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significant terms in spline model using GAM

Hi.. I'm using gam() to fit a spline model for a data set that has two predictor
variables (say A and B). The results indicate that the higher order interaction
terms are significant. The R^2 jumps from .5 to .9 when I change the maximum
order for the interaction from 10 to 15 (i.e. (AB)^10 to (AB)^15). Is there any
way of finding out which of the terms in the model are really "significant" so
that I could drop some of the terms from the model?

Thanks,
nirmal