YES Problem: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) active(hd(cons(X,Y))) -> mark(X) active(tl(cons(X,Y))) -> mark(Y) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [tl](x0) = 2x0 + 4, [hd](x0) = 2x0 + 2, [s](x0) = x0, [incr](x0) = x0, [cons](x0, x1) = 2x0 + x1, [0] = 0, [mark](x0) = x0, [adx](x0) = x0, [zeros] = 0, [active](x0) = x0, [nats] = 0 orientation: active(nats()) = 0 >= 0 = mark(adx(zeros())) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(incr(cons(X,Y))) = 2X + Y >= 2X + Y = mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) = 2X + Y >= 2X + Y = mark(incr(cons(X,adx(Y)))) active(hd(cons(X,Y))) = 4X + 2Y + 2 >= X = mark(X) active(tl(cons(X,Y))) = 4X + 2Y + 4 >= Y = mark(Y) mark(nats()) = 0 >= 0 = active(nats()) mark(adx(X)) = X >= X = active(adx(mark(X))) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = active(cons(X1,X2)) mark(0()) = 0 >= 0 = active(0()) mark(incr(X)) = X >= X = active(incr(mark(X))) mark(s(X)) = X >= X = active(s(X)) mark(hd(X)) = 2X + 2 >= 2X + 2 = active(hd(mark(X))) mark(tl(X)) = 2X + 4 >= 2X + 4 = active(tl(mark(X))) adx(mark(X)) = X >= X = adx(X) adx(active(X)) = X >= X = adx(X) cons(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = cons(X1,X2) cons(active(X1),X2) = 2X1 + X2 >= 2X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = 2X1 + X2 >= 2X1 + X2 = cons(X1,X2) incr(mark(X)) = X >= X = incr(X) incr(active(X)) = X >= X = incr(X) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) hd(mark(X)) = 2X + 2 >= 2X + 2 = hd(X) hd(active(X)) = 2X + 2 >= 2X + 2 = hd(X) tl(mark(X)) = 2X + 4 >= 2X + 4 = tl(X) tl(active(X)) = 2X + 4 >= 2X + 4 = tl(X) problem: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) DP Processor: DPs: active#(nats()) -> adx#(zeros()) active#(nats()) -> mark#(adx(zeros())) active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(incr(cons(X,Y))) -> incr#(Y) active#(incr(cons(X,Y))) -> s#(X) active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) active#(adx(cons(X,Y))) -> adx#(Y) active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(nats()) -> active#(nats()) mark#(adx(X)) -> mark#(X) mark#(adx(X)) -> adx#(mark(X)) mark#(adx(X)) -> active#(adx(mark(X))) mark#(zeros()) -> active#(zeros()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(0()) -> active#(0()) mark#(incr(X)) -> mark#(X) mark#(incr(X)) -> incr#(mark(X)) mark#(incr(X)) -> active#(incr(mark(X))) mark#(s(X)) -> active#(s(X)) mark#(hd(X)) -> mark#(X) mark#(hd(X)) -> hd#(mark(X)) mark#(hd(X)) -> active#(hd(mark(X))) mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> tl#(mark(X)) mark#(tl(X)) -> active#(tl(mark(X))) adx#(mark(X)) -> adx#(X) adx#(active(X)) -> adx#(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) incr#(mark(X)) -> incr#(X) incr#(active(X)) -> incr#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) hd#(mark(X)) -> hd#(X) hd#(active(X)) -> hd#(X) tl#(mark(X)) -> tl#(X) tl#(active(X)) -> tl#(X) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) TDG Processor: DPs: active#(nats()) -> adx#(zeros()) active#(nats()) -> mark#(adx(zeros())) active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(incr(cons(X,Y))) -> incr#(Y) active#(incr(cons(X,Y))) -> s#(X) active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) active#(adx(cons(X,Y))) -> adx#(Y) active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(nats()) -> active#(nats()) mark#(adx(X)) -> mark#(X) mark#(adx(X)) -> adx#(mark(X)) mark#(adx(X)) -> active#(adx(mark(X))) mark#(zeros()) -> active#(zeros()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(0()) -> active#(0()) mark#(incr(X)) -> mark#(X) mark#(incr(X)) -> incr#(mark(X)) mark#(incr(X)) -> active#(incr(mark(X))) mark#(s(X)) -> active#(s(X)) mark#(hd(X)) -> mark#(X) mark#(hd(X)) -> hd#(mark(X)) mark#(hd(X)) -> active#(hd(mark(X))) mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> tl#(mark(X)) mark#(tl(X)) -> active#(tl(mark(X))) adx#(mark(X)) -> adx#(X) adx#(active(X)) -> adx#(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) incr#(mark(X)) -> incr#(X) incr#(active(X)) -> incr#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) hd#(mark(X)) -> hd#(X) hd#(active(X)) -> hd#(X) tl#(mark(X)) -> tl#(X) tl#(active(X)) -> tl#(X) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) graph: tl#(mark(X)) -> tl#(X) -> tl#(active(X)) -> tl#(X) tl#(mark(X)) -> tl#(X) -> tl#(mark(X)) -> tl#(X) tl#(active(X)) -> tl#(X) -> tl#(active(X)) -> tl#(X) tl#(active(X)) -> tl#(X) -> tl#(mark(X)) -> tl#(X) hd#(mark(X)) -> hd#(X) -> hd#(active(X)) -> hd#(X) hd#(mark(X)) -> hd#(X) -> hd#(mark(X)) -> hd#(X) hd#(active(X)) -> hd#(X) -> hd#(active(X)) -> hd#(X) hd#(active(X)) -> hd#(X) -> hd#(mark(X)) -> hd#(X) s#(mark(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(mark(X)) -> s#(X) incr#(mark(X)) -> incr#(X) -> incr#(active(X)) -> incr#(X) incr#(mark(X)) -> incr#(X) -> incr#(mark(X)) -> incr#(X) incr#(active(X)) -> incr#(X) -> incr#(active(X)) -> incr#(X) incr#(active(X)) -> incr#(X) -> incr#(mark(X)) -> incr#(X) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) mark#(tl(X)) -> tl#(mark(X)) -> tl#(active(X)) -> tl#(X) mark#(tl(X)) -> tl#(mark(X)) -> tl#(mark(X)) -> tl#(X) mark#(tl(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(tl(X)) -> mark#(X) -> mark#(tl(X)) -> tl#(mark(X)) mark#(tl(X)) -> mark#(X) -> mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) mark#(tl(X)) -> mark#(X) -> mark#(hd(X)) -> hd#(mark(X)) mark#(tl(X)) -> mark#(X) -> mark#(hd(X)) -> mark#(X) mark#(tl(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(tl(X)) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) mark#(tl(X)) -> mark#(X) -> mark#(incr(X)) -> incr#(mark(X)) mark#(tl(X)) -> mark#(X) -> mark#(incr(X)) -> mark#(X) mark#(tl(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(tl(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(tl(X)) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) mark#(tl(X)) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) mark#(tl(X)) -> mark#(X) -> mark#(adx(X)) -> adx#(mark(X)) mark#(tl(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X) mark#(tl(X)) -> mark#(X) -> mark#(nats()) -> active#(nats()) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(incr(cons(X,Y))) -> s#(X) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(zeros()) -> cons#(0(),zeros()) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(nats()) -> mark#(adx(zeros())) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(nats()) -> adx#(zeros()) mark#(hd(X)) -> hd#(mark(X)) -> hd#(active(X)) -> hd#(X) mark#(hd(X)) -> hd#(mark(X)) -> hd#(mark(X)) -> hd#(X) mark#(hd(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(hd(X)) -> mark#(X) -> mark#(tl(X)) -> tl#(mark(X)) mark#(hd(X)) -> mark#(X) -> mark#(tl(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) mark#(hd(X)) -> mark#(X) -> mark#(hd(X)) -> hd#(mark(X)) mark#(hd(X)) -> mark#(X) -> mark#(hd(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(hd(X)) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) mark#(hd(X)) -> mark#(X) -> mark#(incr(X)) -> incr#(mark(X)) mark#(hd(X)) -> mark#(X) -> mark#(incr(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(hd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(hd(X)) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) mark#(hd(X)) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) mark#(hd(X)) -> mark#(X) -> mark#(adx(X)) -> adx#(mark(X)) mark#(hd(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) -> mark#(nats()) -> active#(nats()) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(incr(cons(X,Y))) -> s#(X) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(zeros()) -> cons#(0(),zeros()) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(nats()) -> mark#(adx(zeros())) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(nats()) -> adx#(zeros()) mark#(s(X)) -> active#(s(X)) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(s(X)) -> active#(s(X)) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(s(X)) -> active#(s(X)) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(s(X)) -> active#(s(X)) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(s(X)) -> active#(s(X)) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(s(X)) -> active#(s(X)) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(s(X)) -> active#(s(X)) -> active#(incr(cons(X,Y))) -> s#(X) mark#(s(X)) -> active#(s(X)) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(s(X)) -> active#(s(X)) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(s(X)) -> active#(s(X)) -> active#(zeros()) -> cons#(0(),zeros()) mark#(s(X)) -> active#(s(X)) -> active#(nats()) -> mark#(adx(zeros())) mark#(s(X)) -> active#(s(X)) -> active#(nats()) -> adx#(zeros()) mark#(incr(X)) -> incr#(mark(X)) -> incr#(active(X)) -> incr#(X) mark#(incr(X)) -> incr#(mark(X)) -> incr#(mark(X)) -> incr#(X) mark#(incr(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(incr(X)) -> mark#(X) -> mark#(tl(X)) -> tl#(mark(X)) mark#(incr(X)) -> mark#(X) -> mark#(tl(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) mark#(incr(X)) -> mark#(X) -> mark#(hd(X)) -> hd#(mark(X)) mark#(incr(X)) -> mark#(X) -> mark#(hd(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(incr(X)) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) mark#(incr(X)) -> mark#(X) -> mark#(incr(X)) -> incr#(mark(X)) mark#(incr(X)) -> mark#(X) -> mark#(incr(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(incr(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(incr(X)) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) mark#(incr(X)) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) mark#(incr(X)) -> mark#(X) -> mark#(adx(X)) -> adx#(mark(X)) mark#(incr(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) -> mark#(nats()) -> active#(nats()) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(incr(cons(X,Y))) -> s#(X) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(zeros()) -> cons#(0(),zeros()) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(nats()) -> mark#(adx(zeros())) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(nats()) -> adx#(zeros()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(incr(cons(X,Y))) -> s#(X) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(zeros()) -> cons#(0(),zeros()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(nats()) -> mark#(adx(zeros())) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(nats()) -> adx#(zeros()) mark#(0()) -> active#(0()) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(0()) -> active#(0()) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(0()) -> active#(0()) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(0()) -> active#(0()) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(0()) -> active#(0()) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(0()) -> active#(0()) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(0()) -> active#(0()) -> active#(incr(cons(X,Y))) -> s#(X) mark#(0()) -> active#(0()) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(0()) -> active#(0()) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(0()) -> active#(0()) -> active#(zeros()) -> cons#(0(),zeros()) mark#(0()) -> active#(0()) -> active#(nats()) -> mark#(adx(zeros())) mark#(0()) -> active#(0()) -> active#(nats()) -> adx#(zeros()) mark#(adx(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(adx(X)) -> mark#(X) -> mark#(tl(X)) -> tl#(mark(X)) mark#(adx(X)) -> mark#(X) -> mark#(tl(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) mark#(adx(X)) -> mark#(X) -> mark#(hd(X)) -> hd#(mark(X)) mark#(adx(X)) -> mark#(X) -> mark#(hd(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(adx(X)) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) mark#(adx(X)) -> mark#(X) -> mark#(incr(X)) -> incr#(mark(X)) mark#(adx(X)) -> mark#(X) -> mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(adx(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(adx(X)) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) mark#(adx(X)) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) mark#(adx(X)) -> mark#(X) -> mark#(adx(X)) -> adx#(mark(X)) mark#(adx(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) -> mark#(nats()) -> active#(nats()) mark#(adx(X)) -> adx#(mark(X)) -> adx#(active(X)) -> adx#(X) mark#(adx(X)) -> adx#(mark(X)) -> adx#(mark(X)) -> adx#(X) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(incr(cons(X,Y))) -> s#(X) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(zeros()) -> cons#(0(),zeros()) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(nats()) -> mark#(adx(zeros())) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(nats()) -> adx#(zeros()) mark#(zeros()) -> active#(zeros()) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(zeros()) -> active#(zeros()) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(zeros()) -> active#(zeros()) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(zeros()) -> active#(zeros()) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(zeros()) -> active#(zeros()) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(zeros()) -> active#(zeros()) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(zeros()) -> active#(zeros()) -> active#(incr(cons(X,Y))) -> s#(X) mark#(zeros()) -> active#(zeros()) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(zeros()) -> active#(zeros()) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) -> active#(zeros()) -> cons#(0(),zeros()) mark#(zeros()) -> active#(zeros()) -> active#(nats()) -> mark#(adx(zeros())) mark#(zeros()) -> active#(zeros()) -> active#(nats()) -> adx#(zeros()) mark#(nats()) -> active#(nats()) