MAYBE Problem: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(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#(sel(0(),cons(X,Y))) -> mark#(X) active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) 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#(sel(X1,X2)) -> mark#(X2) mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) mark#(sel(X1,X2)) -> active#(sel(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) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(active(X1),X2) -> sel#(X1,X2) sel#(X1,active(X2)) -> sel#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(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#(sel(0(),cons(X,Y))) -> mark#(X) active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) 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#(sel(X1,X2)) -> mark#(X2) mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) mark#(sel(X1,X2)) -> active#(sel(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) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(active(X1),X2) -> sel#(X1,X2) sel#(X1,active(X2)) -> sel#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) graph: sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(X1,active(X2)) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(active(X1),X2) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) sel#(active(X1),X2) -> sel#(X1,X2) -> sel#(X1,active(X2)) -> sel#(X1,X2) sel#(active(X1),X2) -> sel#(X1,X2) -> sel#(active(X1),X2) -> sel#(X1,X2) sel#(active(X1),X2) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(active(X1),X2) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(X1,active(X2)) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(active(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,active(X2)) -> sel#(X1,X2) -> sel#(X1,active(X2)) -> sel#(X1,X2) sel#(X1,active(X2)) -> sel#(X1,X2) -> sel#(active(X1),X2) -> sel#(X1,X2) sel#(X1,active(X2)) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(X1,active(X2)) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) -> sel#(X1,active(X2)) -> sel#(X1,X2) mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) -> sel#(active(X1),X2) -> sel#(X1,X2) mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) -> sel#(X1,mark(X2)) -> sel#(X1,X2) mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) -> sel#(mark(X1),X2) -> sel#(X1,X2) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> mark#(X2) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> s#(mark(X)) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> active#(from(mark(X))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> from#(mark(X)) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X2) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> from#(mark(X)) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(sel(0(),cons(X,Y))) -> mark#(X) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(from(X)) -> from#(s(X)) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(from(X)) -> s#(X) mark#(0()) -> active#(0()) -> active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(0()) -> active#(0()) -> active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) mark#(0()) -> active#(0()) -> active#(sel(0(),cons(X,Y))) -> mark#(X) 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#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sel(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#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(sel(0(),cons(X,Y))) -> mark#(X) 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#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(sel(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#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(s(X)) -> active#(s(mark(X))) -> active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) mark#(s(X)) -> active#(s(mark(X))) -> active#(sel(0(),cons(X,Y))) -> mark#(X) 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#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(from(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(sel(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#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(from(X)) -> active#(from(mark(X))) -> active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) mark#(from(X)) -> active#(from(mark(X))) -> active#(sel(0(),cons(X,Y))) -> mark#(X) 