Are these soap ingredients okay to use on my cup?

 Hey Everyone,

I just bought some Avalon Organics lemon glycerin hand soap to wash my cup. I chose it because it seemed to have ingredients that aren't harsh. But I just want to double-check that it's okay to use. Previously I'd used the Diva Wash with no problems. Anyway, the ingredients for Avalon Organics are:

water, aloe, cocamidopropyl betain, glycerin, sodium laurylglucosides,

hydroxypropylsulfonate, sodium cocoyl isethionate, stearic acid, sodium lauroyl sarcosinate,

lemon oil, grapefruit oil, lime oil, orange oil, cedrus atlantica bark oil, litsea cubeba fruit oil,

calendula flower extract, matricaria flower extract, lemon extrac, arginine, bisabolol, sodium citrate,

sodium pca, panthenol, tocopheryl acetate, guar hydroxyproltrimonium chloride, organic alcohol,

benzyl alcohol, potassium sorbate, sodium benzoate, citral, limonene, linalool.

Yeah, most of them i can't pronounce, but I just wanted to know if there seem to be any crazy ingredients that will degrade my cup or that won't wash off cleanly.

Thanks.