YES TRS: active(fst(0(),Z)) -> mark(nil()) active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(len(nil())) -> mark(0()) active(len(cons(X,Z))) -> mark(s(len(Z))) mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(X)) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) mark(len(X)) -> active(len(mark(X))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) max/plus interpretations on N: active_A(x1) = max{110, x1} active#_A(x1) = max{105, 8 + x1} fst_A(x1,x2) = max{102, 100 + x1, 103 + x2} fst#_A(x1,x2) = max{204, 42, 6} 0_A = 53 0#_A = 160 mark_A(x1) = max{37, 62 + x1} mark#_A(x1) = max{113, 111 + x1} nil_A = 49 nil#_A = 203 s_A(x1) = max{95, -7} s#_A(x1) = max{2, 4} cons_A(x1,x2) = max{132, 69 + x1, 31} cons#_A(x1,x2) = max{205, 6, 205} from_A(x1) = max{171, 236 + x1} from#_A(x1) = max{7, 5} add_A(x1,x2) = max{132, 8 + x1, 199 + x2} add#_A(x1,x2) = max{8, 3, 112 + x2} len_A(x1) = max{198, 24 + x1} len#_A(x1) = max{0, 1} precedence: active > fst > nil > 0 = add > mark > from > cons > s > len