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) EDG 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#(mark(X)) -> length#(X) length#(mark(X)) -> length#(X) -> length#(active(X)) -> length#(X) length#(active(X)) -> length#(X) -> length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) -> length#(active(X)) -> length#(X) length1#(mark(X)) -> length1#(X) -> length1#(mark(X)) -> length1#(X) length1#(mark(X)) -> length1#(X) -> length1#(active(X)) -> length1#(X) length1#(active(X)) -> length1#(X) -> length1#(mark(X)) -> length1#(X) length1#(active(X)) -> length1#(X) -> length1#(active(X)) -> length1#(X) mark#(length1(X)) -> active#(length1(X)) -> active#(from(X)) -> s#(X) mark#(length1(X)) -> active#(length1(X)) -> active#(from(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)) -> 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))) -> 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))) -> mark#(s(length1(Y))) mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> length#(X) mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) -> active#(from(X)) -> s#(X) mark#(length(X)) -> active#(length(X)) -> active#(from(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)) -> 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))) -> 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))) -> mark#(s(length1(Y))) mark#(length(X)) -> active#(length(X)) -> active#(length1(X)) -> length#(X) 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)) -> from#(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)) -> cons#(mark(X1),X2) 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)) -> s#(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)) -> cons#(mark(X1),X2) -> cons#(mark(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#(active(X1),X2) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> 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)) -> 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)) -> active#(cons(mark(X1),X2)) -> active#(length(nil())) -> mark#(0()) 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(cons(X,Y))) -> 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)) -> active#(cons(mark(X1),X2)) -> active#(length1(X)) -> length#(X) 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)) -> from#(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)) -> cons#(mark(X1),X2) 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)) -> s#(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)) -> s#(mark(X)) -> s#(mark(X)) -> s#(X) mark#(s(X)) -> s#(mark(X)) -> s#(active(X)) -> s#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> 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)) -> cons#(X,from(s(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))) -> 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))) -> mark#(s(length1(Y))) mark#(s(X)) -> active#(s(mark(X))) -> active#(length1(X)) -> length#(X) 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)) -> from#(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)) -> cons#(mark(X1),X2) 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)) -> s#(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)) -> from#(mark(X)) -> from#(mark(X)) -> from#(X) mark#(from(X)) -> from#(mark(X)) -> from#(active(X)) -> from#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> 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)) -> cons#(X,from(s(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))) -> 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))) -> mark#(s(length1(Y))) mark#(from(X)) -> active#(from(mark(X))) -> active#(length1(X)) -> length#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(length1(X)) -> mark#(length(X)) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X) from#(mark(X)) -> from#(X) -> from#(active(X)) -> from#(X) from#(active(X)) -> from#(X) -> from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) -> from#(active(X)) -> from#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(active(X)) -> s#(X) active#(length1(X)) -> length#(X) -> length#(mark(X)) -> length#(X) active#(length1(X)) -> length#(X) -> length#(active(X)) -> length#(X) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> mark#(X) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> from#(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)) -> cons#(mark(X1),X2) 