YES Problem: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Proof: DP Processor: DPs: active#(from(X)) -> s#(X) active#(from(X)) -> from#(s(X)) active#(from(X)) -> cons#(X,from(s(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(after(0(),XS)) -> mark#(XS) active#(after(s(N),cons(X,XS))) -> after#(N,XS) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> from#(mark(X)) mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(0()) -> active#(0()) from#(mark(X)) -> from#(X) from#(active(X)) -> from#(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) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) after#(mark(X1),X2) -> after#(X1,X2) after#(X1,mark(X2)) -> after#(X1,X2) after#(active(X1),X2) -> after#(X1,X2) after#(X1,active(X2)) -> after#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) TDG Processor: DPs: active#(from(X)) -> s#(X) active#(from(X)) -> from#(s(X)) active#(from(X)) -> cons#(X,from(s(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(after(0(),XS)) -> mark#(XS) active#(after(s(N),cons(X,XS))) -> after#(N,XS) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> from#(mark(X)) mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(0()) -> active#(0()) from#(mark(X)) -> from#(X) from#(active(X)) -> from#(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) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) after#(mark(X1),X2) -> after#(X1,X2) after#(X1,mark(X2)) -> after#(X1,X2) after#(active(X1),X2) -> after#(X1,X2) after#(X1,active(X2)) -> after#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) graph: after#(mark(X1),X2) -> after#(X1,X2) -> after#(X1,active(X2)) -> after#(X1,X2) after#(mark(X1),X2) -> after#(X1,X2) -> after#(active(X1),X2) -> after#(X1,X2) after#(mark(X1),X2) -> after#(X1,X2) -> after#(X1,mark(X2)) -> after#(X1,X2) after#(mark(X1),X2) -> after#(X1,X2) -> after#(mark(X1),X2) -> after#(X1,X2) after#(active(X1),X2) -> after#(X1,X2) -> after#(X1,active(X2)) -> after#(X1,X2) after#(active(X1),X2) -> after#(X1,X2) -> after#(active(X1),X2) -> after#(X1,X2) after#(active(X1),X2) -> after#(X1,X2) -> after#(X1,mark(X2)) -> after#(X1,X2) after#(active(X1),X2) -> after#(X1,X2) -> after#(mark(X1),X2) -> after#(X1,X2) after#(X1,mark(X2)) -> after#(X1,X2) -> after#(X1,active(X2)) -> after#(X1,X2) after#(X1,mark(X2)) -> after#(X1,X2) -> after#(active(X1),X2) -> after#(X1,X2) after#(X1,mark(X2)) -> after#(X1,X2) -> after#(X1,mark(X2)) -> after#(X1,X2) after#(X1,mark(X2)) -> after#(X1,X2) -> after#(mark(X1),X2) -> after#(X1,X2) after#(X1,active(X2)) -> after#(X1,X2) -> after#(X1,active(X2)) -> after#(X1,X2) after#(X1,active(X2)) -> after#(X1,X2) -> after#(active(X1),X2) -> after#(X1,X2) after#(X1,active(X2)) -> after#(X1,X2) -> after#(X1,mark(X2)) -> after#(X1,X2) after#(X1,active(X2)) -> after#(X1,X2) -> after#(mark(X1),X2) -> after#(X1,X2) mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) -> after#(X1,active(X2)) -> after#(X1,X2) mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) -> after#(active(X1),X2) -> after#(X1,X2) mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) -> after#(X1,mark(X2)) -> after#(X1,X2) mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) -> after#(mark(X1),X2) -> after#(X1,X2) mark#(after(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(after(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> s#(mark(X)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(after(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> active#(from(mark(X))) mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> from#(mark(X)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(after(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(after(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> from#(mark(X)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(after(s(N),cons(X,XS))) -> after#(N,XS) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(after(0(),XS)) -> mark#(XS) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(from(X)) -> from#(s(X)) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(from(X)) -> s#(X) mark#(0()) -> active#(0()) -> active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(0()) -> active#(0()) -> active#(after(s(N),cons(X,XS))) -> after#(N,XS) mark#(0()) -> active#(0()) -> active#(after(0(),XS)) -> mark#(XS) mark#(0()) -> active#(0()) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(0()) -> active#(0()) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(0()) -> active#(0()) -> active#(from(X)) -> from#(s(X)) mark#(0()) -> active#(0()) -> active#(from(X)) -> s#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> from#