YES (VAR x) (RULES fac(s(x)) -> *(s(x),fac(x)) fac(0()) -> s(0()) *(x,s(y())) -> +(*(x,y()),x) *(x,0()) -> 0() +(x,s(y())) -> s(+(x,y())) +(x,0()) -> x ) (COMMENT Termination is shown by ELPO with interpretations on natural numbers +_A(x1,x2) = x1 0_A = 1 s_A(x1) = x1 y_A = 1 *_A(x1,x2) = 1 fac_A(x1) = 1 0#_A = 0 s#_A(x1) = 0 y#_A = 0 and precedence: y > fac > * > + > s > 0 )