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(nats()) -> active#(nats()) -> active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) mark#(nats()) -> active#(nats()) -> active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) mark#(nats()) -> active#(nats()) -> active#(adx(cons(X,Y))) -> adx#(Y) mark#(nats()) -> active#(nats()) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(nats()) -> active#(nats()) -> active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) mark#(nats()) -> active#(nats()) -> active#(incr(cons(X,Y))) -> s#(X) mark#(nats()) -> active#(nats()) -> active#(incr(cons(X,Y))) -> incr#(Y) mark#(nats()) -> active#(nats()) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(nats()) -> active#(nats()) -> active#(zeros()) -> cons#(0(),zeros()) mark#(nats()) -> active#(nats()) -> active#(nats()) -> mark#(adx(zeros())) mark#(nats()) -> active#(nats()) -> active#(nats()) -> adx#(zeros()) adx#(mark(X)) -> adx#(X) -> adx#(active(X)) -> adx#(X) adx#(mark(X)) -> adx#(X) -> adx#(mark(X)) -> adx#(X) adx#(active(X)) -> adx#(X) -> adx#(active(X)) -> adx#(X) adx#(active(X)) -> adx#(X) -> adx#(mark(X)) -> adx#(X) active#(incr(cons(X,Y))) -> s#(X) -> s#(active(X)) -> s#(X) active#(incr(cons(X,Y))) -> s#(X) -> s#(mark(X)) -> s#(X) active#(incr(cons(X,Y))) -> incr#(Y) -> incr#(active(X)) -> incr#(X) active#(incr(cons(X,Y))) -> incr#(Y) -> incr#(mark(X)) -> incr#(X) active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(incr(cons(X,Y))) -> cons#(s(X),incr(Y)) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(tl(X)) -> active#(tl(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(tl(X)) -> tl#(mark(X)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(tl(X)) -> mark#(X) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(hd(X)) -> active#(hd(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(hd(X)) -> hd#(mark(X)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(hd(X)) -> mark#(X) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(s(X)) -> active#(s(X)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(incr(X)) -> active#(incr(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(incr(X)) -> incr#(mark(X)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(incr(X)) -> mark#(X) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(0()) -> active#(0()) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(zeros()) -> active#(zeros()) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(adx(X)) -> active#(adx(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(adx(X)) -> adx#(mark(X)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(adx(X)) -> mark#(X) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(nats()) -> active#(nats()) active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) -> incr#(active(X)) -> incr#(X) active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) -> incr#(mark(X)) -> incr#(X) active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(adx(cons(X,Y))) -> cons#(X,adx(Y)) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(tl(X)) -> active#(tl(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(tl(X)) -> tl#(mark(X)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(tl(X)) -> mark#(X) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(hd(X)) -> active#(hd(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(hd(X)) -> hd#(mark(X)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(hd(X)) -> mark#(X) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(s(X)) -> active#(s(X)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(incr(X)) -> active#(incr(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(incr(X)) -> incr#(mark(X)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(incr(X)) -> mark#(X) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(0()) -> active#(0()) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(zeros()) -> active#(zeros()) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(adx(X)) -> active#(adx(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(adx(X)) -> adx#(mark(X)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(adx(X)) -> mark#(X) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(nats()) -> active#(nats()) active#(adx(cons(X,Y))) -> adx#(Y) -> adx#(active(X)) -> adx#(X) active#(adx(cons(X,Y))) -> adx#(Y) -> adx#(mark(X)) -> adx#(X) active#(zeros()) -> cons#(0(),zeros()) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(zeros()) -> cons#(0(),zeros()) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(zeros()) -> cons#(0(),zeros()) