YES TRS: a__fst(0(),Z) -> nil() a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z)) a__from(X) -> cons(mark(X),from(s(X))) a__add(0(),X) -> mark(X) a__add(s(X),Y) -> s(add(X,Y)) a__len(nil()) -> 0() a__len(cons(X,Z)) -> s(len(Z)) mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(add(X1,X2)) -> a__add(mark(X1),mark(X2)) mark(len(X)) -> a__len(mark(X)) mark(0()) -> 0() mark(s(X)) -> s(X) mark(nil()) -> nil() mark(cons(X1,X2)) -> cons(mark(X1),X2) a__fst(X1,X2) -> fst(X1,X2) a__from(X) -> from(X) a__add(X1,X2) -> add(X1,X2) a__len(X) -> len(X) max/plus interpretations on N: a__fst_A(x1,x2) = max{26, x1, 15 + x2} a__fst#_A(x1,x2) = max{29, -6 + x1, 24 + x2} 0_A = 0 0#_A = 27 nil_A = 16 nil#_A = 28 s_A(x1) = max{8, 28} s#_A(x1) = max{0, 1} cons_A(x1,x2) = max{41, 6 + x1, 1} cons#_A(x1,x2) = max{24, 30, 2} mark_A(x1) = max{7, 10 + x1} mark#_A(x1) = max{26, 30 + x1} fst_A(x1,x2) = max{16, x1, 15 + x2} fst#_A(x1,x2) = max{0, 3, 23} a__from_A(x1) = max{10, 41 + x1} a__from#_A(x1) = max{29, 60 + x1} from_A(x1) = max{0, 41 + x1} from#_A(x1) = max{28, 31 + x1} a__add_A(x1,x2) = max{28, 29 + x1, 12 + x2} a__add#_A(x1,x2) = max{43, 15 + x1, 31 + x2} add_A(x1,x2) = max{17, 29 + x1, 12 + x2} add#_A(x1,x2) = max{14, 42, 14} a__len_A(x1) = max{7, x1} a__len#_A(x1) = max{25, 25} len_A(x1) = max{0, x1} len#_A(x1) = max{1, 1} precedence: a__fst > fst = from = add > mark > nil = a__add > 0 > cons = a__len > s = len > a__from