MAYBE 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: 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)))) active#(hd(cons(X,Y))) -> mark#(X) active#(tl(cons(X,Y))) -> mark#(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)))) 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) EDG 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)))) active#(hd(cons(X,Y))) -> mark#(X) active#(tl(cons(X,Y))) -> mark#(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)))) 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) graph: tl#(mark(X)) -> tl#(X) -> tl#(mark(X)) -> tl#(X) tl#(mark(X)) -> tl#(X) -> tl#(active(X)) -> tl#(X) tl#(active(X)) -> tl#(X) -> tl#(mark(X)) -> tl#(X) tl#(active(X)) -> tl#(X) -> tl#(active(X)) -> tl#(X) hd#(mark(X)) -> hd#(X) -> hd#(mark(X)) -> hd#(X) hd#(mark(X)) -> hd#(X) -> hd#(active(X)) -> hd#(X) hd#(active(X)) -> hd#(X) -> hd#(mark(X)) -> hd#(X) hd#(active(X)) -> hd#(X) -> hd#(active(X)) -> hd#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(active(X)) -> s#(X) incr#(mark(X)) -> incr#(X) -> incr#(mark(X)) -> incr#(X) incr#(mark(X)) -> incr#(X) -> incr#(active(X)) -> incr#(X) incr#(active(X)) -> incr#(X) -> incr#(mark(X)) -> incr#(X) incr#(active(X)) -> incr#(X) -> incr#(active(X)) -> incr#(X) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(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#(active(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(mark(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#(active(X1),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#(mark(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#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(mark(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#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) mark#(tl(X)) -> tl#(mark(X)) -> tl#(mark(X)) -> tl#(X) mark#(tl(X)) -> tl#(mark(X)) -> tl#(active(X)) -> tl#(X) 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)) -> adx#(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)) -> incr#(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)) -> hd#(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)) -> tl#(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))) -> 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))) -> 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)) -> active#(tl(mark(X))) -> active#(adx(cons(X,Y))) -> 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))) -> 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)) -> active#(tl(mark(X))) -> active#(hd(cons(X,Y))) -> mark#(X) mark#(tl(X)) -> active#(tl(mark(X))) -> active#(tl(cons(X,Y))) -> mark#(Y) mark#(hd(X)) -> hd#(mark(X)) -> hd#(mark(X)) -> hd#(X) mark#(hd(X)) -> hd#(mark(X)) -> hd#(active(X)) -> hd#(X) 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)) -> adx#(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)) -> incr#(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)) -> hd#(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)) -> tl#(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))) -> 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))) -> 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)) -> active#(hd(mark(X))) -> active#(adx(cons(X,Y))) -> 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))) -> 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)) -> active#(hd(mark(X))) -> active#(hd(cons(X,Y))) -> mark#(X) mark#(hd(X)) -> active#(hd(mark(X))) -> active#(tl(cons(X,Y))) -> mark#(Y) mark#(incr(X)) -> incr#(mark(X)) -> incr#(mark(X)) -> incr#(X) mark#(incr(X)) -> incr#(mark(X)) -> incr#(active(X)) -> incr#(X) 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)) -> adx#(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)) -> incr#(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)) -> hd#(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)) -> tl#(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))) -> 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))) -> 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)) -> active#(incr(mark(X))) -> active#(adx(cons(X,Y))) -> 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))) -> 