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(zeros()) -> cons#(0(),zeros()) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(tl(X)) -> active#(tl(mark(X))) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(tl(X)) -> tl#(mark(X)) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(tl(X)) -> mark#(X) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(hd(X)) -> active#(hd(mark(X))) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(hd(X)) -> hd#(mark(X)) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(hd(X)) -> mark#(X) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(s(X)) -> active#(s(X)) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(incr(X)) -> active#(incr(mark(X))) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(incr(X)) -> incr#(mark(X)) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(incr(X)) -> mark#(X) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(0()) -> active#(0()) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(zeros()) -> active#(zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(adx(X)) -> active#(adx(mark(X))) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(adx(X)) -> adx#(mark(X)) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(adx(X)) -> mark#(X) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) -> mark#(tl(X)) -> active#(tl(mark(X))) active#(nats()) -> mark#(adx(zeros())) -> mark#(tl(X)) -> tl#(mark(X)) active#(nats()) -> mark#(adx(zeros())) -> mark#(tl(X)) -> mark#(X) active#(nats()) -> mark#(adx(zeros())) -> mark#(hd(X)) -> active#(hd(mark(X))) active#(nats()) -> mark#(adx(zeros())) -> mark#(hd(X)) -> hd#(mark(X)) active#(nats()) -> mark#(adx(zeros())) -> mark#(hd(X)) -> mark#(X) active#(nats()) -> mark#(adx(zeros())) -> mark#(s(X)) -> active#(s(X)) active#(nats()) -> mark#(adx(zeros())) -> mark#(incr(X)) -> active#(incr(mark(X))) active#(nats()) -> mark#(adx(zeros())) -> mark#(incr(X)) -> incr#(mark(X)) active#(nats()) -> mark#(adx(zeros())) -> mark#(incr(X)) -> mark#(X) active#(nats()) -> mark#(adx(zeros())) -> mark#(0()) -> active#(0()) active#(nats()) -> mark#(adx(zeros())) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(nats()) -> mark#(adx(zeros())) -> mark#(zeros()) -> active#(zeros()) active#(nats()) -> mark#(adx(zeros())) -> mark#(adx(X)) -> active#(adx(mark(X))) active#(nats()) -> mark#(adx(zeros())) -> mark#(adx(X)) -> adx#(mark(X)) active#(nats()) -> mark#(adx(zeros())) -> mark#(adx(X)) -> mark#(X) active#(nats()) -> mark#(adx(zeros())) -> mark#(nats()) -> active#(nats()) active#(nats()) -> adx#(zeros()) -> adx#(active(X)) -> adx#(X) active#(nats()) -> adx#(zeros()) -> adx#(mark(X)) -> adx#(X) SCC Processor: #sccs: 7 #rules: 31 #arcs: 310/1849 DPs: mark#(tl(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) mark#(adx(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(0()) -> active#(0()) mark#(incr(X)) -> mark#(X) mark#(incr(X)) -> active#(incr(mark(X))) mark#(s(X)) -> active#(s(X)) mark#(hd(X)) -> mark#(X) mark#(hd(X)) -> active#(hd(mark(X))) mark#(tl(X)) -> active#(tl(mark(X))) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) EDG Processor: DPs: mark#(tl(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) mark#(adx(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(0()) -> active#(0()) mark#(incr(X)) -> mark#(X) mark#(incr(X)) -> active#(incr(mark(X))) mark#(s(X)) -> active#(s(X)) mark#(hd(X)) -> mark#(X) mark#(hd(X)) -> active#(hd(mark(X))) mark#(tl(X)) -> active#(tl(mark(X))) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) graph: mark#(tl(X)) -> mark#(X) -> mark#(nats()) -> active#(nats()) mark#(tl(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X) mark#(tl(X)) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) mark#(tl(X)) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) mark#(tl(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(tl(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(tl(X)) -> mark#(X) -> mark#(incr(X)) -> mark#(X) mark#(tl(X)) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) mark#(tl(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(tl(X)) -> mark#(X) -> mark#(hd(X)) -> mark#(X) mark#(tl(X)) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) mark#(tl(X)) -> mark#(X) -> mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(hd(X)) -> mark#(X) -> mark#(nats()) -> active#(nats()) mark#(hd(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) mark#(hd(X)) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) mark#(hd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(hd(