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Goodwill and Intangible Assets
12 Months Ended
Dec. 31, 2018
Goodwill and Intangible Assets [Abstract]  
Goodwill and Intangible Assets Disclosure [Text Block]
Goodwill and Intangible Assets

The change in the carrying amount of goodwill for the years ended December 31, 2018 and 2017, was as follows (in thousands):
Balance as of December 31, 2016
$
20,096

    Goodwill acquired
17,052

    Foreign currency translation adjustments
1,310

Balance as of December 31, 2017
38,458

    Purchase accounting adjustments
252

    Foreign currency translation adjustments
(479
)
Balance as of December 31, 2018
$
38,231



The goodwill balance related to PROS France is denominated in Euro and the goodwill balance related to Vayant is denominated in the U.S. dollar.

Intangible assets consisted of the following as of December 31, (in thousands):
 
 
 
December 31, 2018
 
Weighted average useful life (years)
 
Gross Carrying Amount
 
Accumulated Amortization*
 
Net Carrying Amount
Developed technology
7
 
$
25,584

 
$
13,890

 
$
11,694

Maintenance relationships
8
 
3,485

 
2,488

 
997

Customer relationships
6
 
11,802

 
6,884

 
4,918

Acquired technology
2
 
1,925

 
180

 
1,745

Total
 
 
$
42,796

 
$
23,442

 
$
19,354

*Cumulative foreign currency translation adjustments, reflecting movement in the currencies of the underlying entities, decreased total intangible assets by approximately $0.2 million as of December 31, 2018.

 
 
 
December 31, 2017
 
Weighted average useful life (years)
 
Gross Carrying Amount
 
Accumulated Amortization*
 
Net Carrying Amount
Developed technology
7
 
$
26,023

 
$
9,560

 
$
16,463

Maintenance relationships
8
 
3,565

 
2,207

 
1,358

Customer relationships
6
 
11,840

 
4,482

 
7,358

Acquired technology
3
 
1,750

 

 
1,750

Total

 
$
43,178

 
$
16,249

 
$
26,929


*Cumulative foreign currency translation adjustments, reflecting movement in the currencies of the underlying entities, increased total intangible assets by approximately $0.7 million as of December 31, 2017.

Customer relationships are amortized over five or eight years.

In December 2016, the Company purchased a technology-based intangible asset in connection with the equity securities investment made during the same period. The Company estimates that the intangible will be amortized over approximately a 2-year period. During the second half of 2017 and 2018, the Company purchased an additional technology-based intangible asset which is expected to be amortized over approximately a 1-year period.
    
Intangible asset amortization expense for the years ended December 31, 2018, 2017 and 2016 was $7.6 million, $5.2 million and $3.0 million, respectively. As of December 31, 2018, the expected future amortization expense for the acquired intangible assets for each of the five succeeding years and thereafter was as follows (in thousands):        
Year Ending December 31,
 
Amount
2019
 
$
6,575

2020
 
5,791

2021
 
3,021

2022
 
1,921

2023
 
1,292

2024 and thereafter
 
754

Total amortization expense
 
$
19,354