details

property	value
status	complete
benchmark	practical2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	CAV02

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.7024 seconds
cpu usage	6.13995
user time	5.81581
system time	0.324145
max virtual memory	1.8642224E7
max residence set size	224592.0

stage attributes

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

output

5.97/2.65 WORST_CASE(Omega(n^1), O(n^1)) 5.97/2.66 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.97/2.66 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.97/2.66 5.97/2.66 5.97/2.66 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 5.97/2.66 5.97/2.66 (0) CpxIntTrs 5.97/2.66 (1) Koat Proof [FINISHED, 925 ms] 5.97/2.66 (2) BOUNDS(1, n^1) 5.97/2.66 (3) Loat Proof [FINISHED, 724 ms] 5.97/2.66 (4) BOUNDS(n^1, INF) 5.97/2.66 5.97/2.66 5.97/2.66 ---------------------------------------- 5.97/2.66 5.97/2.66 (0) 5.97/2.66 Obligation: 5.97/2.66 Complexity Int TRS consisting of the following rules: 5.97/2.66 eval0(A, B, C, D) -> Com_1(eval1(B, B, 1, D)) :|: TRUE 5.97/2.66 eval1(A, B, C, D) -> Com_1(end(A, B, C, D)) :|: A >= 101 5.97/2.66 eval1(A, B, C, D) -> Com_1(eval3(A, B, C, D)) :|: 100 >= A 5.97/2.66 eval3(A, B, C, D) -> Com_1(eval3(A + 11, B, C + 1, D)) :|: 100 >= A 5.97/2.66 eval3(A, B, C, D) -> Com_1(eval5(A, B, C, D)) :|: A >= 101 5.97/2.66 eval5(A, B, C, D) -> Com_1(eval7(A - 10, B, C - 1, D)) :|: C >= 2 5.97/2.66 eval7(A, B, C, D) -> Com_1(eval5(A, B, C, A - 10)) :|: A >= 101 && C >= 1 && C <= 1 5.97/2.66 eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: 100 >= A 5.97/2.66 eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: 2 >= C 5.97/2.66 eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: C >= 0 5.97/2.66 eval9(A, B, C, D) -> Com_1(eval11(A - 10, B, C - 1, D)) :|: A >= 101 5.97/2.66 eval9(A, B, C, D) -> Com_1(eval11(A, B, C, D)) :|: 100 >= A 5.97/2.66 eval11(A, B, C, D) -> Com_1(eval5(A + 11, B, C + 1, D)) :|: TRUE 5.97/2.66 5.97/2.66 The start-symbols are:[eval0_4] 5.97/2.66 5.97/2.66 5.97/2.66 ---------------------------------------- 5.97/2.66 5.97/2.66 (1) Koat Proof (FINISHED) 5.97/2.66 YES(?, 84482*ar_1 + 8492880) 5.97/2.66 5.97/2.66 5.97/2.66 5.97/2.66 Initial complexity problem: 5.97/2.66 5.97/2.66 1: T: 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval0(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval1(ar_1, ar_1, 1, ar_3)) 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval1(ar_0, ar_1, ar_2, ar_3) -> Com_1(end(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval1(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval3(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval3(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1, ar_3)) [ 100 >= ar_0 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval3(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval5(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval5(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 2 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval7(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval5(ar_0, ar_1, ar_2, ar_0 - 10)) [ ar_0 >= 101 /\ ar_2 = 1 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval7(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval9(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval7(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval9(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_2 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval7(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval9(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval9(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1, ar_3)) [ ar_0 >= 101 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval9(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval11(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval11(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1, ar_3)) 5.97/2.66 5.97/2.66 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval0(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 5.97/2.66 5.97/2.66 start location: koat_start 5.97/2.66 5.97/2.66 leaf cost: 0 5.97/2.66 5.97/2.66 5.97/2.66 5.97/2.66 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2]. 5.97/2.66 5.97/2.66 We thus obtain the following problem: 5.97/2.66 5.97/2.66 2: T: 5.97/2.66 5.97/2.66 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ] 5.97/2.66 5.97/2.66 (Comp: ?, Cost: 1) eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ] popout

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all output return to Complexity_ITS 2019-03-21 04.46