: f3 5.41/2.96 5.41/2.96 3: f3 -> f0 : A'=5000, C'=free, [ free>=1 ], cost: 1 5.41/2.96 popout

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all output return to Complexity_ITS 2019-03-21 04.46