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	n016.star.cs.uiowa.edu
space	ABC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.53695 seconds
cpu usage	4.8482
user time	4.59509
system time	0.253106
max virtual memory	1.8617144E7
max residence set size	218180.0

stage attributes

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

output

4.71/2.51 WORST_CASE(Omega(n^1), O(n^2)) 4.71/2.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.71/2.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.71/2.52 4.71/2.52 4.71/2.52 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(4, 4 + 2 * Arg_0) + nat(2 + 2 * Arg_0)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)). 4.71/2.52 4.71/2.52 (0) CpxIntTrs 4.71/2.52 (1) Koat2 Proof [FINISHED, 829 ms] 4.71/2.52 (2) BOUNDS(1, max(4, 4 + 2 * Arg_0) + nat(2 + 2 * Arg_0) + nat(Arg_0 + Arg_0^2)) 4.71/2.52 (3) Loat Proof [FINISHED, 325 ms] 4.71/2.52 (4) BOUNDS(n^1, INF) 4.71/2.52 4.71/2.52 4.71/2.52 ---------------------------------------- 4.71/2.52 4.71/2.52 (0) 4.71/2.52 Obligation: 4.71/2.52 Complexity Int TRS consisting of the following rules: 4.71/2.52 evalfstart(A, B, C) -> Com_1(evalfentryin(A, B, C)) :|: TRUE 4.71/2.52 evalfentryin(A, B, C) -> Com_1(evalfbb4in(B, A, C)) :|: TRUE 4.71/2.52 evalfbb4in(A, B, C) -> Com_1(evalfbb2in(A, B, A)) :|: B >= 1 4.71/2.52 evalfbb4in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: 0 >= B 4.71/2.52 evalfbb2in(A, B, C) -> Com_1(evalfbb1in(A, B, C)) :|: C >= A 4.71/2.52 evalfbb2in(A, B, C) -> Com_1(evalfbb3in(A, B, C)) :|: A >= C + 1 4.71/2.52 evalfbb1in(A, B, C) -> Com_1(evalfbb2in(A, B, C - 1)) :|: TRUE 4.71/2.52 evalfbb3in(A, B, C) -> Com_1(evalfbb4in(A, B - 1, C)) :|: TRUE 4.71/2.52 evalfreturnin(A, B, C) -> Com_1(evalfstop(A, B, C)) :|: TRUE 4.71/2.52 4.71/2.52 The start-symbols are:[evalfstart_3] 4.71/2.52 4.71/2.52 4.71/2.52 ---------------------------------------- 4.71/2.52 4.71/2.52 (1) Koat2 Proof (FINISHED) 4.71/2.52 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)}) 4.71/2.52 4.71/2.52 4.71/2.52 4.71/2.52 Initial Complexity Problem: 4.71/2.52 4.71/2.52 Start: evalfstart 4.71/2.52 4.71/2.52 Program_Vars: Arg_0, Arg_1, Arg_2 4.71/2.52 4.71/2.52 Temp_Vars: 4.71/2.52 4.71/2.52 Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfentryin, evalfreturnin, evalfstart, evalfstop 4.71/2.52 4.71/2.52 Transitions: 4.71/2.52 4.71/2.52 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 4.71/2.52 4.71/2.52 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 4.71/2.52 4.71/2.52 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 4.71/2.52 4.71/2.52 evalfbb3in(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2 <= Arg_0 && 1 <= Arg_1 4.71/2.52 4.71/2.52 evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfbb2in(Arg_0,Arg_1,Arg_0):|:1 <= Arg_1 4.71/2.52 4.71/2.52 evalfbb4in(Arg_0,Arg_1,Arg_2) -> evalfreturnin(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 0 4.71/2.52 4.71/2.52 evalfentryin(Arg_0,Arg_1,Arg_2) -> evalfbb4in(Arg_1,Arg_0,Arg_2):|: 4.71/2.52 4.71/2.52 evalfreturnin(Arg_0,Arg_1,Arg_2) -> evalfstop(Arg_0,Arg_1,Arg_2):|:Arg_1 <= 0 4.71/2.52 4.71/2.52 evalfstart(Arg_0,Arg_1,Arg_2) -> evalfentryin(Arg_0,Arg_1,Arg_2):|: 4.71/2.52 4.71/2.52 4.71/2.52 4.71/2.52 Timebounds: 4.71/2.52 4.71/2.52 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)} 4.71/2.52 4.71/2.52 6: evalfbb1in->evalfbb2in: max([0, Arg_0*(1+Arg_0)]) {O(n^2)} 4.71/2.52 4.71/2.52 4: evalfbb2in->evalfbb1in: max([0, 1+Arg_0]) {O(n)} 4.71/2.52 4.71/2.52 5: evalfbb2in->evalfbb3in: max([0, Arg_0]) {O(n)} 4.71/2.52 4.71/2.52 7: evalfbb3in->evalfbb4in: max([0, Arg_0]) {O(n)} 4.71/2.52 4.71/2.52 2: evalfbb4in->evalfbb2in: max([0, 1+Arg_0]) {O(n)} 4.71/2.52 4.71/2.52 3: evalfbb4in->evalfreturnin: 1 {O(1)} 4.71/2.52 4.71/2.52 1: evalfentryin->evalfbb4in: 1 {O(1)} 4.71/2.52 4.71/2.52 8: evalfreturnin->evalfstop: 1 {O(1)} 4.71/2.52 4.71/2.52 0: evalfstart->evalfentryin: 1 {O(1)} 4.71/2.52 4.71/2.52 4.71/2.52 4.71/2.52 Costbounds: 4.71/2.52 4.71/2.52 Overall costbound: 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)} 4.71/2.52 4.71/2.52 6: evalfbb1in->evalfbb2in: max([0, Arg_0*(1+Arg_0)]) {O(n^2)} popout

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all output return to Complexity_ITS 2019-03-21 04.46