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(hd(X)) -> mark#(X) -> mark#(incr(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) mark#(hd(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(hd(X)) -> mark#(X) -> mark#(hd(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) mark#(hd(X)) -> mark#(X) -> mark#(tl(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(s(X)) -> active#(s(X)) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(s(X)) -> active#(s(X)) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) -> mark#(X) -> mark#(nats()) -> active#(nats()) mark#(incr(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) mark#(incr(X)) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) mark#(incr(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(incr(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(incr(X)) -> mark#(X) -> mark#(incr(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) mark#(incr(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(incr(X)) -> mark#(X) -> mark#(hd(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) mark#(incr(X)) -> mark#(X) -> mark#(tl(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(adx(X)) -> mark#(X) -> mark#(nats()) -> active#(nats()) mark#(adx(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) mark#(adx(X)) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) mark#(adx(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(adx(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(adx(X)) -> mark#(X) -> mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) mark#(adx(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(adx(X)) -> mark#(X) -> mark#(hd(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) mark#(adx(X)) -> mark#(X) -> mark#(tl(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(zeros()) -> active#(zeros()) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(nats()) -> active#(nats()) -> active#(nats()) -> mark#(adx(zeros())) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(adx(X)) -> mark#(X) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(adx(X)) -> active#(adx(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(incr(X)) -> mark#(X) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(incr(X)) -> active#(incr(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(s(X)) -> active#(s(X)) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(hd(X)) -> mark#(X) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(hd(X)) -> active#(hd(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(tl(X)) -> mark#(X) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) -> mark#(tl(X)) -> active#(tl(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(adx(X)) -> mark#(X) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(adx(X)) -> active#(adx(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(incr(X)) -> mark#(X) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(incr(X)) -> active#(incr(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(s(X)) -> active#(s(X)) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(hd(X)) -> mark#(X) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(hd(X)) -> active#(hd(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(tl(X)) -> mark#(X) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) -> mark#(tl(X)) -> active#(tl(mark(X))) active#(zeros()) -> mark#(cons(0(),zeros())) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(nats()) -> mark#(adx(zeros())) -> mark#(adx(X)) -> mark#(X) active#(nats()) -> mark#(adx(zeros())) -> mark#(adx(X)) -> active#(adx(mark(X))) SCC Processor: #sccs: 1 #rules: 16 #arcs: 89/289 DPs: mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> active#(tl(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(hd(X)) -> active#(hd(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(hd(X)) -> mark#(X) mark#(s(X)) -> active#(s(X)) mark#(incr(X)) -> active#(incr(mark(X))) mark#(incr(X)) -> mark#(X) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(zeros()) -> active#(zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(adx(X)) -> active#(adx(mark(X))) mark#(adx(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {32} transitions: cons0(33,33) -> 34* f190() -> 33* active{#,0}(34) -> 32* problem: DPs: mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> active#(tl(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(hd(X)) -> active#(hd(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(hd(X)) -> mark#(X) mark#(s(X)) -> active#(s(X)) mark#(incr(X)) -> active#(incr(mark(X))) mark#(incr(X)) -> mark#(X) mark#(zeros()) -> active#(zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(adx(X)) -> active#(adx(mark(X))) mark#(adx(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) SCC