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Your code is wrong. You are confusing wp_enqeue_script function and wp_enqueue_scripts action. It should be:

function theme_script(){
    wp_deregister_script( 'jquery' );

    wp_register_script('jquery',get_template_directory_uri().'/sliderengine/jquery.js');
    wp_enqueue_script('jquery');

    wp_register_script('amazingslider',get_template_directory_uri().'/sliderengine/amazingslider.js',array('jquery'));
    wp_enqueue_script('amazingslider');    

    wp_register_script('initslider-1',get_template_directory_uri().'/sliderengine/initslider-1.js',array('jquery'));
    wp_enqueue_script('initslider-1');
}
add_action('wp_enqueue_scripts','theme_script');