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(active(X1),X2) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(after(s(N),cons(X,XS))) -> after#(N,XS) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(after(0(),XS)) -> mark#(XS) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> from#(s(X)) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> s#(X) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> from#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) -> s#(active(X)) -> s#(X) mark#(s(X)) -> s#(mark(X)) -> s#(mark(X)) -> s#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(s(X)) -> active#(s(mark(X))) -> active#(after(s(N),cons(X,XS))) -> after#(N,XS) mark#(s(X)) -> active#(s(mark(X))) -> active#(after(0(),XS)) -> mark#(XS) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> from#(s(X)) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> s#(X) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> from#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> from#(mark(X)) -> from#(active(X)) -> from#(X) mark#(from(X)) -> from#(mark(X)) -> from#(mark(X)) -> from#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(from(X)) -> active#(from(mark(X))) -> active#(after(s(N),cons(X,XS))) -> after#(N,XS) mark#(from(X)) -> active#(from(mark(X))) -> active#(after(0(),XS)) -> mark#(XS) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> from#(s(X)) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> s#(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) from#(mark(X)) -> from#(X) -> from#(active(X)) -> from#(X) from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) -> from#(active(X)) -> from#(X) from#(active(X)) -> from#(X) -> from#(mark(X)) -> from#(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) active#(after(0(),XS)) -> mark#(XS) -> mark#(0()) -> active#(0()) active#(after(0(),XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(0(),XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) active#(after(0(),XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X1) active#(after(0(),XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X2) active#(after(0(),XS)) -> mark#(XS) -> mark#(s(X)) -> active#(s(mark(X))) active#(after(0(),XS)) -> mark#(XS) -> mark#(s(X)) -> s#(mark(X)) active#(after(0(),XS)) -> mark#(XS) -> mark#(s(X)) -> mark#(X) active#(after(0(),XS)) -> mark#(XS) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(after(0(),XS)) -> mark#(XS) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(after(0(),XS)) -> mark#(XS) -> mark#(cons(X1,X2)) -> mark#(X1) active#(after(0(),XS)) -> mark#(XS) -> mark#(from(X)) -> active#(from(mark(X))) active#(after(0(),XS)) -> mark#(XS) -> mark#(from(X)) -> from#(mark(X)) active#(after(0(),XS)) -> mark#(XS) -> mark#(from(X)) -> mark#(X) active#(after(s(N),cons(X,XS))) -> after#(N,XS) -> after#(X1,active(X2)) -> after#(X1,X2) active#(after(s(N),cons(X,XS))) -> after#(N,XS) -> after#(active(X1),X2) -> after#(X1,X2) active#(after(s(N),cons(X,XS))) -> after#(N,XS) -> after#(X1,mark(X2)) -> after#(X1,X2) active#(after(s(N),cons(X,XS))) -> after#(N,XS) -> after#(mark(X1),X2) -> after#(X1,X2) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(0()) -> active#(0()) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(after(X1,X2)) -> mark#(X1) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(after(X1,X2)) -> mark#(X2) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(s(X)) -> active#(s(mark(X))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(s(X)) -> s#(mark(X)) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(s(X)) -> mark#(X) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(cons(X1,X2)) -> mark#(X1) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(from(X)) -> active#(from(mark(X))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(from(X)) -> from#(mark(X)) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(from(X)) -> mark#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(0()) -> active#(0()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(after(X1,X2)) -> after#(mark(X1),mark(X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(after(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(after(X1,X2)) -> mark#(X2) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> active#(s(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> s#(mark(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> mark#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> from#(mark(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> mark#(X) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(from(X)) -> from#(s(X)) -> from#(active(X)) -> from#(X) active#(from(X)) -> from#(s(X)) -> from#(mark(X)) -> from#(X) active#(from(X)) -> s#(X) -> s#(active(X)) -> s#(X) active#(from(X)) -> s#(X) -> s#(mark(X)) -> s#(X) SCC