details

property	value
status	complete
benchmark	two_arrays2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n123.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.20091 seconds
cpu usage	7.29984
user time	6.9367
system time	0.363143
max virtual memory	1.8747836E7
max residence set size	224048.0

stage attributes

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

output

7.07/3.15 WORST_CASE(Omega(n^1), O(n^1)) 7.07/3.17 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 7.07/3.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.07/3.17 7.07/3.17 7.07/3.17 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 7.07/3.17 7.07/3.17 (0) CpxIntTrs 7.07/3.17 (1) Koat Proof [FINISHED, 616 ms] 7.07/3.17 (2) BOUNDS(1, n^1) 7.07/3.17 (3) Loat Proof [FINISHED, 1434 ms] 7.07/3.17 (4) BOUNDS(n^1, INF) 7.07/3.17 7.07/3.17 7.07/3.17 ---------------------------------------- 7.07/3.17 7.07/3.17 (0) 7.07/3.17 Obligation: 7.07/3.17 Complexity Int TRS consisting of the following rules: 7.07/3.17 f0(A, B, C, D, E, F, G, H, I, J) -> Com_1(f17(0, K, L, 0, E, F, G, H, I, J)) :|: TRUE 7.07/3.17 f17(A, B, C, D, E, F, G, H, I, J) -> Com_1(f17(A, B, C, D + 1, E, F, G, H, I, J)) :|: E >= D + 1 7.07/3.17 f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, B, C, D, E, F + 1, G, H, I, J)) :|: E >= F + 1 7.07/3.17 f37(A, B, C, D, E, F, G, H, I, J) -> Com_1(f37(A, B, C, D, E, F, G + 1, H, I, J)) :|: E >= G + 1 7.07/3.17 f45(A, B, C, D, E, F, G, H, I, J) -> Com_1(f45(A + 1, B, C, D, E, F, G, H, I, J)) :|: E >= A + 1 7.07/3.17 f55(A, B, C, D, E, F, G, H, I, J) -> Com_1(f55(A, B, C, D, E, F, G, H + 1, I, J)) :|: E >= H + 1 7.07/3.17 f65(A, B, C, D, E, F, G, H, I, J) -> Com_1(f65(A, B, C, D, E, F, G, H, I + 1, J)) :|: E >= I + 1 7.07/3.17 f75(A, B, C, D, E, F, G, H, I, J) -> Com_1(f75(A, B, C, D, E, F, G, H, I, J + 1)) :|: E >= J + 1 7.07/3.17 f83(A, B, C, D, E, F, G, H, I, J) -> Com_1(f83(A + 1, B, C, D, E, F, G, H, I, J)) :|: E >= A + 1 7.07/3.17 f83(A, B, C, D, E, F, G, H, I, J) -> Com_1(f93(A, B, C, D, E, F, G, H, I, J)) :|: A >= E 7.07/3.17 f75(A, B, C, D, E, F, G, H, I, J) -> Com_1(f83(0, B, C, D, E, F, G, H, I, J)) :|: J >= E 7.07/3.17 f65(A, B, C, D, E, F, G, H, I, J) -> Com_1(f75(A, B, C, D, E, F, G, H, I, 0)) :|: I >= E 7.07/3.17 f55(A, B, C, D, E, F, G, H, I, J) -> Com_1(f65(A, B, C, D, E, F, G, H, 0, J)) :|: H >= E 7.07/3.17 f45(A, B, C, D, E, F, G, H, I, J) -> Com_1(f55(A, B, C, D, E, F, G, 0, I, J)) :|: A >= E 7.07/3.17 f37(A, B, C, D, E, F, G, H, I, J) -> Com_1(f45(0, B, C, D, E, F, G, H, I, J)) :|: G >= E 7.07/3.17 f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f37(A, B, C, D, E, F, 0, H, I, J)) :|: F >= E 7.07/3.17 f17(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, B, C, D, E, 0, G, H, I, J)) :|: D >= E 7.07/3.17 7.07/3.17 The start-symbols are:[f0_10] 7.07/3.17 7.07/3.17 7.07/3.17 ---------------------------------------- 7.07/3.17 7.07/3.17 (1) Koat Proof (FINISHED) 7.07/3.17 YES(?, 15*ar_4 + 65) 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 Initial complexity problem: 7.07/3.17 7.07/3.17 1: T: 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, k, l, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f65(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 + 1, ar_9)) [ ar_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f65(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9]. 7.07/3.17 7.07/3.17 We thus obtain the following problem: 7.07/3.17 7.07/3.17 2: T: 7.07/3.17 7.07/3.17 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Complexity_ITS 2019-03-21 04.46