details

property	value
status	complete
benchmark	selectSort.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n026.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.52372813225 seconds
cpu usage	5.553202022
max memory	3.18840832E8

stage attributes

key	value
output-size	44670
starexec-result	WORST_CASE(Omega(n^2), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 143 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 940 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f0(A, B, C, D, E, F, G, H) -> Com_1(f10(I, 0, C, D, E, F, G, H)) :|: TRUE f10(A, B, C, D, E, F, G, H) -> Com_1(f10(A, B + 1, C, D, E, F, G, H)) :|: C >= B + 1 f18(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, E, E + 1, H)) :|: D >= 2 + E f22(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, F, G + 1, H)) :|: D >= G + 1 f22(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, G, G + 1, H)) :|: D >= G + 1 f34(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, D, E + 1, F, G, H)) :|: D >= 2 + E f34(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, H)) :|: E + 1 >= D f22(A, B, C, D, E, F, G, H) -> Com_1(f18(A, B, C, D, E + 1, F, G, I)) :|: G >= D f18(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, D, 0, F, G, H)) :|: E + 1 >= D f10(A, B, C, D, E, F, G, H) -> Com_1(f18(A, B, C, C, 0, F, G, H)) :|: B >= C The start-symbols are:[f0_8] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 44*ar_2 + 24*ar_2^2 + 10) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f10(i, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f18(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_4 + 1, ar_7)) [ ar_3 >= ar_4 + 2 ] (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_3 >= ar_6 + 1 ] (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6 + 1, ar_7)) [ ar_3 >= ar_6 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_3 >= ar_4 + 2 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 + 1 >= ar_3 ] (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f18(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, i)) [ ar_6 >= ar_3 ] (Comp: ?, Cost: 1) f18(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 + 1 >= ar_3 ] (Comp: ?, Cost: 1) f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f18(ar_0, ar_1, ar_2, ar_2, 0, ar_5, ar_6, ar_7)) [ ar_1 >= ar_2 ] (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_1, ar_2, ar_3, ar_4, ar_6]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ] (Comp: ?, Cost: 1) f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ] (Comp: ?, Cost: 1) f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ] (Comp: ?, Cost: 1) f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ] (Comp: ?, Cost: 1) f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ] (Comp: ?, Cost: 1) f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ] (Comp: ?, Cost: 1) f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ] popout

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actions

all output return to Compl Integ Trans Syste 26843