YES Problem: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) 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#(length(nil())) -> mark#(0()) active#(length(cons(X,Y))) -> length1#(Y) active#(length(cons(X,Y))) -> s#(length1(Y)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) active#(length1(X)) -> length#(X) active#(length1(X)) -> mark#(length(X)) 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#(length(X)) -> active#(length(X)) mark#(nil()) -> active#(nil()) mark#(0()) -> active#(0()) mark#(length1(X)) -> active#(length1(X)) 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) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) length1#(mark(X)) -> length1#(X) length1#(active(X)) -> length1#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) 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#(length(nil())) -> mark#(0()) active#(length(cons(X,Y))) -> length1#(Y) active#(length(cons(X,Y))) -> s#(length1(Y)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) active#(length1(X)) -> length#(X) active#(length1(X)) -> mark#(length(X)) 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#(length(X)) -> active#(length(X)) mark#(nil()) -> active#(nil()) mark#(0()) -> active#(0()) mark#(length1(X)) -> active#(length1(X)) 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) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) length1#(mark(X)) -> length1#(X) length1#(active(X)) -> length1#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) graph: length#(mark(X)) -> length#(X) -> length#(active(X)) -> length#(X) length#(mark(X)) -> length#(X) -> length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) -> length#(active(X)) -> length#(X) length#(active(X)) -> length#(X) -> length#(mark(X)) -> length#(X) length1#(mark(X)) -> length1#(X) -> length1#(active(X)) -> length1#(X) length1#(mark(X)) -> length1#(X) -> length1#(mark(X)) -> length1#(X) length1#(active(X)) -> length1#(X) -> length1#(active(X)) -> length1#(X) length1#(active(X)) -> length1#(X) -> length1#(mark(X)) -> length1#(X) mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> mark#(length(X)) mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> length#(X) mark#(length1(X)) -> active#(length1(X)) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(length1(X)) -> active#(length1(X)) -> active#(length(cons(X,Y))) -> s#(length1(Y)) mark#(length1(X)) -> active#(length1(X)) -> active#(length(cons(X,Y))) -> length1#(Y) mark#(length1(X)) -> active#(length1(X)) -> active#(length(nil())) -> mark#(0()) mark#(length1(X)) -> active#(length1(X)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(length1(X)) -> active#(length1(X)) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(length1(X)) -> active#(length1(X)) -> active#(from(X)) -> from#(s(X)) mark#(length1(X)) -> active#(length1(X)) -> active#(from(X)) -> s#(X) mark#(0()) -> active#(0()) -> active#(length1(X)) -> mark#(length(X)) mark#(0()) -> active#(0()) -> active#(length1(X)) -> length#(X) mark#(0()) -> active#(0()) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(0()) -> active#(0()) -> active#(length(cons(X,Y))) -> s#(length1(Y)) mark#(0()) -> active#(0()) -> active#(length(cons(X,Y))) -> length1#(Y) mark#(0()) -> active#(0()) -> active#(length(nil())) -> mark#(0()) 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#(length(X)) -> active#(length(X)) -> active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) -> active#(length1(X)) -> length#(X) mark#(length(X)) -> active#(length(X)) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(length(X)) -> active#(length(X)) -> active#(length(cons(X,Y))) -> s#(length1(Y)) mark#(length(X)) -> active#(length(X)) -> active#(length(cons(X,Y))) -> length1#(Y) mark#(length(X)) -> active#(length(X)) -> active#(length(nil())) -> mark#(0()) mark#(length(X)) -> active#(length(X)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(length(X)) -> active#(length(X)) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(length(X)) -> active#(length(X)) -> active#(from(X)) -> from#(s(X)) mark#(length(X)) -> active#(length(X)) -> active#(from(X)) -> s#(X) mark#(nil()) -> active#(nil()) -> active#(length1(X)) -> mark#(length(X)) mark#(nil()) -> active#(nil()) -> active#(length1(X)) -> length#(X) mark#(nil()) -> active#(nil()) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(nil()) -> active#(nil()) -> active#(length(cons(X,Y))) -> s#(length1(Y)) mark#(nil()) -> active#(nil()) -> active#(length(cons(X,Y))) -> length1#(Y) mark#(nil()) -> active#(nil()) -> active#(length(nil())) -> mark#(0()) 