If you are on Linux, use "top" to identify the busy OS thread, and then use jps to correlate that to a Java thread stack trace.  This will tell you which thread has run away.

as david says, create thread dumps and if you don't know how to analize them, attach them (in advanced) editor to this post.

You can try this script that correlate the top thread consuming CPU

scripts/top_threads.sh at master · claudio4j/scripts · GitHub

Looking at that stacktrace, I think this is something that you will have to talk to the ajax4jsf team/community with. It looks like the access to some kind of cache is blocked by a Pattern matching logic, which probably has gone into some kind of a long evaluation:

"default task-104" #328 prio=5 os_prio=0 tid=0x0000000020465000 nid=0x4fc runnable [0x00000000429ad000]

   java.lang.Thread.State: RUNNABLE

    at java.util.regex.Pattern$Node.match(Pattern.java:3408)

    at java.util.regex.Pattern$CharProperty.match(Pattern.java:3777)

    at java.util.regex.Pattern$Curly.match0(Pattern.java:4260)

    at java.util.regex.Pattern$Curly.match(Pattern.java:4234)

    at java.util.regex.Pattern$Start.match(Pattern.java:3461)

    at java.util.regex.Matcher.search(Matcher.java:1248)

    at java.util.regex.Matcher.find(Matcher.java:637)

    at java.util.regex.Matcher.replaceAll(Matcher.java:956)

    at java.lang.String.replaceAll(String.java:2223)

    at org.ajax4jsf.css.CssCompressor.compress(CssCompressor.java:157)

    at org.ajax4jsf.resource.TemplateCSSRenderer.send(TemplateCSSRenderer.java:98)

    at org.ajax4jsf.resource.InternetResourceBase.send(InternetResourceBase.java:374)

    at org.ajax4jsf.resource.ResourceLifecycle.sendResource(ResourceLifecycle.java:221)

    at org.ajax4jsf.resource.ResourceLifecycle.send(ResourceLifecycle.java:148)

    at org.ajax4jsf.resource.InternetResourceService.load(InternetResourceService.java:335)

    at org.ajax4jsf.cache.LRUMapCache.load(LRUMapCache.java:116)

   - locked <0x00000005d4bef898> (a org.ajax4jsf.cache.LRUMapCache)

    at org.ajax4jsf.cache.LRUMapCache.get(LRUMapCache.java:87)

    - locked <0x00000005d4bef898> (a org.ajax4jsf.cache.LRUMapCache)

Try setting the following in the web.xml of your application to disable compression of CSS files and rebuild and redeploy the application:

<context-param>
        <param-name>org.ajax4jsf.COMPRESS_STYLE</param-name>
        <param-value>false</param-value>
</context-param>

That should skip this piece of code which seems to be running into issues doing a pattern matching against some specific CSS file.