CXFNonSpringJaxrsServlet ClassNotFoundException

Question

Ok so I tried to set-up a Jax-rs environment with CXF but unfortanetely I have been getting a very troublesome error that I cannot go around. I am running my application on a Java Web Tomcat 8 Server. My pom.xml file is the following

    some irrelevant code..
    <modelVersion>4.0.0</modelVersion>

    <artifactId>calculatorWeb</artifactId>

    <packaging>war</packaging>

    <properties>
        <maven.test.skip>${skipUnitTests}</maven.test.skip>
    </properties>

    <build>
        <plugins>
            <plugin>
                <groupId>org.apache.maven.plugins</groupId>
                <artifactId>maven-war-plugin</artifactId>
                <configuration>
                    <webXml>WebContent\WEB-INF\web.xml</webXml>
                    <webResources>
                        <resource>
                            <directory>lib</directory>
                            <targetPath>WEB_INF/lib</targetPath>
                            <includes>
                                <include>**/*.jar</include>
                            </includes>
                        </resource>
                    </webResources>
                </configuration>
            </plugin>
        </plugins>
    </build>

    <dependencies>
        <dependency>
            <groupId>javax.ws.rs</groupId>
            <artifactId>javax.ws.rs-api</artifactId>
            <version>2.0</version>
        </dependency>

        <dependency>
            <groupId>org.apache.cxf</groupId>
            <artifactId>cxf-rt-frontend-jaxrs</artifactId>
            <version>3.1.0</version>
        </dependency>

        <dependency>
            <groupId>org.apache.cxf</groupId>
            <artifactId>cxf-bundle-jaxrs</artifactId>
            <version>2.2.8</version>
        </dependency>

        <dependency>
            <groupId>org.apache.cxf</groupId>
            <artifactId>cxf-rt-transports-http</artifactId>
            <version>2.6.1</version>
        </dependency>
    </dependencies>

Everything seems fine with the pom.xml file and when I produce the .war file the lib folder is in the WEB-INF folder. The relevant part of my web.xml file is the following:

<servlet>
        <display-name>CXFNonSpringJaxrsServlet</display-name>
        <servlet-name>CXFNonSpringJaxrsServlet</servlet-name>
        <servlet-class>org.apache.cxf.jaxrs.servlet.CXFNonSpringJaxrsServlet
        </servlet-class>
        <init-param>
            <param-name>javax.ws.rs.core.Application</param-name>
            <param-value>calculator.CalculatorApplication</param-value>
        </init-param>
    </servlet>

    <servlet-mapping>
        <servlet-name>CXFNonSpringJaxrsServlet</servlet-name>
        <url-pattern>/api/*</url-pattern>
    </servlet-mapping>

The general project structure is as follows:

-root
     - lib
     - src
          - main
                - java
                      - calculator
                                  - CalculatorApplication.java
                                  - CalculatorResource.java
          - test
     - target
     - WebContent
                 - WEB-INF
                          - web.xml
                 - resources
                 - META-INF
                           - MANIFEST.MF
     - pom.xml

If you need more information I am happy to provide it. Thank you in advance!