Processor: #sccs: 5 #rules: 25 #arcs: 211/1089 DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(after(0(),XS)) -> mark#(XS) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) EDG Processor: DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(after(0(),XS)) -> mark#(XS) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) graph: mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> active#(from(mark(X))) mark#(after(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(after(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(after(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(after(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(after(0(),XS)) -> mark#(XS) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) -> active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(after(0(),XS)) -> mark#(XS) -> mark#(from(X)) -> mark#(X) active#(after(0(),XS)) -> mark#(XS) -> mark#(from(X)) -> active#(from(mark(X))) active#(after(0(),XS)) -> mark#(XS) -> mark#(cons(X1,X2)) -> mark#(X1) active#(after(0(),XS)) -> mark#(XS) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(after(0(),XS)) -> mark#(XS) -> mark#(s(X)) -> mark#(X) active#(after(0(),XS)) -> mark#(XS) -> mark#(s(X)) -> active#(s(mark(X))) active#(after(0(),XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X2) active#(after(0(),XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X1) active#(after(0(),XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(0(),XS)) -> mark#(XS) -> mark#(0()) -> active#(0()) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(after(X1,X2)) -> mark#(X2) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(after(X1,X2)) -> mark#(X1) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) -> mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) SCC Processor: #sccs: 1 #rules: 10 #arcs: 68/169 DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(after(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) active#(after(0(),XS)) -> mark#(XS) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) interpretation: [mark](x0) = x0, [active](x0) = x0, [cons](x0, x1) = x0 + x1 + 4, [0] = 0, [from](x0) = 1x0 + 7, [active#](x0) = x0 + 0, [mark#](x0) = x0 + 0, [after](x0, x1) = x0 + 3x1 + 0, [s](x0) = x0 orientation: mark#(after(X1,X2)) = X1 + 3X2 + 0 >= X2 + 0 = mark#(X2) mark#(after(X1,X2)) = X1 + 3X2 + 0 >= X1 + 3X2 + 0 = active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) = N + 3X + 3XS + 7 >= N + 3XS + 0 = mark#(after(N,XS)) mark#(after(X1,X2)) = X1 + 3X2 + 0 >= X1 + 0 = mark#(X1) mark#(s(X)) = X + 0 >= X + 0 = mark#(X) mark#(cons(X1,X2)) = X1 + X2 + 4 >= X1 + 0 = mark#(X1) mark#(from(X)) = 1X + 7 >= 1X + 7 = active#(from(mark(X))) active#(from(X)) = 1X + 7 >= 1X + 7 = mark#(cons(X,from(s(X)))) mark#(from(X)) = 1X + 7 >= X + 0 = mark#(X) active#(after(0(),XS)) = 3XS + 0 >= XS + 0 = mark#(XS) active(from(X)) = 1X + 7 >= 1X + 7 = mark(cons(X,from(s(X)))) active(after(0(),XS)) = 3XS + 0 >= XS = mark(XS) active(after(s(N),cons(X,XS))) = N + 3X + 3XS + 7 >= N + 3XS + 0 = mark(after(N,XS)) mark(from(X)) = 1X + 7 >= 1X + 7 = active(from(mark(X))) mark(cons(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = active(cons(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(after(X1,X2)) = X1 + 3X2 + 0 >= X1 + 3X2 + 0 = active(after(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) from(mark(X)) = 1X + 7 >= 1X + 7 = from(X) from(active(X)) = 1X + 7 >= 1X + 7 = from(X) cons(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = cons(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) after(mark(X1),X2) = X1 + 3X2 + 0 >= X1 + 3X2 + 0 = after(X1,X2) after(X1,mark(X2)) = X1 + 3X2 + 0 >= X1 + 3X2 + 0 = after(X1,X2) after(active(X1),X2) = X1 + 3X2 + 0 >= X1 + 3X2 + 0 = after(X1,X2) after(X1,active(X2)) = X1 + 3X2 + 0 >= X1 + 3X2 + 0 = after(X1,X2) problem: DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(after(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(after(0(),XS)) -> mark#(XS) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Restore Modifier: DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(after(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(after(0(),XS)) -> mark#(XS) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) interpretation: [mark](x0) = x0, [active](x0) = x0 + 0, [cons](x0, x1) = x0 + x1 + 0, [0] = 0, [from](x0) = x0 + 2, [active#](x0) = x0 + 0, [mark#](x0) = x0, [after](x0, x1) = 7x0 + x1 + 7, [s](x0) = x0 + 0 orientation: mark#(after(X1,X2)) = 7X1 + X2 + 7 >= X2 = mark#(X2) mark#(after(X1,X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) = 7N + X + XS + 7 >= 7N + XS + 7 = mark#(after(N,XS)) mark#(after(X1,X2)) = 7X1 + X2 + 7 >= X1 = mark#(X1) mark#(s(X)) = X + 0 >= X = mark#(X) mark#(cons(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1) mark#(from(X)) = X + 2 >= X + 2 = active#(from(mark(X))) active#(from(X)) = X + 2 >= X + 2 = mark#(cons(X,from(s(X)))) active#(after(0(),XS)) = XS + 7 >= XS = mark#(XS) active(from(X)) = X + 2 >= X + 2 = mark(cons(X,from(s(X)))) active(after(0(),XS)) = XS + 7 >= XS = mark(XS) active(after(s(N),cons(X,XS))) = 7N + X + XS + 7 >= 7N + XS + 7 = mark(after(N,XS)) mark(from(X)) = X + 2 >= X + 2 = active(from(mark(X))) mark(cons(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(cons(mark(X1),X2)) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(after(X1,X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = active(after(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) from(mark(X)) = X + 2 >= X + 2 = from(X) from(active(X)) = X + 2 >= X + 2 = from(X) cons(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) after(mark(X1),X2) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = after(X1,X2) after(X1,mark(X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = after(X1,X2) after(active(X1),X2) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = after(X1,X2) after(X1,active(X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = after(X1,X2) problem: DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(after(0(),XS)) -> mark#(XS) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Restore Modifier: DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(after(0(),XS)) -> mark#(XS) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) interpretation: [mark](x0) = x0, [active](x0) = x0, [cons](x0, x1) = x0 + x1 + 0, [0] = 0, [from](x0) = 2x0 + 2, [active#](x0) = x0, [mark#](x0) = x0 + 0, [after](x0, x1) = 1x0 + 7x1, [s](x0) = x0 + 0 orientation: mark#(after(X1,X2)) = 1X1 + 7X2 + 0 >= X2 + 0 = mark#(X2) mark#(after(X1,X2)) = 1X1 + 7X2 + 0 >= 1X1 + 7X2 = active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) = 1N + 7X + 7XS + 7 >= 1N + 7XS + 0 = mark#(after(N,XS)) mark#(s(X)) = X + 0 >= X + 0 = mark#(X) mark#(cons(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(from(X)) = 2X + 2 >= 2X + 2 = active#(from(mark(X))) active#(from(X)) = 2X + 2 >= 2X + 2 = mark#(cons(X,from(s(X)))) active#(after(0(),XS)) = 7XS + 1 >= XS + 0 = mark#(XS) active(from(X)) = 2X + 2 >= 2X + 2 = mark(cons(X,from(s(X)))) active(after(0(),XS)) = 7XS + 1 >= XS = mark(XS) active(after(s(N),cons(X,XS))) = 1N + 7X + 7XS + 7 >= 1N + 7XS = mark(after(N,XS)) mark(from(X)) = 2X + 2 >= 2X + 2 = active(from(mark(X))) mark(cons(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(cons(mark(X1),X2)) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(after(X1,X2)) = 1X1 + 7X2 >= 1X1 + 7X2 = active(after(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) from(mark(X)) = 2X + 2 >= 2X + 2 = from(X) from(active(X)) = 2X + 2 >= 2X + 2 = from(X) cons(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) after(mark(X1),X2) = 1X1 + 7X2 >= 1X1 + 7X2 = after(X1,X2) after(X1,mark(X2)) = 1X1 + 7X2 >= 1X1 + 7X2 = after(X1,X2) after(active(X1),X2) = 1X1 + 7X2 >= 1X1 + 7X2 = after(X1,X2) after(X1,active(X2)) = 1X1 + 7X2 >= 1X1 + 7X2 = after(X1,X2) problem: DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Restore Modifier: DPs: mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) interpretation: [mark](x0) = x0, [active](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 5, [from](x0) = x0, [active#](x0) = x0, [mark#](x0) = x0, [after](x0, x1) = 1x0 + 4x1 + 1, [s](x0) = x0 orientation: mark#(after(X1,X2)) = 1X1 + 4X2 + 1 >= X2 = mark#(X2) mark#(after(X1,X2)) = 1X1 + 4X2 + 1 >= 1X1 + 4X2 + 1 = active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) = 1N + 4X + 4XS + 1 >= 1N + 4XS + 1 = mark#(after(N,XS)) mark#(s(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(from(X)) = X >= X = active#(from(mark(X))) active#(from(X)) = X >= X = mark#(cons(X,from(s(X)))) active(from(X)) = X >= X = mark(cons(X,from(s(X)))) active(after(0(),XS)) = 4XS + 6 >= XS = mark(XS) active(after(s(N),cons(X,XS))) = 1N + 4X + 4XS + 1 >= 1N + 4XS + 1 = mark(after(N,XS)) mark(from(X)) = X >= X = active(from(mark(X))) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(after(X1,X2)) = 1X1 + 4X2 + 1 >= 1X1 + 4X2 + 1 = active(after(mark(X1),mark(X2))) mark(0()) = 5 >= 5 = active(0()) from(mark(X)) = X >= X = from(X) from(active(X)) = X >= X = from(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) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) after(mark(X1),X2) = 1X1 + 4X2 + 1 >= 1X1 + 4X2 + 1 = after(X1,X2) after(X1,mark(X2)) = 1X1 + 4X2 + 1 >= 1X1 + 4X2 + 1 = after(X1,X2) after(active(X1),X2) = 1X1 + 4X2 + 1 >= 1X1 + 4X2 + 1 = after(X1,X2) after(X1,active(X2)) = 1X1 + 4X2 + 1 >= 1X1 + 4X2 + 1 = after(X1,X2) problem: DPs: mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Restore Modifier: DPs: mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) SCC Processor: #sccs: 2 #rules: 6 #arcs: 49/36 DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Arctic Interpretation Processor: dimension: 1 usable rules: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) interpretation: [mark](x0) = x0, [active](x0) = x0, [cons](x0, x1) = 1x0 + x1, [0] = 2, [from](x0) = 1x0, [active#](x0) = x0, [mark#](x0) = x0, [after](x0, x1) = x1 + 0, [s](x0) = x0 orientation: mark#(cons(X1,X2)) = 1X1 + X2 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) mark#(from(X)) = 1X >= 1X = active#(from(mark(X))) active#(from(X)) = 1X >= 1X = mark#(cons(X,from(s(X)))) active(from(X)) = 1X >= 1X = mark(cons(X,from(s(X)))) active(after(0(),XS)) = XS + 0 >= XS = mark(XS) active(after(s(N),cons(X,XS))) = 1X + XS + 0 >= XS + 0 = mark(after(N,XS)) mark(from(X)) = 1X >= 1X = active(from(mark(X))) mark(cons(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = active(cons(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(after(X1,X2)) = X2 + 0 >= X2 + 0 = active(after(mark(X1),mark(X2))) mark(0()) = 2 >= 2 = active(0()) from(mark(X)) = 1X >= 1X = from(X) from(active(X)) = 1X >= 1X = from(X) cons(mark(X1),X2) = 1X1 + X2 >= 1X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = 1X1 + X2 >= 1X1 + X2 = cons(X1,X2) cons(active(X1),X2) = 1X1 + X2 >= 1X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = 1X1 + X2 >= 1X1 + X2 = cons(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) after(mark(X1),X2) = X2 + 0 >= X2 + 0 = after(X1,X2) after(X1,mark(X2)) = X2 + 0 >= X2 + 0 = after(X1,X2) after(active(X1),X2) = X2 + 0 >= X2 + 0 = after(X1,X2) after(X1,active(X2)) = X2 + 0 >= X2 + 0 = after(X1,X2) problem: DPs: mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Restore Modifier: DPs: mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) SCC Processor: #sccs: 1 #rules: 1 #arcs: 8/9 DPs: mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Size-Change Termination Processor: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) The DP: mark#(s(X)) -> mark#(X) has the edges: 0 > 0 Qed DPs: mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) active#(after(s(N),cons(X,XS))) -> mark#(after(N,XS)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) KBO Processor: argument filtering: pi(from) = [] pi(active) = 0 pi(s) = [0] pi(cons) = 1 pi(mark) = 0 pi(0) = [] pi(after) = [0,1] pi(active#) = 0 pi(mark#) = 0 usable rules: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) weight function: w0 = 1 w(mark#) = w(active#) = w(0) = w(s) = w(from) = 1 w(after) = w(mark) = w(cons) = w(active) = 0 precedence: mark > active# > 0 > mark# > s > after > cons > from > active problem: DPs: mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Restore Modifier: DPs: mark#(after(X1,X2)) -> active#(after(mark(X1),mark(X2))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/1 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(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Subterm Criterion Processor: simple projection: pi(cons#) = 1 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Qed DPs: from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Subterm Criterion Processor: simple projection: pi(from#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Qed DPs: after#(mark(X1),X2) -> after#(X1,X2) after#(X1,mark(X2)) -> after#(X1,X2) after#(active(X1),X2) -> after#(X1,X2) after#(X1,active(X2)) -> after#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Subterm Criterion Processor: simple projection: pi(after#) = 0 problem: DPs: after#(X1,mark(X2)) -> after#(X1,X2) after#(X1,active(X2)) -> after#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Subterm Criterion Processor: simple projection: pi(after#) = 1 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(after(0(),XS)) -> mark(XS) active(after(s(N),cons(X,XS))) -> mark(after(N,XS)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(after(X1,X2)) -> active(after(mark(X1),mark(X2))) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) after(mark(X1),X2) -> after(X1,X2) after(X1,mark(X2)) -> after(X1,X2) after(active(X1),X2) -> after(X1,X2) after(X1,active(X2)) -> after(X1,X2) Qed