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)) -> active#(incr(mark(X))) -> active#(hd(cons(X,Y))) -> mark#(X) mark#(incr(X)) -> active#(incr(mark(X))) -> active#(tl(cons(X,Y))) -> mark#(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)) -> adx#(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)) -> incr#(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)) -> hd#(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)) -> tl#(mark(X)) mark#(adx(X)) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) mark#(adx(X)) -> adx#(mark(X)) -> adx#(mark(X)) -> adx#(X) mark#(adx(X)) -> adx#(mark(X)) -> adx#(active(X)) -> adx#(X) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(incr(cons(X,Y))) -> 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))) -> 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)) -> active#(adx(mark(X))) -> active#(adx(cons(X,Y))) -> 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))) -> 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)) -> active#(adx(mark(X))) -> active#(hd(cons(X,Y))) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) -> active#(tl(cons(X,Y))) -> mark#(Y) mark#(zeros()) -> active#(zeros()) -> active#(zeros()) -> cons#(0(),zeros()) mark#(zeros()) -> active#(zeros()) -> active#(zeros()) -> mark#(cons(0(),zeros())) mark#(nats()) -> active#(nats()) -> active#(nats()) -> adx#(zeros()) mark#(nats()) -> active#(nats()) -> active#(nats()) -> mark#(adx(zeros())) adx#(mark(X)) -> adx#(X) -> adx#(mark(X)) -> adx#(X) adx#(mark(X)) -> adx#(X) -> adx#(active(X)) -> adx#(X) adx#(active(X)) -> adx#(X) -> adx#(mark(X)) -> adx#(X) adx#(active(X)) -> adx#(X) -> adx#(active(X)) -> adx#(X) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(nats()) -> active#(nats()) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(adx(X)) -> mark#(X) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(adx(X)) -> adx#(mark(X)) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(adx(X)) -> active#(adx(mark(X))) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(zeros()) -> active#(zeros()) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(0()) -> active#(0()) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(incr(X)) -> mark#(X) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(incr(X)) -> incr#(mark(X)) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(incr(X)) -> active#(incr(mark(X))) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(s(X)) -> active#(s(X)) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(hd(X)) -> mark#(X) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(hd(X)) -> hd#(mark(X)) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(hd(X)) -> active#(hd(mark(X))) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(tl(X)) -> mark#(X) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(tl(X)) -> tl#(mark(X)) active#(tl(cons(X,Y))) -> mark#(Y) -> mark#(tl(X)) -> active#(tl(mark(X))) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(nats()) -> active#(nats()) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(adx(X)) -> mark#(X) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(adx(X)) -> adx#(mark(X)) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(adx(X)) -> active#(adx(mark(X))) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(zeros()) -> active#(zeros()) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(0()) -> active#(0()) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(incr(X)) -> mark#(X) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(incr(X)) -> incr#(mark(X)) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(incr(X)) -> active#(incr(mark(X))) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(hd(X)) -> mark#(X) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(hd(X)) -> hd#(mark(X)) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(hd(X)) -> active#(hd(mark(X))) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(tl(X)) -> mark#(X) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(tl(X)) -> tl#(mark(X)) active#(hd(cons(X,Y))) -> mark#(X) -> mark#(tl(X)) -> active#(tl(mark(X))) 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#(X1,active(X2)) -> cons#(X1,X2) 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)) -> 