details

property	value
status	complete
benchmark	NestedMultiple.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	POPL09

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.46935606003 seconds
cpu usage	5.552971688
max memory	3.19356928E8

stage attributes

key	value
output-size	43445
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).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, 332 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 837 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalNestedMultiplestart(A, B, C, D, E) -> Com_1(evalNestedMultipleentryin(A, B, C, D, E)) :|: TRUE evalNestedMultipleentryin(A, B, C, D, E) -> Com_1(evalNestedMultiplebb5in(B, A, D, C, E)) :|: TRUE evalNestedMultiplebb5in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb2in(A, B, C, D, D)) :|: A >= B + 1 evalNestedMultiplebb5in(A, B, C, D, E) -> Com_1(evalNestedMultiplereturnin(A, B, C, D, E)) :|: B >= A evalNestedMultiplebb2in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb4in(A, B, C, D, E)) :|: E >= C evalNestedMultiplebb2in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb3in(A, B, C, D, E)) :|: C >= E + 1 evalNestedMultiplebb3in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb1in(A, B, C, D, E)) :|: 0 >= F + 1 evalNestedMultiplebb3in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb1in(A, B, C, D, E)) :|: F >= 1 evalNestedMultiplebb3in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb4in(A, B, C, D, E)) :|: TRUE evalNestedMultiplebb1in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb2in(A, B, C, D, E + 1)) :|: TRUE evalNestedMultiplebb4in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb5in(A, B + 1, C, E, E)) :|: TRUE evalNestedMultiplereturnin(A, B, C, D, E) -> Com_1(evalNestedMultiplestop(A, B, C, D, E)) :|: TRUE The start-symbols are:[evalNestedMultiplestart_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 11*ar_0 + 11*ar_1 + 12*ar_2 + 12*ar_3 + 17) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) (Comp: ?, Cost: 1) evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 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) evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ] popout

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all output return to Compl Integ Trans Syste 26843