YES

This TRS is terminating using the deltasimple interpretation 
f(delta1, X1) =  + 0*X1 + 1 + 1*X1*delta1 + 0*delta1
g(delta0, X0) =  + 1*X0 + 0 + 0*X0*delta0 + 0*delta0
f_tau_1(delta1) =  + (delta1/(0 + 1 * delta1))
g_tau_1(delta0) =  + (delta0/(1 + 0 * delta0))
SUCCESS

Statistics:
Number of monomials: 54