Processor: #sccs: 1 #rules: 13 #arcs: 85/225 DPs: mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> active#(tl(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(hd(X)) -> active#(hd(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(hd(X)) -> mark#(X) mark#(s(X)) -> active#(s(X)) mark#(incr(X)) -> active#(incr(mark(X))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) mark#(adx(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {23} transitions: active{#,0}(25) -> 23* f340() -> 24* s0(24) -> 25* problem: DPs: mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> active#(tl(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(hd(X)) -> active#(hd(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(hd(X)) -> mark#(X) mark#(incr(X)) -> active#(incr(mark(X))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) mark#(adx(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {16} transitions: mark{#,0}(20) -> 16* incr0(17) -> 18* cons0(19,18) -> 20* f360() -> 17* s0(17) -> 19* problem: DPs: mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> active#(tl(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(hd(X)) -> active#(hd(mark(X))) mark#(hd(X)) -> mark#(X) mark#(incr(X)) -> active#(incr(mark(X))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) mark#(adx(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {7} transitions: mark{#,0}(10) -> 7* mark{#,0}(11) -> 7* active{#,0}(38) -> 7* active0(10) -> 37* mark0(10) -> 37* incr0(10) -> 38,11 incr0(37) -> 38* cons0(8,9) -> 10* adx0(8) -> 9* f380() -> 8* problem: DPs: mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> active#(tl(mark(X))) mark#(hd(X)) -> active#(hd(mark(X))) mark#(hd(X)) -> mark#(X) mark#(incr(X)) -> active#(incr(mark(X))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) mark#(adx(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) SCC Processor: #sccs: 1 #rules: 6 #arcs: 71/100 DPs: mark#(tl(X)) -> mark#(X) mark#(hd(X)) -> mark#(X) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> mark#(X) mark#(nats()) -> active#(nats()) active#(nats()) -> mark#(adx(zeros())) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Bounds Processor: bound: 2 enrichment: match-dp automaton: final states: {5,3,1} transitions: adx0(6) -> 7* f400() -> 2* mark{#,1}(14) -> 15* zeros0() -> 6* adx1(16) -> 17* zeros1() -> 16* nats0() -> 4* mark{#,2}(22) -> 23* mark{#,0}(7) -> 5* mark{#,0}(2) -> 1* mark{#,0}(8) -> 9* active{#,0}(4) -> 3* 3 -> 1* 5 -> 3* 6 -> 14,8 9 -> 5* 15 -> 5,3,1 16 -> 22* 17 -> 14* 23 -> 15,5 problem: DPs: TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Qed DPs: adx#(mark(X)) -> adx#(X) adx#(active(X)) -> adx#(X) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Subterm Criterion Processor: simple projection: pi(adx#) = 0 problem: DPs: TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Qed DPs: 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) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Subterm Criterion Processor: simple projection: pi(cons#) = 1 problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Qed DPs: incr#(mark(X)) -> incr#(X) incr#(active(X)) -> incr#(X) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Subterm Criterion Processor: simple projection: pi(incr#) = 0 problem: DPs: TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Qed DPs: hd#(mark(X)) -> hd#(X) hd#(active(X)) -> hd#(X) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Subterm Criterion Processor: simple projection: pi(hd#) = 0 problem: DPs: TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Qed DPs: tl#(mark(X)) -> tl#(X) tl#(active(X)) -> tl#(X) TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Subterm Criterion Processor: simple projection: pi(tl#) = 0 problem: DPs: TRS: active(nats()) -> mark(adx(zeros())) active(zeros()) -> mark(cons(0(),zeros())) active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y)))) mark(nats()) -> active(nats()) mark(adx(X)) -> active(adx(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(X)) mark(hd(X)) -> active(hd(mark(X))) mark(tl(X)) -> active(tl(mark(X))) adx(mark(X)) -> adx(X) adx(active(X)) -> adx(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) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) hd(mark(X)) -> hd(X) hd(active(X)) -> hd(X) tl(mark(X)) -> tl(X) tl(active(X)) -> tl(X) Qed