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#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(0()) -> active#(0()) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(s(X)) -> mark#(X) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(from(X)) -> from#(mark(X)) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(from(X)) -> mark#(X) active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) -> sel#(X1,active(X2)) -> sel#(X1,X2) active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) -> sel#(active(X1),X2) -> sel#(X1,X2) active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) -> sel#(X1,mark(X2)) -> sel#(X1,X2) active#(sel(s(X),cons(Y,Z))) -> sel#(X,Z) -> sel#(mark(X1),X2) -> sel#(X1,X2) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(0()) -> active#(0()) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> mark#(X1) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> mark#(X2) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(s(X)) -> active#(s(mark(X))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(s(X)) -> s#(mark(X)) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(s(X)) -> mark#(X) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(cons(X1,X2)) -> mark#(X1) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(from(X)) -> active#(from(mark(X))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(from(X)) -> from#(mark(X)) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> 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#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(sel(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(sel(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#(sel(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#(sel(0(),cons(X,Y))) -> mark#(X) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) EDG Processor: DPs: mark#(sel(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#(sel(0(),cons(X,Y))) -> mark#(X) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) graph: mark#(sel(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> active#(from(mark(X))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> mark#(X2) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X2) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(sel(0(),cons(X,Y))) -> mark#(X) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) 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#(sel(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) 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#(sel(0(),cons(X,Y))) -> mark#(X) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) 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#(sel(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> active#(s(mark(X))) -> active#(sel(0(),cons(X,Y))) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) 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#(sel(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> active#(sel(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)))) mark#(from(X)) -> active#(from(mark(X))) -> active#(sel(0(),cons(X,Y))) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(from(X)) -> mark#(X) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(s(X)) -> mark#(X) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(0()) -> active#(0()) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(from(X)) -> mark#(X) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(from(X)) -> active#(from(mark(X))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(cons(X1,X2)) -> mark#(X1) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(s(X)) -> mark#(X) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(s(X)) -> active#(s(mark(X))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> mark#(X2) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> mark#(X1) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> mark#(X) 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#(cons(X1,X2)) -> mark#(X1) 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#(s(X)) -> mark#(X) 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#(sel(X1,X2)) -> mark#(X2) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(sel(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) CDG Processor: DPs: mark#(sel(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#(sel(0(),cons(X,Y))) -> mark#(X) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) graph: mark#(sel(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> mark#(X2) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> active#(from(mark(X))) mark#(sel(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X2) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(sel(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) -> active#(sel(0(),cons(X,Y))) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sel(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)) -> 