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)) -> s#(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))) -> length1#(Y) -> length1#(mark(X)) -> length1#(X) active#(length(cons(X,Y))) -> length1#(Y) -> length1#(active(X)) -> length1#(X) 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)) -> from#(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)) -> 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))) -> mark#(s(length1(Y))) -> mark#(s(X)) -> 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)) -> 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#(length(cons(X,Y))) -> s#(length1(Y)) -> s#(mark(X)) -> s#(X) active#(length(cons(X,Y))) -> s#(length1(Y)) -> s#(active(X)) -> s#(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)) -> from#(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)) -> 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)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> 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)) -> 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)) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(mark(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#(active(X1),X2) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(from(X)) -> from#(s(X)) -> from#(mark(X)) -> from#(X) active#(from(X)) -> from#(s(X)) -> from#(active(X)) -> from#(X) active#(from(X)) -> s#(X) -> s#(mark(X)) -> s#(X) active#(from(X)) -> s#(X) -> s#(active(X)) -> s#(X) CDG 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#(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#(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#(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#(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#(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#(length(X)) -> active#(length(X)) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) 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#(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#(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)) -> cons#(X,from(s(X))) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(mark(X1),X2) -> cons#(X1,X2) 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: 21 #arcs: 105/1225 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) Matrix Interpretation Processor: dim=2 interpretation: [mark#](x0) = [2 2]x0, [active#](x0) = [0 2]x0 + [1], [0 0] [1] [length1](x0) = [3 0]x0 + [1], [1] [0] = [3], [0 0] [1] [length](x0) = [3 0]x0 + [0], [1] [nil] = [0], [1 1] [mark](x0) = [0 0]x0, [1 1] [1 0] [1] [cons](x0, x1) = [0 0]x0 + [0 0]x1 + [0], [0 0] [0] [s](x0) = [1 1]x0 + [1], [1 1] [active](x0) = [0 0]x0, [0 0] [1] [from](x0) = [1 1]x0 + [2] orientation: mark#(length1(X)) = [6 0]X + [4] >= [6 0]X + [3] = active#(length1(X)) active#(length1(X)) = [6 0]X + [3] >= [6 0]X + [2] = mark#(length(X)) mark#(length(X)) = [6 0]X + [2] >= [6 0]X + [1] = active#(length(X)) active#(length(cons(X,Y))) = [6 6]X + [6 0]Y + [7] >= [6 0]Y + [6] = mark#(s(length1(Y))) mark#(s(X)) = [2 2]X + [2] >= [2 2]X = mark#(X) mark#(from(X)) = [2 2]X + [6] >= [2 2]X = mark#(X) mark#(from(X)) = [2 2]X + [6] >= [2 2]X + [5] = active#(from(mark(X))) active#(from(X)) = [2 2]X + [5] >= [2 2]X + [4] = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = [2 2]X1 + [2 0]X2 + [2] >= [2 2]X1 = mark#(X1) [1 1] [3] [1 1] [2] active(from(X)) = [0 0]X + [0] >= [0 0]X + [0] = mark(cons(X,from(s(X)))) [4] [4] active(length(nil())) = [0] >= [0] = mark(0()) [3 3] [3 0] [4] [3 0] [3] active(length(cons(X,Y))) = [0 0]X + [0 0]Y + [0] >= [0 0]Y + [0] = mark(s(length1(Y))) [3 0] [2] [3 0] [1] active(length1(X)) = [0 0]X + [0] >= [0 0]X + [0] = mark(length(X)) [1 1] [3] [1 1] [3] mark(from(X)) = [0 0]X + [0] >= [0 0]X + [0] = active(from(mark(X))) [1 1] [1 0] [1] [1 1] [1 0] [1] mark(cons(X1,X2)) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = active(cons(mark(X1),X2)) [1 1] [1] [1 