details

property	value
status	complete
benchmark	ex12.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n089.star.cs.uiowa.edu
space	ABC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.44528603554 seconds
cpu usage	4.772000229
max memory	2.78523904E8

stage attributes

key	value
output-size	11492
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

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^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(4, 4 + 2 * Arg_0) + nat(2 + 2 * Arg_0) + nat(Arg_0 + Arg_0^2)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 856 ms] (2) BOUNDS(1, max(4, 4 + 2 * Arg_0) + nat(2 + 2 * Arg_0) + nat(Arg_0 + Arg_0^2)) (3) Loat Proof [FINISHED, 318 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B, C) -> Com_1(evalfentryin(A, B, C)) :|: TRUE evalfentryin(A, B, C) -> Com_1(evalfbb4in(B, A, C)) :|: TRUE evalfbb4in(A, B, C) -> Com_1(evalfbb2in(A, B, A)) :|: B >= 1 evalfbb4in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: 0 >= B evalfbb2in(A, B, C) -> Com_1(evalfbb1in(A, B, C)) :|: C >= A evalfbb2in(A, B, C) -> Com_1(evalfbb3in(A, B, C)) :|: A >= C + 1 evalfbb1in(A, B, C) -> Com_1(evalfbb2in(A, B, C - 1)) :|: TRUE evalfbb3in(A, B, C) -> Com_1(evalfbb4in(A, B - 1, C)) :|: TRUE evalfreturnin(A, B, C) -> Com_1(evalfstop(A, B, C)) :|: TRUE The start-symbols are:[evalfstart_3] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 4+2*max([0, Arg_0])+max([0, 1+Arg_0])+max([0, Arg_0*(1+Arg_0)])+max([0, 1+Arg_0]) {O(n^2)}) Initial Complexity Problem: Start: evalfstart Program_Vars: Arg_0, Arg_1, Arg_2 Temp_Vars: Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfentryin, evalfreturnin, evalfstart, evalfstop Transitions: evalfbb1in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_2-1):|:Arg_2 <= Arg_0 && Arg_0 <= Arg_2 && 1 <= Arg_1 evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb1in(Arg_0,Arg_1,Arg_2):|:Arg_2 <= Arg_0 && 1 <= Arg_1 && Arg_0 <= Arg_2 evalfbb2in(Arg_0,Arg_1,Arg_2) -> evalfbb3in(Arg_0,Arg_1,Arg_2):|:Arg_2 <= Arg_0 && 1 <= Arg_1 && Arg_2+1 <= Arg_0 evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2 <= Arg_0 && 1 <= Arg_1 evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1 <= Arg_1 evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 0 evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_1,Arg_0,Arg_2):|: evalfreturnin(Arg_0,Arg_1,Arg_2) -> evalfstop(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 0 evalfstart(Arg_0,Arg_1,Arg_2) -> evalfentryin(Arg_0,Arg_1,Arg_2):|: Timebounds: Overall timebound: 4+2*max([0, Arg_0])+max([0, 1+Arg_0])+max([0, Arg_0*(1+Arg_0)])+max([0, 1+Arg_0]) {O(n^2)} 6: evalfbb1in->evalfbb2in: max([0, Arg_0*(1+Arg_0)]) {O(n^2)} 4: evalfbb2in->evalfbb1in: max([0, 1+Arg_0]) {O(n)} 5: evalfbb2in->evalfbb3in: max([0, Arg_0]) {O(n)} 7: evalfbb3in->evalfbb4in: max([0, Arg_0]) {O(n)} 2: evalfbb4in->evalfbb2in: max([0, 1+Arg_0]) {O(n)} 3: evalfbb4in->evalfreturnin: 1 {O(1)} 1: evalfentryin->evalfbb4in: 1 {O(1)} 8: evalfreturnin->evalfstop: 1 {O(1)} 0: evalfstart->evalfentryin: 1 {O(1)} popout

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all output return to Compl Integ Trans Syste 26843