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)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(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)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) mark#(from(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> active#(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)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(0()) -> active#(0()) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(s(X)) -> mark#(X) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) active#(sel(0(),cons(X,Y))) -> mark#(X) -> mark#(from(X)) -> mark#(X) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> mark#(X1) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) -> mark#(sel(X1,X2)) -> mark#(X2) 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)) -> mark#(X1) SCC Processor: #sccs: 1 #rules: 10 #arcs: 68/169 DPs: mark#(sel(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#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(0(),cons(X,Y))) -> mark#(X) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 0, [active#](x0) = x0 + 0, [sel](x0, x1) = x0 + 5x1 + 0, [0] = 1, [mark](x0) = x0, [cons](x0, x1) = 1x0 + x1, [s](x0) = x0, [active](x0) = x0, [from](x0) = 7x0 + 0 orientation: mark#(sel(X1,X2)) = X1 + 5X2 + 0 >= X2 + 0 = mark#(X2) mark#(from(X)) = 7X + 0 >= X + 0 = mark#(X) mark#(from(X)) = 7X + 0 >= 7X + 0 = active#(from(mark(X))) active#(from(X)) = 7X + 0 >= 7X + 0 = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = 1X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(s(X)) = X + 0 >= X + 0 = mark#(X) mark#(sel(X1,X2)) = X1 + 5X2 + 0 >= X1 + 0 = mark#(X1) mark#(sel(X1,X2)) = X1 + 5X2 + 0 >= X1 + 5X2 + 0 = active#(sel(mark(X1),mark(X2))) active#(sel(0(),cons(X,Y))) = 6X + 5Y + 1 >= X + 0 = mark#(X) active#(sel(s(X),cons(Y,Z))) = X + 6Y + 5Z + 0 >= X + 5Z + 0 = mark#(sel(X,Z)) active(from(X)) = 7X + 0 >= 7X + 0 = mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) = 6X + 5Y + 1 >= X = mark(X) active(sel(s(X),cons(Y,Z))) = X + 6Y + 5Z + 0 >= X + 5Z + 0 = mark(sel(X,Z)) mark(from(X)) = 7X + 0 >= 7X + 0 = 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(sel(X1,X2)) = X1 + 5X2 + 0 >= X1 + 5X2 + 0 = active(sel(mark(X1),mark(X2))) mark(0()) = 1 >= 1 = active(0()) from(mark(X)) = 7X + 0 >= 7X + 0 = from(X) from(active(X)) = 7X + 0 >= 7X + 0 = 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) sel(mark(X1),X2) = X1 + 5X2 + 0 >= X1 + 5X2 + 0 = sel(X1,X2) sel(X1,mark(X2)) = X1 + 5X2 + 0 >= X1 + 5X2 + 0 = sel(X1,X2) sel(active(X1),X2) = X1 + 5X2 + 0 >= X1 + 5X2 + 0 = sel(X1,X2) sel(X1,active(X2)) = X1 + 5X2 + 0 >= X1 + 5X2 + 0 = sel(X1,X2) problem: DPs: mark#(sel(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#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> mark#(X1) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [sel](x0, x1) = 5x0 + x1 + 7, [0] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1 + 0, [s](x0) = x0 + 1, [active](x0) = x0 + 0, [from](x0) = x0 + 1 orientation: mark#(sel(X1,X2)) = 5X1 + X2 + 7 >= X2 = mark#(X2) mark#(from(X)) = X + 1 >= X = mark#(X) mark#(from(X)) = X + 1 >= X + 1 = active#(from(mark(X))) active#(from(X)) = X + 1 >= X + 1 = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1) mark#(s(X)) = X + 1 >= X = mark#(X) mark#(sel(X1,X2)) = 5X1 + X2 + 7 >= X1 = mark#(X1) mark#(sel(X1,X2)) = 5X1 + X2 + 7 >= 5X1 + X2 + 7 = active#(sel(mark(X1),mark(X2))) active#(sel(s(X),cons(Y,Z))) = 5X + Y + Z + 7 >= 5X + Z + 7 = mark#(sel(X,Z)) active(from(X)) = X + 1 >= X + 1 = mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) = X + Y + 7 >= X = mark(X) active(sel(s(X),cons(Y,Z))) = 5X + Y + Z + 7 >= 5X + Z + 7 = mark(sel(X,Z)) mark(from(X)) = X + 1 >= X + 1 = active(from(mark(X))) mark(cons(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(cons(mark(X1),X2)) mark(s(X)) = X + 1 >= X + 1 = active(s(mark(X))) mark(sel(X1,X2)) = 5X1 + X2 + 7 >= 5X1 + X2 + 7 = active(sel(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) from(mark(X)) = X + 1 >= X + 1 = from(X) from(active(X)) = X + 1 >= X + 1 = 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 + 1 >= X + 1 = s(X) s(active(X)) = X + 1 >= X + 1 = s(X) sel(mark(X1),X2) = 5X1 + X2 + 7 >= 5X1 + X2 + 7 = sel(X1,X2) sel(X1,mark(X2)) = 5X1 + X2 + 7 >= 5X1 + X2 + 7 = sel(X1,X2) sel(active(X1),X2) = 5X1 + X2 + 7 >= 5X1 + X2 + 7 = sel(X1,X2) sel(X1,active(X2)) = 5X1 + X2 + 7 >= 5X1 + X2 + 7 = sel(X1,X2) problem: DPs: mark#(sel(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#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 0, [active#](x0) = x0 + 0, [sel](x0, x1) = 2x0 + 2x1 + 1, [0] = 1, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [s](x0) = x0, [active](x0) = x0, [from](x0) = x0 orientation: mark#(sel(X1,X2)) = 2X1 + 2X2 + 1 >= X2 + 