details

property	value
status	complete
benchmark	realbubble.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n057.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.23034095764 seconds
cpu usage	9.6837779
max memory	4.83364864E8

stage attributes

key	value
output-size	97059
starexec-result	WORST_CASE(Omega(n^2), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).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, 787 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 2440 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: start(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J, H - 1, L)) :|: 1 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A && I >= J && I <= J && K >= L && K <= L start(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl71(A, B, C, 0, E, M, G, H, 0, J, H - 1, L)) :|: A >= 2 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A && I >= J && I <= J && K >= L && K <= L start(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl53(A, 0, C, 0, E, F, G, H, 1, J, H - 1, L)) :|: A >= 2 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A && I >= J && I <= J && K >= L && K <= L lbl71(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl53(A, I, C, 1, E, F, G, H, 1 + I, J, K, L)) :|: D >= 0 && I >= D && K >= I + 1 && A >= K + 1 && H >= A && H <= A lbl53(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J, K, L)) :|: B >= 0 && A >= B + 2 && I >= B + 1 && I <= B + 1 && D >= 0 && D <= 0 && K >= B + 1 && K <= B + 1 && H >= A && H <= A lbl53(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl13(A, B, C, D, E, F, G, H, I, J, K - 1, L)) :|: 0 >= D + 1 && B >= 0 && D >= 0 && 1 >= D && A >= B + 2 && I >= B + 1 && I <= B + 1 && K >= B + 1 && K <= B + 1 && H >= A && H <= A lbl53(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl13(A, B, C, D, E, F, G, H, I, J, K - 1, L)) :|: B >= 0 && A >= B + 2 && D >= 1 && D <= 1 && I >= B + 1 && I <= B + 1 && K >= B + 1 && K <= B + 1 && H >= A && H <= A lbl53(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl71(A, B, C, D, E, M, G, H, I, J, K, L)) :|: K >= B + 2 && B >= 0 && D >= 0 && K >= B + 1 && 1 >= D && A >= K + 1 && I >= B + 1 && I <= B + 1 && H >= A && H <= A lbl53(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl53(A, I, C, D, E, F, G, H, 1 + I, J, K, L)) :|: K >= B + 2 && B >= 0 && D >= 0 && K >= B + 1 && 1 >= D && A >= K + 1 && I >= B + 1 && I <= B + 1 && H >= A && H <= A lbl13(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J, K, L)) :|: A >= 2 && K >= 0 && K <= 0 && D >= 1 && D <= 1 && H >= A && H <= A && I >= 1 && I <= 1 && B >= 0 && B <= 0 lbl13(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl71(A, B, C, 0, E, M, G, H, 0, J, K, L)) :|: B >= 1 && B >= 0 && A >= 2 + B && D >= 1 && D <= 1 && H >= A && H <= A && K >= B && K <= B && I >= 1 + B && I <= 1 + B lbl13(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(lbl53(A, 0, C, 0, E, F, G, H, 1, J, K, L)) :|: B >= 1 && B >= 0 && A >= 2 + B && D >= 1 && D <= 1 && H >= A && H <= A && K >= B && K <= B && I >= 1 + B && I <= 1 + B start0(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(start(A, C, C, E, E, G, G, A, J, J, L, L)) :|: TRUE The start-symbols are:[start0_12] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 24*ar_0 + 24*ar_0^2 + 9) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_7 - 1, ar_11)) [ 1 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 /\ ar_8 = ar_9 /\ ar_10 = ar_11 ] (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl71(ar_0, ar_1, ar_2, 0, ar_4, m, ar_6, ar_7, 0, ar_9, ar_7 - 1, ar_11)) [ ar_0 >= 2 