details

property	value
status	complete
benchmark	c.01.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n040.star.cs.uiowa.edu
space	LICS04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.40819 seconds
cpu usage	8.59165
user time	8.29216
system time	0.299497
max virtual memory	1.8731684E7
max residence set size	215488.0

stage attributes

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

output

8.46/6.37 WORST_CASE(?, O(n^2)) 8.46/6.38 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 8.46/6.38 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.46/6.38 8.46/6.38 8.46/6.38 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(1, 3 + 2 * Arg_0) + nat(2 * Arg_0) + nat(Arg_0 * max(2 * Arg_0, -2) + max(2 * Arg_0, -2))). 8.46/6.38 8.46/6.38 (0) CpxIntTrs 8.46/6.38 (1) Koat2 Proof [FINISHED, 227 ms] 8.46/6.38 (2) BOUNDS(1, max(1, 3 + 2 * Arg_0) + nat(2 * Arg_0) + nat(Arg_0 * max(2 * Arg_0, -2) + max(2 * Arg_0, -2))) 8.46/6.38 8.46/6.38 8.46/6.38 ---------------------------------------- 8.46/6.38 8.46/6.38 (0) 8.46/6.38 Obligation: 8.46/6.38 Complexity Int TRS consisting of the following rules: 8.46/6.38 eval1(A, B) -> Com_1(eval2(A, 1)) :|: A >= 0 8.46/6.38 eval2(A, B) -> Com_1(eval2(A, 2 * B)) :|: A >= 0 && B >= 1 && A >= B + 1 8.46/6.38 eval2(A, B) -> Com_1(eval1(A - 1, B)) :|: A >= 0 && B >= 1 && B >= A 8.46/6.38 start(A, B) -> Com_1(eval1(A, B)) :|: TRUE 8.46/6.38 8.46/6.38 The start-symbols are:[start_2] 8.46/6.38 8.46/6.38 8.46/6.38 ---------------------------------------- 8.46/6.38 8.46/6.38 (1) Koat2 Proof (FINISHED) 8.46/6.38 YES( ?, 1+2*max([0, 1+Arg_0])+max([0, 2*Arg_0])+max([0, (1+Arg_0)*max([-2, 2*Arg_0])]) {O(n^2)}) 8.46/6.38 8.46/6.38 8.46/6.38 8.46/6.38 Initial Complexity Problem: 8.46/6.38 8.46/6.38 Start: start 8.46/6.38 8.46/6.38 Program_Vars: Arg_0, Arg_1 8.46/6.38 8.46/6.38 Temp_Vars: 8.46/6.38 8.46/6.38 Locations: eval1, eval2, start 8.46/6.38 8.46/6.38 Transitions: 8.46/6.38 8.46/6.38 eval1(Arg_0,Arg_1) -> eval2(Arg_0,1):|:0 <= Arg_0 8.46/6.38 8.46/6.38 eval2(Arg_0,Arg_1) -> eval1(Arg_0-1,Arg_1):|:1 <= Arg_1 && 1 <= Arg_0+Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && 1 <= Arg_1 && Arg_0 <= Arg_1 8.46/6.38 8.46/6.38 eval2(Arg_0,Arg_1) -> eval2(Arg_0,(2)*Arg_1):|:1 <= Arg_1 && 1 <= Arg_0+Arg_1 && 0 <= Arg_0 && 0 <= Arg_0 && 1 <= Arg_1 && Arg_1+1 <= Arg_0 8.46/6.38 8.46/6.38 start(Arg_0,Arg_1) -> eval1(Arg_0,Arg_1):|: 8.46/6.38 8.46/6.38 8.46/6.38 8.46/6.38 Timebounds: 8.46/6.38 8.46/6.38 Overall timebound: 1+2*max([0, 1+Arg_0])+max([0, 2*Arg_0])+max([0, (1+Arg_0)*max([-2, 2*Arg_0])]) {O(n^2)} 8.46/6.38 8.46/6.38 0: eval1->eval2: max([0, 1+Arg_0]) {O(n)} 8.46/6.38 8.46/6.38 1: eval2->eval2: max([0, 2*Arg_0])+max([0, (1+Arg_0)*max([-2, 2*Arg_0])]) {O(n^2)} 8.46/6.38 8.46/6.38 2: eval2->eval1: max([0, 1+Arg_0]) {O(n)} 8.46/6.38 8.46/6.38 3: start->eval1: 1 {O(1)} 8.46/6.38 8.46/6.38 8.46/6.38 8.46/6.38 Costbounds: 8.46/6.38 8.46/6.38 Overall costbound: 1+2*max([0, 1+Arg_0])+max([0, 2*Arg_0])+max([0, (1+Arg_0)*max([-2, 2*Arg_0])]) {O(n^2)} 8.46/6.38 8.46/6.38 0: eval1->eval2: max([0, 1+Arg_0]) {O(n)} 8.46/6.38 8.46/6.38 1: eval2->eval2: max([0, 2*Arg_0])+max([0, (1+Arg_0)*max([-2, 2*Arg_0])]) {O(n^2)} 8.46/6.38 8.46/6.38 2: eval2->eval1: max([0, 1+Arg_0]) {O(n)} 8.46/6.38 8.46/6.38 3: start->eval1: 1 {O(1)} 8.46/6.38 8.46/6.38 8.46/6.38 8.46/6.38 Sizebounds: 8.46/6.38 8.46/6.38 `Lower: 8.46/6.38 8.46/6.38 0: eval1->eval2, Arg_0: 0 {O(1)} 8.46/6.38 8.46/6.38 0: eval1->eval2, Arg_1: 1 {O(1)} 8.46/6.38 8.46/6.38 1: eval2->eval2, Arg_0: 2 {O(1)} 8.46/6.38 8.46/6.38 1: eval2->eval2, Arg_1: 2 {O(1)} 8.46/6.38 8.46/6.38 2: eval2->eval1, Arg_0: -1 {O(1)} 8.46/6.38 8.46/6.38 2: eval2->eval1, Arg_1: 1 {O(1)} 8.46/6.38 8.46/6.38 3: start->eval1, Arg_0: Arg_0 {O(n)} 8.46/6.38 popout

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all output return to Complexity_ITS 2019-03-21 04.46