0 = mark#(X2) mark#(from(X)) = X + 0 >= X + 0 = mark#(X) mark#(from(X)) = X + 0 >= X + 0 = active#(from(mark(X))) active#(from(X)) = X + 0 >= X + 0 = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(s(X)) = X + 0 >= X + 0 = mark#(X) mark#(sel(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = active#(sel(mark(X1),mark(X2))) active#(sel(s(X),cons(Y,Z))) = 2X + 2Y + 2Z + 1 >= 2X + 2Z + 1 = mark#(sel(X,Z)) active(from(X)) = X >= X = mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) = 2X + 2Y + 3 >= X = mark(X) active(sel(s(X),cons(Y,Z))) = 2X + 2Y + 2Z + 1 >= 2X + 2Z + 1 = mark(sel(X,Z)) 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(sel(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = active(sel(mark(X1),mark(X2))) mark(0()) = 1 >= 1 = 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) sel(mark(X1),X2) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = sel(X1,X2) sel(X1,mark(X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = sel(X1,X2) sel(active(X1),X2) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = sel(X1,X2) sel(X1,active(X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = sel(X1,X2) problem: DPs: 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#(s(X)) -> mark#(X) mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) SCC Processor: #sccs: 2 #rules: 7 #arcs: 49/49 DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [sel](x0, x1) = x0 + 6x1 + 2, [0] = 5, [mark](x0) = x0, [cons](x0, x1) = 1x0 + x1 + 0, [s](x0) = x0, [active](x0) = x0, [from](x0) = 4x0 + 0 orientation: mark#(cons(X1,X2)) = 1X1 + X2 + 0 >= X1 = mark#(X1) mark#(from(X)) = 4X + 0 >= X = mark#(X) mark#(from(X)) = 4X + 0 >= 4X + 0 = active#(from(mark(X))) active#(from(X)) = 4X + 0 >= 4X + 0 = mark#(cons(X,from(s(X)))) mark#(s(X)) = X >= X = mark#(X) active(from(X)) = 4X + 0 >= 4X + 0 = mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) = 7X + 6Y + 6 >= X = mark(X) active(sel(s(X),cons(Y,Z))) = X + 7Y + 6Z + 6 >= X + 6Z + 2 = mark(sel(X,Z)) mark(from(X)) = 4X + 0 >= 4X + 0 = active(from(mark(X))) mark(cons(X1,X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = active(cons(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(sel(X1,X2)) = X1 + 6X2 + 2 >= X1 + 6X2 + 2 = active(sel(mark(X1),mark(X2))) mark(0()) = 5 >= 5 = active(0()) from(mark(X)) = 4X + 0 >= 4X + 0 = from(X) from(active(X)) = 4X + 0 >= 4X + 0 = from(X) cons(mark(X1),X2) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = cons(X1,X2) cons(X1,mark(X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = cons(X1,X2) cons(active(X1),X2) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = cons(X1,X2) cons(X1,active(X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = cons(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) sel(mark(X1),X2) = X1 + 6X2 + 2 >= X1 + 6X2 + 2 = sel(X1,X2) sel(X1,mark(X2)) = X1 + 6X2 + 2 >= X1 + 6X2 + 2 = sel(X1,X2) sel(active(X1),X2) = X1 + 6X2 + 2 >= X1 + 6X2 + 2 = sel(X1,X2) sel(X1,active(X2)) = X1 + 6X2 + 2 >= X1 + 6X2 + 2 = sel(X1,X2) problem: DPs: mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) SCC Processor: #sccs: 1 #rules: 1 #arcs: 14/9 DPs: mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Qed DPs: mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2))) active#(sel(s(X),cons(Y,Z))) -> mark#(sel(X,Z)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Open 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(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Subterm Criterion Processor: simple projection: pi(cons#) = 1 problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(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(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(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(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Subterm Criterion Processor: simple projection: pi(from#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Qed DPs: sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(active(X1),X2) -> sel#(X1,X2) sel#(X1,active(X2)) -> sel#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Subterm Criterion Processor: simple projection: pi(sel#) = 1 problem: DPs: sel#(mark(X1),X2) -> sel#(X1,X2) sel#(active(X1),X2) -> sel#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Subterm Criterion Processor: simple projection: pi(sel#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,Y))) -> mark(X) active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(sel(X1,X2)) -> active(sel(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) sel(mark(X1),X2) -> sel(X1,X2) sel(X1,mark(X2)) -> sel(X1,X2) sel(active(X1),X2) -> sel(X1,X2) sel(X1,active(X2)) -> sel(X1,X2) Qed