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 /\ ar_8 = ar_9 /\ ar_10 = ar_11 ] (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl53(ar_0, 0, ar_2, 0, ar_4, ar_5, ar_6, ar_7, 1, ar_9, ar_7 - 1, ar_11)) [ ar_0 >= 2 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 /\ ar_8 = ar_9 /\ ar_10 = ar_11 ] (Comp: ?, Cost: 1) lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl53(ar_0, ar_8, ar_2, 1, ar_4, ar_5, ar_6, ar_7, ar_8 + 1, ar_9, ar_10, ar_11)) [ ar_3 >= 0 /\ ar_8 >= ar_3 /\ ar_10 >= ar_8 + 1 /\ ar_0 >= ar_10 + 1 /\ ar_7 = ar_0 ] (Comp: ?, Cost: 1) lbl53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_1 >= 0 /\ ar_0 >= ar_1 + 2 /\ ar_8 = ar_1 + 1 /\ ar_3 = 0 /\ ar_10 = ar_1 + 1 /\ ar_7 = ar_0 ] (Comp: ?, Cost: 1) lbl53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 - 1, ar_11)) [ 0 >= ar_3 + 1 /\ ar_1 >= 0 /\ ar_3 >= 0 /\ 1 >= ar_3 /\ ar_0 >= ar_1 + 2 /\ ar_8 = ar_1 + 1 /\ ar_10 = ar_1 + 1 /\ ar_7 = ar_0 ] (Comp: ?, Cost: 1) lbl53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 - 1, ar_11)) [ ar_1 >= 0 /\ ar_0 >= ar_1 + 2 /\ ar_3 = 1 /\ ar_8 = ar_1 + 1 /\ ar_10 = ar_1 + 1 /\ ar_7 = ar_0 ] (Comp: ?, Cost: 1) lbl53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_10 >= ar_1 + 2 /\ ar_1 >= 0 /\ ar_3 >= 0 /\ ar_10 >= ar_1 + 1 /\ 1 >= ar_3 /\ ar_0 >= ar_10 + 1 /\ ar_8 = ar_1 + 1 /\ ar_7 = ar_0 ] (Comp: ?, Cost: 1) lbl53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl53(ar_0, ar_8, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 + 1, ar_9, ar_10, ar_11)) [ ar_10 >= ar_1 + 2 /\ ar_1 >= 0 /\ ar_3 >= 0 /\ ar_10 >= ar_1 + 1 /\ 1 >= ar_3 /\ ar_0 >= ar_10 + 1 /\ ar_8 = ar_1 + 1 /\ ar_7 = ar_0 ] (Comp: ?, Cost: 1) lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 2 /\ ar_10 = 0 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_8 = 1 /\ ar_1 = 0 ] (Comp: ?, Cost: 1) lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl71(ar_0, ar_1, ar_2, 0, ar_4, m, ar_6, ar_7, 0, ar_9, ar_10, ar_11)) [ ar_1 >= 1 /\ ar_1 >= 0 /\ ar_0 >= ar_1 + 2 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_10 = ar_1 /\ ar_8 = ar_1 + 1 ] (Comp: ?, Cost: 1) lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl53(ar_0, 0, ar_2, 0, ar_4, ar_5, ar_6, ar_7, 1, ar_9, ar_10, ar_11)) [ ar_1 >= 1 /\ ar_1 >= 0 /\ ar_0 >= ar_1 + 2 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_10 = ar_1 /\ ar_8 = ar_1 + 1 ] (Comp: ?, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0, ar_9, ar_9, ar_11, ar_11)) (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, ar_10, ar_11) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: lbl53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 - 1, ar_11)) [ 0 >= ar_3 + 1 /\ ar_1 >= 0 /\ ar_3 >= 0 /\ 1 >= ar_3 /\ ar_0 >= ar_1 + 2 /\ ar_8 = ar_1 + 1 /\ ar_10 = ar_1 + 1 /\ ar_7 = ar_0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl53(ar_0, 0, ar_2, 0, ar_4, ar_5, ar_6, ar_7, 1, ar_9, ar_10, ar_11)) [ ar_1 >= 1 /\ ar_1 >= 0 /\ ar_0 >= ar_1 + 2 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_10 = ar_1 /\ ar_8 = ar_1 + 1 ] (Comp: ?, Cost: 1) lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(lbl71(ar_0, ar_1, ar_2, 0, ar_4, m, ar_6, ar_7, 0, ar_9, ar_10, ar_11)) [ ar_1 >= 1 /\ ar_1 >= 0 /\ ar_0 >= ar_1 + 2 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_10 = ar_1 /\ ar_8 = ar_1 + 1 ] (Comp: ?, Cost: 1) lbl13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 2 /\ ar_10 = 0 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_8 = 1 /\ ar_1 = 0 ] popout

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actions

all output return to Compl Integ Trans Syste 26843