YES Problem: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Proof: DP Processor: DPs: active#(first(0(),X)) -> mark#(nil()) active#(first(s(X),cons(Y,Z))) -> first#(X,Z) active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) 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)))) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(0()) -> active#(0()) mark#(nil()) -> active#(nil()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(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#(from(X)) -> mark#(X) mark#(from(X)) -> from#(mark(X)) mark#(from(X)) -> active#(from(mark(X))) first#(mark(X1),X2) -> first#(X1,X2) first#(X1,mark(X2)) -> first#(X1,X2) first#(active(X1),X2) -> first#(X1,X2) first#(X1,active(X2)) -> first#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(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) from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) TDG Processor: DPs: active#(first(0(),X)) -> mark#(nil()) active#(first(s(X),cons(Y,Z))) -> first#(X,Z) active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) 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)))) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(0()) -> active#(0()) mark#(nil()) -> active#(nil()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(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#(from(X)) -> mark#(X) mark#(from(X)) -> from#(mark(X)) mark#(from(X)) -> active#(from(mark(X))) first#(mark(X1),X2) -> first#(X1,X2) first#(X1,mark(X2)) -> first#(X1,X2) first#(active(X1),X2) -> first#(X1,X2) first#(X1,active(X2)) -> first#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(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) from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) graph: 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) 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) first#(mark(X1),X2) -> first#(X1,X2) -> first#(X1,active(X2)) -> first#(X1,X2) first#(mark(X1),X2) -> first#(X1,X2) -> first#(active(X1),X2) -> first#(X1,X2) first#(mark(X1),X2) -> first#(X1,X2) -> first#(X1,mark(X2)) -> first#(X1,X2) first#(mark(X1),X2) -> first#(X1,X2) -> first#(mark(X1),X2) -> first#(X1,X2) first#(active(X1),X2) -> first#(X1,X2) -> first#(X1,active(X2)) -> first#(X1,X2) first#(active(X1),X2) -> first#(X1,X2) -> first#(active(X1),X2) -> first#(X1,X2) first#(active(X1),X2) -> first#(X1,X2) -> first#(X1,mark(X2)) -> first#(X1,X2) first#(active(X1),X2) -> first#(X1,X2) -> first#(mark(X1),X2) -> first#(X1,X2) first#(X1,mark(X2)) -> first#(X1,X2) -> first#(X1,active(X2)) -> first#(X1,X2) first#(X1,mark(X2)) -> first#(X1,X2) -> first#(active(X1),X2) -> first#(X1,X2) first#(X1,mark(X2)) -> first#(X1,X2) -> first#(X1,mark(X2)) -> first#(X1,X2) first#(X1,mark(X2)) -> first#(X1,X2) -> first#(mark(X1),X2) -> first#(X1,X2) first#(X1,active(X2)) -> first#(X1,X2) -> first#(X1,active(X2)) -> first#(X1,X2) first#(X1,active(X2)) -> first#(X1,X2) -> first#(active(X1),X2) -> first#(X1,X2) first#(X1,active(X2)) -> first#(X1,X2) -> first#(X1,mark(X2)) -> first#(X1,X2) first#(X1,active(X2)) -> first#(X1,X2) -> first#(mark(X1),X2) -> first#(X1,X2) 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)) -> 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)) -> 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#(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#(nil()) -> active#(nil()) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X2) 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) mark#(from(X)) -> active#(from(mark(X))) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(from(X)) -> active#(from(mark(X))) -> active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) mark#(from(X)) -> active#(from(mark(X))) -> active#(first(s(X),cons(Y,Z))) -> first#(X,Z) mark#(from(X)) -> active#(from(mark(X))) -> active#(first(0(),X)) -> mark#(nil()) 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)) -> 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)) -> 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#(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#(nil()) -> active#(nil()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X2) 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#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(first(s(X),cons(Y,Z))) -> first#(X,Z) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(first(0(),X)) -> mark#(nil()) 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)) -> 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)) -> 