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#(cons(X1,X2)) -> mark#(X1) -> mark#(length1(X)) -> active#(length1(X)) 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#(length(X)) -> active#(length(X)) 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#(length1(X)) -> mark#(length(X)) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length1(X)) -> length#(X) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length(cons(X,Y))) -> s#(length1(Y)) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length(cons(X,Y))) -> length1#(Y) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length(nil())) -> mark#(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#(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#(length1(X)) -> active#(length1(X)) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(X)) 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#(length1(X)) -> mark#(length(X)) mark#(s(X)) -> active#(s(mark(X))) -> active#(length1(X)) -> length#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> active#(s(mark(X))) -> active#(length(cons(X,Y))) -> s#(length1(Y)) mark#(s(X)) -> active#(s(mark(X))) -> active#(length(cons(X,Y))) -> length1#(Y) mark#(s(X)) -> active#(s(mark(X))) -> active#(length(nil())) -> mark#(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#(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#(length1(X)) -> active#(length1(X)) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(from(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(X)) 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#(length1(X)) -> mark#(length(X)) mark#(from(X)) -> active#(from(mark(X))) -> active#(length1(X)) -> length#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(from(X)) -> active#(from(mark(X))) -> active#(length(cons(X,Y))) -> s#(length1(Y)) mark#(from(X)) -> active#(from(mark(X))) -> active#(length(cons(X,Y))) -> length1#(Y) mark#(from(X)) -> active#(from(mark(X))) -> active#(length(nil())) -> mark#(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#(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#(length1(X)) -> length#(X) -> length#(active(X)) -> length#(X) active#(length1(X)) -> length#(X) -> length#(mark(X)) -> length#(X) active#(length1(X)) -> mark#(length(X)) -> mark#(length1(X)) -> active#(length1(X)) active#(length1(X)) -> mark#(length(X)) -> mark#(0()) -> active#(0()) active#(length1(X)) -> mark#(length(X)) -> mark#(nil()) -> active#(nil()) active#(length1(X)) -> mark#(length(X)) -> mark#(length(X)) -> active#(length(X)) active#(length1(X)) -> mark#(length(X)) -> mark#(s(X)) -> active#(s(mark(X))) active#(length1(X)) -> mark#(length(X)) -> mark#(s(X)) -> s#(mark(X)) active#(length1(X)) -> mark#(length(X)) -> mark#(s(X)) -> mark#(X) active#(length1(X)) -> mark#(length(X)) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length1(X)) -> mark#(length(X)) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(length1(X)) -> mark#(length(X)) -> mark#(cons(X1,X2)) -> mark#(X1) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> active#(from(mark(X))) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> from#(mark(X)) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> mark#(X) active#(length(nil())) -> mark#(0()) -> mark#(length1(X)) -> active#(length1(X)) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(length(nil())) -> mark#(0()) -> mark#(nil()) -> active#(nil()) active#(length(nil())) -> mark#(0()) -> mark#(length(X)) -> active#(length(X)) active#(length(nil())) -> mark#(0()) -> mark#(s(X)) -> active#(s(mark(X))) active#(length(nil())) -> mark#(0()) -> mark#(s(X)) -> s#(mark(X)) active#(length(nil())) -> mark#(0()) -> mark#(s(X)) -> mark#(X) active#(length(nil())) -> mark#(0()) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length(nil())) -> mark#(0()) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(length(nil())) -> mark#(0()) -> mark#(cons(X1,X2)) -> mark#(X1) active#(length(nil())) -> mark#(0()) -> mark#(from(X)) -> active#(from(mark(X))) active#(length(nil())) -> mark#(0()) -> mark#(from(X)) -> from#(mark(X)) active#(length(nil())) -> mark#(0()) -> mark#(from(X)) -> mark#(X) active#(length(cons(X,Y))) -> length1#(Y) -> length1#(active(X)) -> length1#(X) active#(length(cons(X,Y))) -> length1#(Y) -> length1#(mark(X)) -> length1#(X) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(length1(X)) -> active#(length1(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(0()) -> active#(0()) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(nil()) -> active#(nil()) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(length(X)) -> active#(