YES TRS: a__pairNs() -> cons(0(),incr(oddNs())) a__oddNs() -> a__incr(a__pairNs()) a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS)) a__take(0(),XS) -> nil() a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS)) a__zip(nil(),XS) -> nil() a__zip(X,nil()) -> nil() a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS)) a__tail(cons(X,XS)) -> mark(XS) a__repItems(nil()) -> nil() a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS))) mark(pairNs()) -> a__pairNs() mark(incr(X)) -> a__incr(mark(X)) mark(oddNs()) -> a__oddNs() mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2)) mark(tail(X)) -> a__tail(mark(X)) mark(repItems(X)) -> a__repItems(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() mark(pair(X1,X2)) -> pair(mark(X1),mark(X2)) a__pairNs() -> pairNs() a__incr(X) -> incr(X) a__oddNs() -> oddNs() a__take(X1,X2) -> take(X1,X2) a__zip(X1,X2) -> zip(X1,X2) a__tail(X) -> tail(X) a__repItems(X) -> repItems(X) max/plus interpretations on N: a__pairNs_A = 11 a__pairNs#_A = 11 cons_A(x1,x2) = max{3, 9 + x1, x2} cons#_A(x1,x2) = max{3, 9 + x1, x2} 0_A = 1 0#_A = 1 incr_A(x1) = max{4, x1} incr#_A(x1) = max{4, x1} oddNs_A = 11 oddNs#_A = 11 a__oddNs_A = 11 a__oddNs#_A = 11 a__incr_A(x1) = max{4, x1} a__incr#_A(x1) = max{4, x1} s_A(x1) = max{0, x1} s#_A(x1) = max{0, x1} mark_A(x1) = max{0, x1} mark#_A(x1) = max{0, x1} a__take_A(x1,x2) = max{11, 10 + x1, 1 + x2} a__take#_A(x1,x2) = max{11, 10 + x1, 1 + x2} nil_A = 0 nil#_A = 0 take_A(x1,x2) = max{11, 10 + x1, 1 + x2} take#_A(x1,x2) = max{11, 10 + x1, 1 + x2} a__zip_A(x1,x2) = max{4, 6 + x1, 3 + x2} a__zip#_A(x1,x2) = max{4, 6 + x1, 3 + x2} pair_A(x1,x2) = max{5, 1 + x1, 2 + x2} pair#_A(x1,x2) = max{5, 1 + x1, 2 + x2} zip_A(x1,x2) = max{2, 6 + x1, 3 + x2} zip#_A(x1,x2) = max{2, 6 + x1, 3 + x2} a__tail_A(x1) = max{2, 3 + x1} a__tail#_A(x1) = max{2, 3 + x1} a__repItems_A(x1) = max{10, 12 + x1} a__repItems#_A(x1) = max{10, 12 + x1} repItems_A(x1) = max{11, 12 + x1} repItems#_A(x1) = max{11, 12 + x1} pairNs_A = 11 pairNs#_A = 11 tail_A(x1) = max{1, 3 + x1} tail#_A(x1) = max{1, 3 + x1} precedence: nil > mark = pair = a__repItems > 0 = a__oddNs = a__take = a__zip = a__tail > a__pairNs = a__incr = take = zip = tail > cons > incr = oddNs = s = repItems = pairNs