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))) -> 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)) -> 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))) -> 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)) -> 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))) -> 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)) -> 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))) -> incr#(cons(X,adx(Y))) -> incr#(mark(X)) -> incr#(X) active#(adx(cons(X,Y))) -> incr#(cons(X,adx(Y))) -> incr#(active(X)) -> incr#(X) 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#(X1,active(X2)) -> cons#(X1,X2) 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)) -> 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))) -> 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)) -> 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))) -> 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)) -> 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))) -> 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)) -> tl#(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)) -> adx#(mark(X)) active#(nats()) -> mark#(adx(zeros())) -> mark#(adx(X)) -> active#(adx(mark(X))) SCC Processor: #sccs: 7 #rules: 28 #arcs: 228/2025 DPs: mark#(tl(X)) -> mark#(X) mark#(tl(X)) -> active#(tl(mark(X))) active#(tl(cons(X,Y))) -> mark#(Y) mark#(hd(X)) -> active#(hd(mark(X))) active#(hd(cons(X,Y))) -> mark#(X) mark#(hd(X)) -> mark#(X) mark#(incr(X)) -> active#(incr(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) 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)))) 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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [active#](x0) = x0 + 1, [tl](x0) = x0 + 1, [hd](x0) = x0 + 1, [s](x0) = 0, [incr](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [mark](x0) = x0, [adx](x0) = x0, [zeros] = 0, [active](x0) = x0, [nats] = 1 orientation: mark#(tl(X)) = X + 2 >= X + 1 = mark#(X) mark#(tl(X)) = X + 2 >= X + 2 = active#(tl(mark(X))) active#(tl(cons(X,Y))) = X + Y + 2 >= Y + 1 = mark#(Y) mark#(hd(X)) = X + 2 >= X + 2 = active#(hd(mark(X))) active#(hd(cons(X,Y))) = X + Y + 2 >= X + 1 = mark#(X) mark#(hd(X)) = X + 2 >= X + 1 = mark#(X) mark#(incr(X)) = X + 1 >= X + 1 = active#(incr(mark(X))) active#(adx(cons(X,Y))) = X + Y + 1 >= X + Y + 1 = mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) = X + 1 >= X + 1 = mark#(X) mark#(adx(X)) = X + 1 >= X + 1 = active#(adx(mark(X))) active#(incr(cons(X,Y))) = X + Y + 1 >= Y + 1 = mark#(cons(s(X),incr(Y))) mark#(adx(X)) = X + 1 >= X + 1 = mark#(X) mark#(nats()) = 2 >= 2 = active#(nats()) active#(nats()) = 2 >= 1 = mark#(adx(zeros())) active(nats()) = 1 >= 0 = mark(adx(zeros())) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(incr(cons(X,Y))) = X + Y >= Y = mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) = X + Y >= X + Y = mark(incr(cons(X,adx(Y)))) active(hd(cons(X,Y))) = X + Y + 1 >= X = mark(X) active(tl(cons(X,Y))) = X + Y + 1 >= Y = mark(Y) mark(nats()) = 1 >= 1 = active(nats()) mark(adx(X)) = X >= X = active(adx(mark(X))) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(X1,X2)) mark(0()) = 0 >= 0 = active(0()) mark(incr(X)) = X >= X = active(incr(mark(X))) mark(s(X)) = 0 >= 0 = active(s(X)) mark(hd(X)) = X + 1 >= X + 1 = active(hd(mark(X))) mark(tl(X)) = X + 1 >= X + 1 = active(tl(mark(X))) adx(mark(X)) = X >= X = adx(X) adx(active(X)) = X >= X = adx(X) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) incr(mark(X)) = X >= X = incr(X) incr(active(X)) = X >= X = incr(X) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) hd(mark(X)) = X + 1 >= X + 1 = hd(X) hd(active(X)) = X + 1 >= X + 1 = hd(X) tl(mark(X)) = X + 1 >= X + 1 = tl(X) tl(active(X)) = X + 1 >= X + 1 = tl(X) problem: DPs: mark#(tl(X)) -> active#(tl(mark(X))) mark#(hd(X)) -> active#(hd(mark(X))) mark#(incr(X)) -> active#(incr(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(adx(X)) -> mark#(X) mark#(nats()) -> active#(nats()) 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)))) 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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [tl](x0) = 1, [hd](x0) = 1, [s](x0) = 