details

property	value
status	complete
benchmark	Example3.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	PLDI09

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.43658089638 seconds
cpu usage	5.674088684
max memory	3.21998848E8

stage attributes

key	value
output-size	53522
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).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, 424 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 822 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B, C, D) -> Com_1(evalfentryin(A, B, C, D)) :|: TRUE evalfentryin(A, B, C, D) -> Com_1(evalfbb3in(A, B, 0, 0)) :|: A >= 1 && B >= A + 1 evalfbb3in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: D >= B evalfbb3in(A, B, C, D) -> Com_1(evalfbb4in(A, B, C, D)) :|: B >= D + 1 evalfbb4in(A, B, C, D) -> Com_1(evalfbbin(A, B, C, D)) :|: 0 >= E + 1 evalfbb4in(A, B, C, D) -> Com_1(evalfbbin(A, B, C, D)) :|: E >= 1 evalfbb4in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: TRUE evalfbbin(A, B, C, D) -> Com_1(evalfbb1in(A, B, C, D)) :|: A >= C + 1 evalfbbin(A, B, C, D) -> Com_1(evalfbb2in(A, B, C, D)) :|: C >= A evalfbb1in(A, B, C, D) -> Com_1(evalfbb3in(A, B, C + 1, D)) :|: TRUE evalfbb2in(A, B, C, D) -> Com_1(evalfbb3in(A, B, 0, D + 1)) :|: TRUE evalfreturnin(A, B, C, D) -> Com_1(evalfstop(A, B, C, D)) :|: TRUE The start-symbols are:[evalfstart_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 20*ar_1 + 10*ar_0 + 20*ar_0*ar_1 + 16) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ] (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ] (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) (Comp: ?, Cost: 1) evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) (Comp: ?, Cost: 1) evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 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) evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ] (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ] (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ] popout

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job log

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actions

all output return to Compl Integ Trans Syste 26843