details

property	value
status	complete
benchmark	logarithmic.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n050.star.cs.uiowa.edu
space	misc

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.64538 seconds
cpu usage	3.37962
user time	3.16709
system time	0.212527
max virtual memory	1.840904E7
max residence set size	214404.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

3.27/1.58 WORST_CASE(?, O(1)) 3.27/1.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 3.27/1.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.27/1.59 3.27/1.59 3.27/1.59 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 3.27/1.59 3.27/1.59 (0) CpxIntTrs 3.27/1.59 (1) Koat Proof [FINISHED, 8 ms] 3.27/1.59 (2) BOUNDS(1, 1) 3.27/1.59 3.27/1.59 3.27/1.59 ---------------------------------------- 3.27/1.59 3.27/1.59 (0) 3.27/1.59 Obligation: 3.27/1.59 Complexity Int TRS consisting of the following rules: 3.27/1.59 start(A) -> Com_1(a(A)) :|: A >= 1 3.27/1.59 start(A) -> Com_1(a(A)) :|: A >= 2 3.27/1.59 start(A) -> Com_1(a(A)) :|: A >= 4 3.27/1.59 a(A) -> Com_1(a(A * B)) :|: 1 >= 2 * B && 3 * B >= 2 && A >= 2 3.27/1.59 3.27/1.59 The start-symbols are:[start_1] 3.27/1.59 3.27/1.59 3.27/1.59 ---------------------------------------- 3.27/1.59 3.27/1.59 (1) Koat Proof (FINISHED) 3.27/1.59 YES(?, 3) 3.27/1.59 3.27/1.59 3.27/1.59 3.27/1.59 Initial complexity problem: 3.27/1.59 3.27/1.59 1: T: 3.27/1.59 3.27/1.59 (Comp: ?, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 1 ] 3.27/1.59 3.27/1.59 (Comp: ?, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 2 ] 3.27/1.59 3.27/1.59 (Comp: ?, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 4 ] 3.27/1.59 3.27/1.59 (Comp: ?, Cost: 1) a(ar_0) -> Com_1(a(ar_0*b)) [ 1 >= 2*b /\ 3*b >= 2 /\ ar_0 >= 2 ] 3.27/1.59 3.27/1.59 (Comp: 1, Cost: 0) koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ] 3.27/1.59 3.27/1.59 start location: koat_start 3.27/1.59 3.27/1.59 leaf cost: 0 3.27/1.59 3.27/1.59 3.27/1.59 3.27/1.59 Testing for reachability in the complexity graph removes the following transition from problem 1: 3.27/1.59 3.27/1.59 a(ar_0) -> Com_1(a(ar_0*b)) [ 1 >= 2*b /\ 3*b >= 2 /\ ar_0 >= 2 ] 3.27/1.59 3.27/1.59 We thus obtain the following problem: 3.27/1.59 3.27/1.59 2: T: 3.27/1.59 3.27/1.59 (Comp: ?, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 4 ] 3.27/1.59 3.27/1.59 (Comp: ?, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 2 ] 3.27/1.59 3.27/1.59 (Comp: ?, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 1 ] 3.27/1.59 3.27/1.59 (Comp: 1, Cost: 0) koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ] 3.27/1.59 3.27/1.59 start location: koat_start 3.27/1.59 3.27/1.59 leaf cost: 0 3.27/1.59 3.27/1.59 3.27/1.59 3.27/1.59 Repeatedly propagating knowledge in problem 2 produces the following problem: 3.27/1.59 3.27/1.59 3: T: 3.27/1.59 3.27/1.59 (Comp: 1, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 4 ] 3.27/1.59 3.27/1.59 (Comp: 1, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 2 ] 3.27/1.59 3.27/1.59 (Comp: 1, Cost: 1) start(ar_0) -> Com_1(a(ar_0)) [ ar_0 >= 1 ] 3.27/1.59 3.27/1.59 (Comp: 1, Cost: 0) koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ] 3.27/1.59 3.27/1.59 start location: koat_start 3.27/1.59 3.27/1.59 leaf cost: 0 3.27/1.59 3.27/1.59 3.27/1.59 3.27/1.59 Complexity upper bound 3 3.27/1.59 3.27/1.59 3.27/1.59 3.27/1.59 Time: 0.012 sec (SMT: 0.011 sec) 3.27/1.59 3.27/1.59 3.27/1.59 ---------------------------------------- popout

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all output return to Complexity_ITS 2019-03-21 04.46