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#(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#(nil()) -> active#(nil()) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X2) 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#(s(X)) -> active#(s(mark(X))) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(s(X)) -> active#(s(mark(X))) -> active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) mark#(s(X)) -> active#(s(mark(X))) -> active#(first(s(X),cons(Y,Z))) -> first#(X,Z) mark#(s(X)) -> active#(s(mark(X))) -> active#(first(0(),X)) -> mark#(nil()) mark#(nil()) -> active#(nil()) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(nil()) -> active#(nil()) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(nil()) -> active#(nil()) -> active#(from(X)) -> from#(s(X)) mark#(nil()) -> active#(nil()) -> active#(from(X)) -> s#(X) mark#(nil()) -> active#(nil()) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(nil()) -> active#(nil()) -> active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) mark#(nil()) -> active#(nil()) -> active#(first(s(X),cons(Y,Z))) -> first#(X,Z) mark#(nil()) -> active#(nil()) -> active#(first(0(),X)) -> mark#(nil()) mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) -> first#(X1,active(X2)) -> first#(X1,X2) mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) -> first#(active(X1),X2) -> first#(X1,X2) mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) -> first#(X1,mark(X2)) -> first#(X1,X2) mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) -> first#(mark(X1),X2) -> first#(X1,X2) mark#(first(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> active#(from(mark(X))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> from#(mark(X)) mark#(first(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(first(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(first(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> s#(mark(X)) mark#(first(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(first(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> from#(mark(X)) mark#(first(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(first(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(first(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(first(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(first(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(from(X)) -> from#(s(X)) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(from(X)) -> s#(X) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(first(s(X),cons(Y,Z))) -> first#(X,Z) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(first(0(),X)) -> mark#(nil()) 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#(0()) -> active#(0()) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(0()) -> active#(0()) -> active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) mark#(0()) -> active#(0()) -> active#(first(s(X),cons(Y,Z))) -> first#(X,Z) mark#(0()) -> active#(0()) -> active#(first(0(),X)) -> mark#(nil()) 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) 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)) -> 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)) -> 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#(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#(nil()) -> active#(nil()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(0()) -> active#(0()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(first(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(first(X1,X2)) -> mark#(X2) active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(first(s(X),cons(Y,Z))) -> cons#(Y,first(X,Z)) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(first(s(X),cons(Y,Z))) -> first#(X,Z) -> first#(X1,active(X2)) -> first#(X1,X2) active#(first(s(X),cons(Y,Z))) -> first#(X,Z) -> first#(active(X1),X2) -> first#(X1,X2) active#(first(s(X),cons(Y,Z))) -> first#(X,Z) -> first#(X1,mark(X2)) -> first#(X1,X2) active#(first(s(X),cons(Y,Z))) -> first#(X,Z) -> first#(mark(X1),X2) -> first#(X1,X2) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(from(X)) -> active#(from(mark(X))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(from(X)) -> from#(mark(X)) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(from(X)) -> mark#(X) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(s(X)) -> active#(s(mark(X))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(s(X)) -> s#(mark(X)) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(s(X)) -> mark#(X) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(nil()) -> active#(nil()) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