details

property	value
status	complete
benchmark	mspe.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	misc

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.73800110817 seconds
cpu usage	7.765719781
max memory	3.23117056E8

stage attributes

key	value
output-size	12276
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

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^1), O(n^1)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 224 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 2035 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: start(A, B, C, D, E, F) -> Com_1(m1(A, B, C, D, E, F)) :|: A >= 0 && B + A + 2 >= 2 * C && B >= A + 1 && 2 * C >= B + A && D >= 0 && E + 1 >= C && E + 1 <= C && F >= A && F <= A m1(A, B, C, D, E, F) -> Com_1(m1(A, B, H, D, E, G)) :|: B >= 1 && D >= 0 && A >= E + 1 && B + 1 >= G && C + 1 >= H && H >= 1 + C && F + 1 >= G && G >= 1 + F m1(A, B, C, D, E, F) -> Com_1(m1(H, B, C, D, E, G)) :|: B >= 1 && D >= 0 && B >= F && E + 1 >= H && C >= B + 1 && F + 1 >= G && G >= 1 + F && A + 1 >= H && H >= 1 + A m1(A, B, C, D, E, F) -> Com_1(m1(A, B, H, D, E, G)) :|: B >= 1 && D >= 0 && B >= F && B + 1 >= H && E >= A && F + 1 >= G && G >= 1 + F && C + 1 >= H && H >= 1 + C m1(A, B, C, D, E, F) -> Com_1(m1(H, B, C, D, E, G)) :|: B >= 1 && D >= 0 && B >= F && B >= C && E + 1 >= H && A + 1 >= H && H >= 1 + A && F + 1 >= G && G >= 1 + F The start-symbols are:[start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 4*ar_1 + 5) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 0 /\ ar_1 + ar_0 + 2 >= 2*ar_2 /\ ar_1 >= ar_0 + 1 /\ 2*ar_2 >= ar_1 + ar_0 /\ ar_3 >= 0 /\ ar_4 + 1 = ar_2 /\ ar_5 = ar_0 ] (Comp: ?, Cost: 1) m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_4 + 1 /\ ar_1 >= ar_5 ] (Comp: ?, Cost: 1) m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_4 >= ar_0 /\ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_1 >= ar_2 /\ ar_4 >= ar_0 ] (Comp: ?, Cost: 1) m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_1 >= ar_2 /\ ar_4 >= ar_0 ] (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 0 /\ ar_1 + ar_0 + 2 >= 2*ar_2 /\ ar_1 >= ar_0 + 1 /\ 2*ar_2 >= ar_1 + ar_0 /\ ar_3 >= 0 /\ ar_4 + 1 = ar_2 /\ ar_5 = ar_0 ] (Comp: ?, Cost: 1) m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_4 + 1 /\ ar_1 >= ar_5 ] (Comp: ?, Cost: 1) m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_4 >= ar_0 /\ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_1 >= ar_2 /\ ar_4 >= ar_0 ] (Comp: ?, Cost: 1) m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_1 >= ar_2 /\ ar_4 >= ar_0 ] (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = V_2 + 1 Pol(m1) = V_2 - V_6 + 1 Pol(koat_start) = V_2 + 1 orients all transitions weakly and the transitions m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_4 >= ar_0 /\ ar_2 >= ar_1 + 1 ] m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_1 >= ar_2 /\ ar_4 >= ar_0 ] m1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(m1(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5 + 1)) [ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_1 >= ar_5 /\ ar_1 >= ar_2 /\ ar_4 >= ar_0 ] popout

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actions

all output return to Compl Integ Trans Syste 26843