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Goodwill and Other Intangible Assets
12 Months Ended
Dec. 31, 2017
Goodwill and Intangible Assets Disclosure [Abstract]  
Goodwill and Intangible Assets Disclosure
GOODWILL AND OTHER INTANGIBLE ASSETS
The following table shows the changes in the carrying amount of goodwill for the years ended December 31:
 
2017
 
2016
Balance at beginning of year
$
476,378

 
$
446,284

Goodwill acquired
52,229

 
41,308

Foreign currency translation
11,231

 
(11,214
)
Balance at year end
$
539,838

 
$
476,378


Goodwill and indefinite-lived assets are reviewed for impairment on an annual basis in the fourth quarter. The Company completed its impairment review and determined that, through December 31, 2017, there had been no impairment of these assets.
The components of other intangible assets as of December 31 are as follows:
 
2017
 
2016
 
Gross
Amount
 
Accumulated
Amortization
 
Intangibles, Net
 
Gross
Amount
 
Accumulated
Amortization
 
Intangibles, Net
Customer relationships
$
198,527

 
$
(41,794
)
 
$
156,733

 
$
147,466

 
$
(34,672
)
 
$
112,794

Proven technology and patents
70,311

 
(38,890
)
 
31,421

 
58,394

 
(35,128
)
 
23,266

Tradenames (finite life)
4,518

 
(2,807
)
 
1,711

 
4,182

 
(2,514
)
 
1,668

Tradenames (indefinite life)
35,562

 

 
35,562

 
28,272

 

 
28,272

Other
3,490

 
(2,199
)
 
1,291

 
2,871

 
(1,816
)
 
1,055

 
$
312,408

 
$
(85,690
)
 
$
226,718

 
$
241,185

 
$
(74,130
)
 
$
167,055


The Company recognized amortization expense associated with the above intangible assets of $11.5 million, $8.3 million, and $6.3 million for the years ended December 31, 2017, 2016, and 2015, respectively. The annual aggregate amortization expense based on the current balance of other intangible assets is estimated at $13.9 million for 2018, $13.4 million for 2019, $13.0 million for 2020, $12.4 million for 2021, and $11.9 million for 2022. The finite-lived intangible assets are amortized on a straight-line basis over periods ranging from 3 to 45 years. The straight-line method of amortization reflects an appropriate allocation of the cost of the intangible assets to earnings in proportion to the amount of economic benefits obtained by the Company in each reporting period. Purchased intangibles amortization was $10.9 million, $7.1 million after tax, $7.4 million, $5.0 million after tax, and $5.7 million, $3.9 million after tax, for the years ended December 31, 2017, 2016, and 2015, respectively.
In addition to the above amortization, the Company recorded amortization expense associated with capitalized software of $31.0 million, $27.5 million, and $24.4 million for the years ended December 31, 2017, 2016, and 2015, respectively.