(0()) -> active#(0()) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(first(X1,X2)) -> mark#(X1) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(first(X1,X2)) -> mark#(X2) active#(first(0(),X)) -> mark#(nil()) -> mark#(from(X)) -> active#(from(mark(X))) active#(first(0(),X)) -> mark#(nil()) -> mark#(from(X)) -> from#(mark(X)) active#(first(0(),X)) -> mark#(nil()) -> mark#(from(X)) -> mark#(X) active#(first(0(),X)) -> mark#(nil()) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(first(0(),X)) -> mark#(nil()) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(first(0(),X)) -> mark#(nil()) -> mark#(cons(X1,X2)) -> mark#(X1) active#(first(0(),X)) -> mark#(nil()) -> mark#(s(X)) -> active#(s(mark(X))) active#(first(0(),X)) -> mark#(nil()) -> mark#(s(X)) -> s#(mark(X)) active#(first(0(),X)) -> mark#(nil()) -> mark#(s(X)) -> mark#(X) active#(first(0(),X)) -> mark#(nil()) -> mark#(nil()) -> active#(nil()) active#(first(0(),X)) -> mark#(nil()) -> mark#(0()) -> active#(0()) active#(first(0(),X)) -> mark#(nil()) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(0(),X)) -> mark#(nil()) -> mark#(first(X1,X2)) -> first#(mark(X1),mark(X2)) active#(first(0(),X)) -> mark#(nil()) -> mark#(first(X1,X2)) -> mark#(X1) active#(first(0(),X)) -> mark#(nil()) -> mark#(first(X1,X2)) -> mark#(X2) SCC Processor: #sccs: 5 #rules: 26 #arcs: 236/1225 DPs: mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(0(),X)) -> mark#(nil()) mark#(0()) -> active#(0()) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(nil()) -> active#(nil()) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> active#(from(mark(X))) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) EDG Processor: DPs: mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(0(),X)) -> mark#(nil()) mark#(0()) -> active#(0()) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(nil()) -> active#(nil()) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> active#(from(mark(X))) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) graph: mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) 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#(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#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(from(X)) -> active#(from(mark(X))) -> active#(first(0(),X)) -> mark#(nil()) mark#(from(X)) -> active#(from(mark(X))) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) 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#(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#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(first(0(),X)) -> mark#(nil()) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) 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#(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#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> active#(s(mark(X))) -> active#(first(0(),X)) -> mark#(nil()) mark#(s(X)) -> active#(s(mark(X))) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(first(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(first(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(first(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> active#(from(mark(X))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(first(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(first(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(first(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(first(0(),X)) -> mark#(nil()) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(first(X1,X2)) -> mark#(X2) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(first(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(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#(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#(from(X)) -> mark#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> active#(from(mark(X))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(first(X1,X2)) -> mark#(X2) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(first(X1,X2)) -> mark#(X1) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(s(X)) -> mark#(X) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(s(X)) -> active#(s(mark(X))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(from(X)) -> mark#(X) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(from(X)) -> active#(from(mark(X))) active#(first(0(),X)) -> mark#(nil()) -> mark#(nil()) -> active#(nil()) CDG Processor: DPs: mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(0(),X)) -> mark#(nil()) mark#(0()) -> active#(0()) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(nil()) -> active#(nil()) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> active#(from(mark(X))) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) graph: 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)) -> 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#(s(X)) -> active#(s(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X2) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) 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#(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#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(from(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#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> active#(from(mark(X))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(first(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(first(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X2) -> mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(first(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(first(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> mark#(X1) -> mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) -> active#(first(0(),X)) -> mark#(nil()) 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) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(first(0(),X)) -> mark#(nil()) -> mark#(nil()) -> active#(nil()) SCC Processor: #sccs: 1 #rules: 9 #arcs: 63/196 DPs: mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> mark#(X1) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) 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(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Arctic Interpretation Processor: dimension: 1 usable rules: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [from](x0) = x0 + 7, [cons](x0, x1) = x0 + x1 + 7, [s](x0) = x0 + 0, [mark](x0) = x0, [nil] = 0, [active](x0) = x0 + 0, [first](x0, x1) = 7x0 + x1 + 0, [0] = 0 orientation: mark#(from(X)) = X + 7 >= X = mark#(X) mark#(first(X1,X2)) = 7X1 + X2 + 0 >= X2 = mark#(X2) mark#(first(X1,X2)) = 7X1 + X2 + 0 >= X1 = mark#(X1) mark#(first(X1,X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) = 7X + Y + Z + 7 >= 7X + Y + Z + 7 = mark#(cons(Y,first(X,Z))) mark#(cons(X1,X2)) = X1 + X2 + 7 >= X1 = mark#(X1) mark#(s(X)) = X + 0 >= X = mark#(X) mark#(from(X)) = X + 7 >= X + 7 = active#(from(mark(X))) active#(from(X)) = X + 7 >= X + 7 = mark#(cons(X,from(s(X)))) active(first(0(),X)) = X + 7 >= 0 = mark(nil()) active(first(s(X),cons(Y,Z))) = 7X + Y + Z + 7 >= 7X + Y + Z + 7 = mark(cons(Y,first(X,Z))) active(from(X)) = X + 7 >= X + 7 = mark(cons(X,from(s(X)))) mark(first(X1,X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = active(first(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) mark(nil()) = 0 >= 0 = active(nil()) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(cons(X1,X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = active(cons(mark(X1),X2)) mark(from(X)) = X + 7 >= X + 7 = active(from(mark(X))) first(mark(X1),X2) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = first(X1,X2) first(X1,mark(X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = first(X1,X2) first(active(X1),X2) = 7X1 + X2 + 7 >= 7X1 + X2 + 0 = first(X1,X2) first(X1,active(X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = first(X1,X2) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) cons(mark(X1),X2) = X1 + X2 + 7 >= X1 + X2 + 7 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 + 7 >= X1 + X2 + 7 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = cons(X1,X2) from(mark(X)) = X + 7 >= X + 7 = from(X) from(active(X)) = X + 7 >= X + 7 = from(X) problem: DPs: mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) 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(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Restore Modifier: DPs: mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) 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(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Arctic Interpretation Processor: dimension: 1 usable rules: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) interpretation: [mark#](x0) = x0, [active#](x0) = x0, [from](x0) = x0 + 2, [cons](x0, x1) = x0 + 2, [s](x0) = 2x0 + 0, [mark](x0) = x0, [nil] = 2, [active](x0) = x0, [first](x0, x1) = 1x0 + x1, [0] = 1 orientation: mark#(from(X)) = X + 2 >= X = mark#(X) mark#(first(X1,X2)) = 1X1 + X2 >= X2 = mark#(X2) mark#(first(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) = 3X + Y + 2 >= Y + 2 = mark#(cons(Y,first(X,Z))) mark#(cons(X1,X2)) = X1 + 2 >= X1 = mark#(X1) mark#(s(X)) = 