length(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(s(X)) -> active#(s(mark(X))) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(s(X)) -> s#(mark(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(s(X)) -> mark#(X) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(from(X)) -> active#(from(mark(X))) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(from(X)) -> from#(mark(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(from(X)) -> mark#(X) active#(length(cons(X,Y))) -> s#(length1(Y)) -> s#(active(X)) -> s#(X) active#(length(cons(X,Y))) -> s#(length1(Y)) -> s#(mark(X)) -> s#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(length1(X)) -> active#(length1(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(0()) -> active#(0()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(nil()) -> active#(nil()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(length(X)) -> active#(length(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#(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: 6 #rules: 26 #arcs: 215/1225 DPs: mark#(length1(X)) -> active#(length1(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) mark#(nil()) -> active#(nil()) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) EDG Processor: DPs: mark#(length1(X)) -> active#(length1(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) mark#(nil()) -> active#(nil()) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) graph: mark#(length1(X)) -> active#(length1(X)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(length1(X)) -> active#(length1(X)) -> active#(length(nil())) -> mark#(0()) mark#(length1(X)) -> active#(length1(X)) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(length(X)) -> active#(length(X)) -> active#(length(nil())) -> mark#(0()) mark#(length(X)) -> active#(length(X)) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(length(X)) -> active#(length(X)) -> active#(length1(X)) -> mark#(length(X)) 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#(length(X)) -> active#(length(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#(length1(X)) -> active#(length1(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#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length1(X)) -> mark#(length(X)) 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#(length(X)) -> active#(length(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#(length1(X)) -> active#(length1(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#(length(nil())) -> mark#(0()) mark#(s(X)) -> active#(s(mark(X))) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> active#(s(mark(X))) -> active#(length1(X)) -> mark#(length(X)) 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#(length(X)) -> active#(length(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#(length1(X)) -> active#(length1(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#(length(nil())) -> mark#(0()) mark#(from(X)) -> active#(from(mark(X))) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(from(X)) -> active#(from(mark(X))) -> active#(length1(X)) -> mark#(length(X)) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> mark#(X) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> active#(from(mark(X))) active#(length1(X)) -> mark#(length(X)) -> mark#(cons(X1,X2)) -> mark#(X1) active#(length1(X)) -> mark#(length(X)) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length1(X)) -> mark#(length(X)) -> mark#(s(X)) -> mark#(X) active#(length1(X)) -> mark#(length(X)) -> mark#(s(X)) -> active#(s(mark(X))) active#(length1(X)) -> mark#(length(X)) -> mark#(length(X)) -> active#(length(X)) active#(length1(X)) -> mark#(length(X)) -> mark#(length1(X)) -> active#(length1(X)) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(from(X)) -> mark#(X) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(from(X)) -> active#(from(mark(X))) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(s(X)) -> mark#(X) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(s(X)) -> active#(s(mark(X))) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(length(X)) -> active#(length(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(length1(X)) -> active#(length1(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#(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#(length(X)) -> active#(length(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(length1(X)) -> active#(length1(X)) CDG Processor: DPs: mark#(length1(X)) -> active#(length1(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) mark#(nil()) -> active#(nil()) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) graph: mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) -> active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(length(X)) -> active#(length(X)) -> active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length1(X)) -> active#(length1(X)) 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#(length(X)) -> active#(length(X)) 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#(length1(X)) -> active#(length1(X)) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(X)) 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#(length1(X)) -> active#(length1(X)) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(from(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(X)) 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#(length1(X)) -> mark#(length(X)) -> mark#(length(X)) -> active#(length(X)) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> mark#(s(X)) -> active#(s(mark(X))) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) -> 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)) -> mark#(X1) SCC Processor: #sccs: 1 #rules: 9 #arcs: 40/196 DPs: mark#(length1(X)) -> active#(length1(X)) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> mark#(X) 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) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [length1](x0) = x0 + 2, [0] = 2, [length](x0) = x0 + 2, [nil] = 1, [mark](x0) = x0 + 0, [cons](x0, x1) = x0 + x1, [s](x0) = x0 + 0, [active](x0) = x0 + 0, [from](x0) = 7x0 + 7 orientation: mark#(length1(X)) = X + 2 >= X + 2 = active#(length1(X)) active#(length1(X)) = X + 2 >= X + 2 = mark#(length(X)) mark#(length(X)) = X + 2 >= X + 2 = active#(length(X)) active#(length(cons(X,Y))) = X + Y + 2 >= Y + 2 = mark#(s(length1(Y))) mark#(s(X)) = X + 0 >= X = mark#(X) mark#(from(X)) = 7X + 7 >= X = mark#(X) mark#(from(X)) = 7X + 7 >= 7X + 7 = active#(from(mark(X))) active#(from(X)) = 7X + 7 >= 7X + 7 = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1) active(from(X)) = 7X + 7 >= 7X + 7 = mark(cons(X,from(s(X)))) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(X,Y))) = X + Y + 2 >= Y + 2 = mark(s(length1(Y))) active(length1(X)) = X + 2 >= X + 2 = mark(length(X)) mark(from(X)) = 7X + 7 >= 7X + 7 = active(from(mark(X))) mark(cons(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(cons(mark(X1),X2)) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(length(X)) = X + 2 >= X + 2 = active(length(X)) mark(nil()) = 1 >= 1 = active(nil()) mark(0()) = 2 >= 2 = active(0()) mark(length1(X)) = X + 2 >= X + 2 = active(length1(X)) from(mark(X)) = 7X + 7 >= 7X + 7 = from(X) from(active(X)) = 7X + 7 >= 7X + 7 = from(X) cons(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 = cons(X1,X2) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) length(mark(X)) = X + 2 >= X + 2 = length(X) length(active(X)) = X + 2 >= X + 2 = length(X) length1(mark(X)) = X + 2 >= X + 2 = length1(X) length1(active(X)) = X + 2 >= X + 2 = length1(X) problem: DPs: mark#(length1(X)) -> active#(length1(X)) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(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) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [length1](x0) = 3, [0] = 2, [length](x0) = 3, [nil] = 2, [mark](x0) = x0 + 0, [cons](x0, x1) = x0, [s](x0) = x0 + 0, [active](x0) = x0 + 0, [from](x0) = 1x0 + 4 orientation: mark#(length1(X)) = 3 >= 3 = active#(length1(X)) active#(length1(X)) = 3 >= 3 = mark#(length(X)) mark#(length(X)) = 3 >= 3 = active#(length(X)) active#(length(cons(X,Y))) = 3 >= 3 = mark#(s(length1(Y))) mark#(s(X)) = X + 0 >= X = mark#(X) mark#(from(X)) = 1X + 4 >= 1X + 4 = active#(from(mark(X))) active#(from(X)) = 1X + 4 >= X = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = X1 >= X1 = mark#(X1) active(from(X)) = 1X + 4 >= X + 0 = mark(cons(X,from(s(X)))) active(length(nil())) = 3 >= 2 = mark(0()) active(length(cons(X,Y))) = 3 >= 3 = mark(s(length1(Y))) active(length1(X)) = 3 >= 3 = mark(length(X)) mark(from(X)) = 1X + 4 >= 1X + 4 = active(from(mark(X))) mark(cons(X1,X2)) = X1 + 0 >= X1 + 0 = active(cons(mark(X1),X2)) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(length(X)) = 3 >= 3 = active(length(X)) mark(nil()) = 2 >= 2 = active(nil()) mark(0()) = 2 >= 2 = active(0()) mark(length1(X)) = 3 >= 3 = active(length1(X)) from(mark(X)) = 1X + 4 >= 1X + 4 = from(X) from(active(X)) = 1X + 4 >= 1X + 4 = from(X) cons(mark(X1),X2) = X1 + 0 >= X1 = cons(X1,X2) cons(X1,mark(X2)) = X1 >= X1 = cons(X1,X2) cons(active(X1),X2) = X1 + 0 >= X1 = cons(X1,X2) cons(X1,active(X2)) = X1 >= X1 = cons(X1,X2) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) length(mark(X)) = 3 >= 3 = length(X) length(active(X)) = 3 >= 3 = length(X) length1(mark(X)) = 3 >= 3 = length1(X) length1(active(X)) = 3 >= 3 = length1(X) problem: DPs: mark#(length1(X)) -> active#(length1(X)) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) SCC Processor: #sccs: 1 #rules: 6 #arcs: 24/49 DPs: mark#(length1(X)) -> active#(length1(X)) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [length1](x0) = x0 + 0, [0] = 5, [length](x0) = x0 + 0, [nil] = 5, [mark](x0) = x0, [cons](x0, x1) = 1x0 + x1, [s](x0) = x0, [active](x0) = x0, [from](x0) = 1x0 + 3 orientation: mark#(length1(X)) = X + 0 >= X + 0 = active#(length1(X)) active#(length1(X)) = X + 0 >= X + 0 = mark#(length(X)) mark#(length(X)) = X + 0 >= X + 0 = active#(length(X)) active#(length(cons(X,Y))) = 1X + Y + 0 >= Y + 0 = mark#(s(length1(Y))) mark#(s(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = 1X1 + X2 >= X1 = mark#(X1) active(from(X)) = 1X + 3 >= 1X + 3 = mark(cons(X,from(s(X)))) active(length(nil())) = 5 >= 5 = mark(0()) active(length(cons(X,Y))) = 1X + Y + 0 >= Y + 0 = mark(s(length1(Y))) active(length1(X)) = X + 0 >= X + 0 = mark(length(X)) mark(from(X)) = 1X + 3 >= 1X + 3 = 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(length(X)) = X + 0 >= X + 0 = active(length(X)) mark(nil()) = 5 >= 5 = active(nil()) mark(0()) = 5 >= 5 = active(0()) mark(length1(X)) = X + 0 >= X + 0 = active(length1(X)) from(mark(X)) = 1X + 3 >= 1X + 3 = from(X) from(active(X)) = 1X + 3 >= 1X + 3 = 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) length(mark(X)) = X + 0 >= X + 0 = length(X) length(active(X)) = X + 0 >= X + 0 = length(X) length1(mark(X)) = X + 0 >= X + 0 = length1(X) length1(active(X)) = X + 0 >= X + 0 = length1(X) problem: DPs: mark#(length1(X)) -> active#(length1(X)) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) active#(length(cons(X,Y))) -> mark#(s(length1(Y))) mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 4x0 + 0, [active#](x0) = 4x0 + 0, [length1](x0) = x0 + 0, [0] = 0, [length](x0) = x0, [nil] = 4, [mark](x0) = x0 + 2, [cons](x0, x1) = 1x1 + 1, [s](x0) = x0 + 0, [active](x0) = x0 + 2, [from](x0) = 0 orientation: mark#(length1(X)) = 4X + 4 >= 4X + 4 = active#(length1(X)) active#(length1(X)) = 4X + 4 >= 4X + 0 = mark#(length(X)) mark#(length(X)) = 4X + 0 >= 4X + 0 = active#(length(X)) active#(length(cons(X,Y))) = 5Y + 5 >= 4Y + 4 = mark#(s(length1(Y))) mark#(s(X)) = 4X + 4 >= 4X + 0 = mark#(X) active(from(X)) = 2 >= 2 = mark(cons(X,from(s(X)))) active(length(nil())) = 4 >= 2 = mark(0()) active(length(cons(X,Y))) = 1Y + 2 >= Y + 2 = mark(s(length1(Y))) active(length1(X)) = X + 2 >= X + 2 = mark(length(X)) mark(from(X)) = 2 >= 2 = active(from(mark(X))) mark(cons(X1,X2)) = 1X2 + 2 >= 1X2 + 2 = active(cons(mark(X1),X2)) mark(s(X)) = X + 2 >= X + 2 = active(s(mark(X))) mark(length(X)) = X + 2 >= X + 2 = active(length(X)) mark(nil()) = 4 >= 4 = active(nil()) mark(0()) = 2 >= 2 = active(0()) mark(length1(X)) = X + 2 >= X + 2 = active(length1(X)) from(mark(X)) = 0 >= 0 = from(X) from(active(X)) = 0 >= 0 = from(X) cons(mark(X1),X2) = 1X2 + 1 >= 1X2 + 1 = cons(X1,X2) cons(X1,mark(X2)) = 1X2 + 3 >= 1X2 + 1 = cons(X1,X2) cons(active(X1),X2) = 1X2 + 1 >= 1X2 + 1 = cons(X1,X2) cons(X1,active(X2)) = 1X2 + 3 >= 1X2 + 1 = cons(X1,X2) s(mark(X)) = X + 2 >= X + 0 = s(X) s(active(X)) = X + 2 >= X + 0 = s(X) length(mark(X)) = X + 2 >= X = length(X) length(active(X)) = X + 2 >= X = length(X) length1(mark(X)) = X + 2 >= X + 0 = length1(X) length1(active(X)) = X + 2 >= X + 0 = length1(X) problem: DPs: mark#(length1(X)) -> active#(length1(X)) active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) SCC Processor: #sccs: 1 #rules: 1 #arcs: 12/16 DPs: mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(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(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(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(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Qed DPs: from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(from#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Qed DPs: length1#(mark(X)) -> length1#(X) length1#(active(X)) -> length1#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(length1#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Qed DPs: length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(length#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) 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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Qed