##bash 111

    #!/bin/bash
    s=$1
    l=${#s}
    for i in $(seq 1 $((l-2)))
    do
    test "${s:i:$(((l-i)/2))}" = "${s:$(((l+i)/2))}"&&exit 0
    done||false

111 chars without shebang. 
Invocation:

    ./tailrepeated.sh foobalaa && echo "true" || echo "false"