2X + 0 >= X = mark#(X) 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(first(0(),X)) = X + 2 >= 2 = mark(nil()) active(first(s(X),cons(Y,Z))) = 3X + Y + 2 >= Y + 2 = mark(cons(Y,first(X,Z))) active(from(X)) = X + 2 >= X + 2 = mark(cons(X,from(s(X)))) mark(first(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = active(first(mark(X1),mark(X2))) mark(0()) = 1 >= 1 = active(0()) mark(nil()) = 2 >= 2 = active(nil()) mark(s(X)) = 2X + 0 >= 2X + 0 = active(s(mark(X))) mark(cons(X1,X2)) = X1 + 2 >= X1 + 2 = active(cons(mark(X1),X2)) mark(from(X)) = X + 2 >= X + 2 = active(from(mark(X))) first(mark(X1),X2) = 1X1 + X2 >= 1X1 + X2 = first(X1,X2) first(X1,mark(X2)) = 1X1 + X2 >= 1X1 + X2 = first(X1,X2) first(active(X1),X2) = 1X1 + X2 >= 1X1 + X2 = first(X1,X2) first(X1,active(X2)) = 1X1 + X2 >= 1X1 + X2 = first(X1,X2) s(mark(X)) = 2X + 0 >= 2X + 0 = s(X) s(active(X)) = 2X + 0 >= 2X + 0 = s(X) cons(mark(X1),X2) = X1 + 2 >= X1 + 2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + 2 >= X1 + 2 = cons(X1,X2) cons(active(X1),X2) = X1 + 2 >= X1 + 2 = cons(X1,X2) cons(X1,active(X2)) = X1 + 2 >= X1 + 2 = cons(X1,X2) from(mark(X)) = X + 2 >= X + 2 = from(X) from(active(X)) = X + 2 >= X + 2 = from(X) problem: DPs: mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Restore Modifier: DPs: mark#(from(X)) -> mark#(X) mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Arctic Interpretation Processor: dimension: 1 usable rules: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) interpretation: [mark#](x0) = x0, [active#](x0) = x0, [from](x0) = 4x0 + 4, [cons](x0, x1) = 1x0 + x1, [s](x0) = x0 + 0, [mark](x0) = x0, [nil] = 4, [active](x0) = x0, [first](x0, x1) = 1x0 + x1, [0] = 6 orientation: mark#(from(X)) = 4X + 4 >= X = mark#(X) mark#(first(X1,X2)) = 1X1 + X2 >= X2 = mark#(X2) mark#(first(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) = 1X + 1Y + Z + 1 >= 1X + 1Y + Z = mark#(cons(Y,first(X,Z))) mark#(cons(X1,X2)) = 1X1 + X2 >= X1 = mark#(X1) mark#(from(X)) = 4X + 4 >= 4X + 4 = active#(from(mark(X))) active#(from(X)) = 4X + 4 >= 4X + 4 = mark#(cons(X,from(s(X)))) active(first(0(),X)) = X + 7 >= 4 = mark(nil()) active(first(s(X),cons(Y,Z))) = 1X + 1Y + Z + 1 >= 1X + 1Y + Z = mark(cons(Y,first(X,Z))) active(from(X)) = 4X + 4 >= 4X + 4 = mark(cons(X,from(s(X)))) mark(first(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = active(first(mark(X1),mark(X2))) mark(0()) = 6 >= 6 = active(0()) mark(nil()) = 4 >= 4 = active(nil()) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(cons(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = active(cons(mark(X1),X2)) mark(from(X)) = 4X + 4 >= 4X + 4 = active(from(mark(X))) first(mark(X1),X2) = 1X1 + X2 >= 1X1 + X2 = first(X1,X2) first(X1,mark(X2)) = 1X1 + X2 >= 1X1 + X2 = first(X1,X2) first(active(X1),X2) = 1X1 + X2 >= 1X1 + X2 = first(X1,X2) first(X1,active(X2)) = 1X1 + X2 >= 1X1 + X2 = first(X1,X2) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(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) from(mark(X)) = 4X + 4 >= 4X + 4 = from(X) from(active(X)) = 4X + 4 >= 4X + 4 = from(X) problem: DPs: mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Restore Modifier: DPs: mark#(first(X1,X2)) -> mark#(X2) mark#(first(X1,X2)) -> active#(first(mark(X1),mark(X2))) active#(first(s(X),cons(Y,Z))) -> mark#(cons(Y,first(X,Z))) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) SCC Processor: #sccs: 1 #rules: 1 #arcs: 39/25 DPs: mark#(first(X1,X2)) -> mark#(X2) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Qed DPs: first#(mark(X1),X2) -> first#(X1,X2) first#(X1,mark(X2)) -> first#(X1,X2) first#(active(X1),X2) -> first#(X1,X2) first#(X1,active(X2)) -> first#(X1,X2) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Subterm Criterion Processor: simple projection: pi(first#) = 1 problem: DPs: first#(mark(X1),X2) -> first#(X1,X2) first#(active(X1),X2) -> first#(X1,X2) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Subterm Criterion Processor: simple projection: pi(first#) = 0 problem: DPs: TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Qed DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Subterm Criterion Processor: simple projection: pi(cons#) = 1 problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Qed DPs: from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Subterm Criterion Processor: simple projection: pi(from#) = 0 problem: DPs: TRS: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(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) from(mark(X)) -> from(X) from(active(X)) -> from(X) Qed