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	n103.star.cs.uiowa.edu
space	Loopus

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.89869689941 seconds
cpu usage	6.403530746
max memory	4.19364864E8

stage attributes

key	value
output-size	9251
starexec-result	WORST_CASE(?, 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(?, 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(5, 5 + -16948680941280 * Arg_0 + 4304981706793560 * Arg_1) + nat(-4253917943760 * Arg_0 + -1080511905423480 * Arg_1) + nat(32967930 * Arg_0) + nat(510 + -2 * Arg_0) + nat(-1012 * Arg_0 + 257049 * Arg_1) + nat(-254 * Arg_0 + -64517 * Arg_1)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 869 ms] (2) BOUNDS(1, max(5, 5 + -16948680941280 * Arg_0 + 4304981706793560 * Arg_1) + nat(-4253917943760 * Arg_0 + -1080511905423480 * Arg_1) + nat(32967930 * Arg_0) + nat(510 + -2 * Arg_0) + nat(-1012 * Arg_0 + 257049 * Arg_1) + nat(-254 * Arg_0 + -64517 * Arg_1)) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B) -> Com_1(evalfentryin(A, B)) :|: TRUE evalfentryin(A, B) -> Com_1(evalfbb3in(B, A)) :|: TRUE evalfbb3in(A, B) -> Com_1(evalfbbin(A, B)) :|: B >= 1 && 254 >= B evalfbb3in(A, B) -> Com_1(evalfreturnin(A, B)) :|: 0 >= B evalfbb3in(A, B) -> Com_1(evalfreturnin(A, B)) :|: B >= 255 evalfbbin(A, B) -> Com_1(evalfbb1in(A, B)) :|: 0 >= A + 1 evalfbbin(A, B) -> Com_1(evalfbb1in(A, B)) :|: A >= 1 evalfbbin(A, B) -> Com_1(evalfbb2in(A, B)) :|: A >= 0 && A <= 0 evalfbb1in(A, B) -> Com_1(evalfbb3in(A, B + 1)) :|: TRUE evalfbb2in(A, B) -> Com_1(evalfbb3in(A, B - 1)) :|: TRUE evalfreturnin(A, B) -> Com_1(evalfstop(A, B)) :|: TRUE The start-symbols are:[evalfstart_2] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 5+2*64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 255-Arg_0])+max([0, 257049*Arg_1+-1012*Arg_0])+max([0, 255-Arg_0])+max([0, -64517*Arg_1+-254*Arg_0])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)}) Initial Complexity Problem: Start: evalfstart Program_Vars: Arg_0, Arg_1 Temp_Vars: Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop Transitions: evalfbb1in(Arg_0,Arg_1) -> evalfbb3in(Arg_0,Arg_1+1):|:Arg_1 <= 254 && 1 <= Arg_1 evalfbb2in(Arg_0,Arg_1) -> evalfbb3in(Arg_0,Arg_1-1):|:Arg_1 <= 254 && Arg_1 <= 254+Arg_0 && Arg_0+Arg_1 <= 254 && 1 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && Arg_0 <= 0 && 0 <= Arg_0 evalfbb3in(Arg_0,Arg_1) -> evalfbbin(Arg_0,Arg_1):|:1 <= Arg_1 && Arg_1 <= 254 evalfbb3in(Arg_0,Arg_1) -> evalfreturnin(Arg_0,Arg_1):|:Arg_1 <= 0 evalfbb3in(Arg_0,Arg_1) -> evalfreturnin(Arg_0,Arg_1):|:255 <= Arg_1 evalfbbin(Arg_0,Arg_1) -> evalfbb1in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && Arg_0+1 <= 0 evalfbbin(Arg_0,Arg_1) -> evalfbb1in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && 1 <= Arg_0 evalfbbin(Arg_0,Arg_1) -> evalfbb2in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && Arg_0 <= 0 && 0 <= Arg_0 evalfentryin(Arg_0,Arg_1) -> evalfbb3in(Arg_1,Arg_0):|: evalfreturnin(Arg_0,Arg_1) -> evalfstop(Arg_0,Arg_1):|: evalfstart(Arg_0,Arg_1) -> evalfentryin(Arg_0,Arg_1):|: Timebounds: Overall timebound: 5+2*64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 255-Arg_0])+max([0, 257049*Arg_1+-1012*Arg_0])+max([0, 255-Arg_0])+max([0, -64517*Arg_1+-254*Arg_0])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)} 8: evalfbb1in->evalfbb3in: 64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 255-Arg_0]) {O(n)} 9: evalfbb2in->evalfbb3in: 254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0])) {O(n)} 2: evalfbb3in->evalfbbin: 64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 255-Arg_0]) {O(n)} 3: evalfbb3in->evalfreturnin: 1 {O(1)} 4: evalfbb3in->evalfreturnin: 1 {O(1)} 5: evalfbbin->evalfbb1in: max([0, -64517*Arg_1+-254*Arg_0]) {O(n)} 6: evalfbbin->evalfbb1in: max([0, 257049*Arg_1+-1012*Arg_0]) {O(n)} 7: evalfbbin->evalfbb2in: max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)} popout

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all output return to Compl Integ Trans Syste 26843