1] [1] mark(s(X)) = [0 0]X + [0] >= [0 0]X + [0] = active(s(mark(X))) [3 0] [1] [3 0] [1] mark(length(X)) = [0 0]X + [0] >= [0 0]X + [0] = active(length(X)) [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [4] [4] mark(0()) = [0] >= [0] = active(0()) [3 0] [2] [3 0] [2] mark(length1(X)) = [0 0]X + [0] >= [0 0]X + [0] = active(length1(X)) [0 0] [1] [0 0] [1] from(mark(X)) = [1 1]X + [2] >= [1 1]X + [2] = from(X) [0 0] [1] [0 0] [1] from(active(X)) = [1 1]X + [2] >= [1 1]X + [2] = from(X) [1 1] [1 0] [1] [1 1] [1 0] [1] cons(mark(X1),X2) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = cons(X1,X2) [1 1] [1 1] [1] [1 1] [1 0] [1] cons(X1,mark(X2)) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = cons(X1,X2) [1 1] [1 0] [1] [1 1] [1 0] [1] cons(active(X1),X2) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = cons(X1,X2) [1 1] [1 1] [1] [1 1] [1 0] [1] cons(X1,active(X2)) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = cons(X1,X2) [0 0] [0] [0 0] [0] s(mark(X)) = [1 1]X + [1] >= [1 1]X + [1] = s(X) [0 0] [0] [0 0] [0] s(active(X)) = [1 1]X + [1] >= [1 1]X + [1] = s(X) [0 0] [1] [0 0] [1] length(mark(X)) = [3 3]X + [0] >= [3 0]X + [0] = length(X) [0 0] [1] [0 0] [1] length(active(X)) = [3 3]X + [0] >= [3 0]X + [0] = length(X) [0 0] [1] [0 0] [1] length1(mark(X)) = [3 3]X + [1] >= [3 0]X + [1] = length1(X) [0 0] [1] [0 0] [1] length1(active(X)) = [3 3]X + [1] >= [3 0]X + [1] = length1(X) 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) Matrix Interpretation Processor: dim=1 interpretation: [cons#](x0, x1) = x0 + x1, [length1](x0) = 4, [0] = 0, [length](x0) = 0, [nil] = 2, [mark](x0) = 2x0 + 1, [cons](x0, x1) = 2x1, [s](x0) = 0, [active](x0) = 2x0 + 1, [from](x0) = 0 orientation: cons#(mark(X1),X2) = 2X1 + X2 + 1 >= X1 + X2 = cons#(X1,X2) cons#(X1,mark(X2)) = X1 + 2X2 + 1 >= X1 + X2 = cons#(X1,X2) cons#(active(X1),X2) = 2X1 + X2 + 1 >= X1 + X2 = cons#(X1,X2) cons#(X1,active(X2)) = X1 + 2X2 + 1 >= X1 + X2 = cons#(X1,X2) active(from(X)) = 1 >= 1 = mark(cons(X,from(s(X)))) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(X,Y))) = 1 >= 1 = mark(s(length1(Y))) active(length1(X)) = 9 >= 1 = mark(length(X)) mark(from(X)) = 1 >= 1 = active(from(mark(X))) mark(cons(X1,X2)) = 4X2 + 1 >= 4X2 + 1 = active(cons(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(X)) mark(nil()) = 5 >= 5 = active(nil()) mark(0()) = 1 >= 1 = active(0()) mark(length1(X)) = 9 >= 9 = active(length1(X)) from(mark(X)) = 0 >= 0 = from(X) from(active(X)) = 0 >= 0 = from(X) cons(mark(X1),X2) = 2X2 >= 2X2 = cons(X1,X2) cons(X1,mark(X2)) = 4X2 + 2 >= 2X2 = cons(X1,X2) cons(active(X1),X2) = 2X2 >= 2X2 = cons(X1,X2) cons(X1,active(X2)) = 4X2 + 2 >= 2X2 = cons(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) length1(mark(X)) = 4 >= 4 = length1(X) length1(active(X)) = 4 >= 4 = length1(X) 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) LPO Processor: argument filtering: pi(from) = [] pi(active) = [0] pi(s) = [] pi(cons) = [] pi(mark) = [0] pi(nil) = [] pi(length) = [] pi(0) = [] pi(length1) = [] pi(s#) = 0 precedence: length1 > length > from > mark > s# ~ 0 ~ nil ~ cons ~ s ~ active 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) LPO Processor: argument filtering: pi(from) = [] pi(active) = [0] pi(s) = [] pi(cons) = [] pi(mark) = [0] pi(nil) = [] pi(length) = [] pi(0) = [] pi(length1) = [] pi(from#) = 0 precedence: length1 > length > from > mark > from# ~ 0 ~ nil ~ cons ~ s ~ active 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) LPO Processor: argument filtering: pi(from) = [] pi(active) = [0] pi(s) = [] pi(cons) = [] pi(mark) = [0] pi(nil) = [] pi(length) = [] pi(0) = [] pi(length1) = [] pi(length1#) = 0 precedence: length1 > length > from > mark > length1# ~ 0 ~ nil ~ cons ~ s ~ active 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) LPO Processor: argument filtering: pi(from) = [] pi(active) = [0] pi(s) = [] pi(cons) = [] pi(mark) = [0] pi(nil) = [] pi(length) = [] pi(0) = [] pi(length1) = [] pi(length#) = 0 precedence: length1 > length > from > mark > length# ~ 0 ~ nil ~ cons ~ s ~ active 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