0, [incr](x0) = 1, [cons](x0, x1) = 0, [0] = 0, [mark](x0) = 1, [adx](x0) = 1, [zeros] = 0, [active](x0) = 1, [nats] = 0 orientation: mark#(tl(X)) = 1 >= 1 = active#(tl(mark(X))) mark#(hd(X)) = 1 >= 1 = active#(hd(mark(X))) mark#(incr(X)) = 1 >= 1 = active#(incr(mark(X))) active#(adx(cons(X,Y))) = 1 >= 1 = mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) = 1 >= 1 = mark#(X) mark#(adx(X)) = 1 >= 1 = active#(adx(mark(X))) active#(incr(cons(X,Y))) = 1 >= 1 = mark#(cons(s(X),incr(Y))) mark#(adx(X)) = 1 >= 1 = mark#(X) mark#(nats()) = 1 >= 0 = active#(nats()) active(nats()) = 1 >= 1 = mark(adx(zeros())) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(incr(cons(X,Y))) = 1 >= 1 = mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) = 1 >= 1 = mark(incr(cons(X,adx(Y)))) active(hd(cons(X,Y))) = 1 >= 1 = mark(X) active(tl(cons(X,Y))) = 1 >= 1 = mark(Y) mark(nats()) = 1 >= 1 = active(nats()) mark(adx(X)) = 1 >= 1 = active(adx(mark(X))) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(X1,X2)) mark(0()) = 1 >= 1 = active(0()) mark(incr(X)) = 1 >= 1 = active(incr(mark(X))) mark(s(X)) = 1 >= 1 = active(s(X)) mark(hd(X)) = 1 >= 1 = active(hd(mark(X))) mark(tl(X)) = 1 >= 1 = active(tl(mark(X))) adx(mark(X)) = 1 >= 1 = adx(X) adx(active(X)) = 1 >= 1 = adx(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) incr(mark(X)) = 1 >= 1 = incr(X) incr(active(X)) = 1 >= 1 = incr(X) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) hd(mark(X)) = 1 >= 1 = hd(X) hd(active(X)) = 1 >= 1 = hd(X) tl(mark(X)) = 1 >= 1 = tl(X) tl(active(X)) = 1 >= 1 = tl(X) problem: DPs: mark#(tl(X)) -> active#(tl(mark(X))) mark#(hd(X)) -> active#(hd(mark(X))) mark#(incr(X)) -> active#(incr(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(adx(X)) -> 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)))) 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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [tl](x0) = 1, [hd](x0) = 0, [s](x0) = 0, [incr](x0) = 1, [cons](x0, x1) = 0, [0] = 0, [mark](x0) = 0, [adx](x0) = 1, [zeros] = 0, [active](x0) = 0, [nats] = 0 orientation: mark#(tl(X)) = 1 >= 1 = active#(tl(mark(X))) mark#(hd(X)) = 1 >= 0 = active#(hd(mark(X))) mark#(incr(X)) = 1 >= 1 = active#(incr(mark(X))) active#(adx(cons(X,Y))) = 1 >= 1 = mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) = 1 >= 1 = mark#(X) mark#(adx(X)) = 1 >= 1 = active#(adx(mark(X))) active#(incr(cons(X,Y))) = 1 >= 1 = mark#(cons(s(X),incr(Y))) mark#(adx(X)) = 1 >= 1 = mark#(X) active(nats()) = 0 >= 0 = mark(adx(zeros())) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(incr(cons(X,Y))) = 0 >= 0 = mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) = 0 >= 0 = mark(incr(cons(X,adx(Y)))) active(hd(cons(X,Y))) = 0 >= 0 = mark(X) active(tl(cons(X,Y))) = 0 >= 0 = mark(Y) mark(nats()) = 0 >= 0 = active(nats()) mark(adx(X)) = 0 >= 0 = active(adx(mark(X))) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(X1,X2)) mark(0()) = 0 >= 0 = active(0()) mark(incr(X)) = 0 >= 0 = active(incr(mark(X))) mark(s(X)) = 0 >= 0 = active(s(X)) mark(hd(X)) = 0 >= 0 = active(hd(mark(X))) mark(tl(X)) = 0 >= 0 = active(tl(mark(X))) adx(mark(X)) = 1 >= 1 = adx(X) adx(active(X)) = 1 >= 1 = adx(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) incr(mark(X)) = 1 >= 1 = incr(X) incr(active(X)) = 1 >= 1 = incr(X) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) hd(mark(X)) = 0 >= 0 = hd(X) hd(active(X)) = 0 >= 0 = hd(X) tl(mark(X)) = 1 >= 1 = tl(X) tl(active(X)) = 1 >= 1 = tl(X) problem: DPs: mark#(tl(X)) -> active#(tl(mark(X))) mark#(incr(X)) -> active#(incr(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) mark#(adx(X)) -> 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)))) 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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [tl](x0) = x0, [hd](x0) = x0, [s](x0) = 0, [incr](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [mark](x0) = x0, [adx](x0) = x0 + 1, [zeros] = 0, [active](x0) = x0, [nats] = 1 orientation: mark#(tl(X)) = X >= X = active#(tl(mark(X))) mark#(incr(X)) = X >= X = active#(incr(mark(X))) active#(adx(cons(X,Y))) = X + Y + 1 >= X + Y + 1 = mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) = X >= X = mark#(X) mark#(adx(X)) = X + 1 >= X + 1 = active#(adx(mark(X))) active#(incr(cons(X,Y))) = X + Y >= Y = mark#(cons(s(X),incr(Y))) mark#(adx(X)) = X + 1 >= X = mark#(X) active(nats()) = 1 >= 1 = mark(adx(zeros())) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(incr(cons(X,Y))) = X + Y >= Y = mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) = X + Y + 1 >= X + Y + 1 = mark(incr(cons(X,adx(Y)))) active(hd(cons(X,Y))) = X + Y >= X = mark(X) active(tl(cons(X,Y))) = X + Y >= Y = mark(Y) mark(nats()) = 1 >= 1 = active(nats()) mark(adx(X)) = X + 1 >= X + 1 = active(adx(mark(X))) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(X1,X2)) mark(0()) = 0 >= 0 = active(0()) mark(incr(X)) = X >= X = active(incr(mark(X))) mark(s(X)) = 0 >= 0 = active(s(X)) mark(hd(X)) = X >= X = active(hd(mark(X))) mark(tl(X)) = X >= X = active(tl(mark(X))) adx(mark(X)) = X + 1 >= X + 1 = adx(X) adx(active(X)) = X + 1 >= X + 1 = adx(X) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) incr(mark(X)) = X >= X = incr(X) incr(active(X)) = X >= X = incr(X) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) hd(mark(X)) = X >= X = hd(X) hd(active(X)) = X >= X = hd(X) tl(mark(X)) = X >= X = tl(X) tl(active(X)) = X >= X = tl(X) problem: DPs: mark#(tl(X)) -> active#(tl(mark(X))) mark#(incr(X)) -> active#(incr(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) 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)))) 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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [tl](x0) = 0, [hd](x0) = 0, [s](x0) = 0, [incr](x0) = 1, [cons](x0, x1) = 0, [0] = 0, [mark](x0) = 0, [adx](x0) = 1, [zeros] = 0, [active](x0) = 0, [nats] = 0 orientation: mark#(tl(X)) = 1 >= 0 = active#(tl(mark(X))) mark#(incr(X)) = 1 >= 1 = active#(incr(mark(X))) active#(adx(cons(X,Y))) = 1 >= 1 = mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) = 1 >= 1 = mark#(X) mark#(adx(X)) = 1 >= 1 = active#(adx(mark(X))) active#(incr(cons(X,Y))) = 1 >= 1 = mark#(cons(s(X),incr(Y))) active(nats()) = 0 >= 0 = mark(adx(zeros())) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(incr(cons(X,Y))) = 0 >= 0 = mark(cons(s(X),incr(Y))) active(adx(cons(X,Y))) = 0 >= 0 = mark(incr(cons(X,adx(Y)))) active(hd(cons(X,Y))) = 0 >= 0 = mark(X) active(tl(cons(X,Y))) = 0 >= 0 = mark(Y) mark(nats()) = 0 >= 0 = active(nats()) mark(adx(X)) = 0 >= 0 = active(adx(mark(X))) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(X1,X2)) mark(0()) = 0 >= 0 = active(0()) mark(incr(X)) = 0 >= 0 = active(incr(mark(X))) mark(s(X)) = 0 >= 0 = active(s(X)) mark(hd(X)) = 0 >= 0 = active(hd(mark(X))) mark(tl(X)) = 0 >= 0 = active(tl(mark(X))) adx(mark(X)) = 1 >= 1 = adx(X) adx(active(X)) = 1 >= 1 = adx(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) incr(mark(X)) = 1 >= 1 = incr(X) incr(active(X)) = 1 >= 1 = incr(X) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) hd(mark(X)) = 0 >= 0 = hd(X) hd(active(X)) = 0 >= 0 = hd(X) tl(mark(X)) = 0 >= 0 = tl(X) tl(active(X)) = 0 >= 0 = tl(X) problem: DPs: mark#(incr(X)) -> active#(incr(mark(X))) active#(adx(cons(X,Y))) -> mark#(incr(cons(X,adx(Y)))) mark#(incr(X)) -> mark#(X) mark#(adx(X)) -> active#(adx(mark(X))) active#(incr(cons(X,Y))) -> mark#(cons(s(X),incr(Y))) 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)))) 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) Open DPs: adx#(active(X)) -> adx#(X) adx#(mark(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)))) 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) Open DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(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)))) 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) Open 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)))) 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) Open 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)))) 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) Open 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)))) 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) Open 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)))) 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) Open