MAYBE 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) 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#(length1(X)) -> length#(X) mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> mark#(length(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#(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#(active(X1),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)) -> 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#(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)) SCC Processor: #sccs: 6 #rules: 23 #arcs: 139/1225 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)) -> active#(s(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) mark#(from(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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [length1](x0) = 1, [0] = 0, [length](x0) = 1, [nil] = 0, [mark](x0) = x0, [cons](x0, x1) = 0, [s](x0) = 1, [active](x0) = x0, [from](x0) = 1 orientation: mark#(length1(X)) = 1 >= 1 = active#(length1(X)) active#(length1(X)) = 1 >= 1 = mark#(length(X)) mark#(length(X)) = 1 >= 1 = active#(length(X)) active#(length(cons(X,Y))) = 1 >= 1 = mark#(s(length1(Y))) mark#(s(X)) = 1 >= 1 = active#(s(mark(X))) active#(from(X)) = 1 >= 1 = mark#(cons(X,from(s(X)))) mark#(s(X)) = 1 >= 1 = mark#(X) mark#(cons(X1,X2)) = 1 >= 0 = active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) = 1 >= 1 = mark#(X1) mark#(from(X)) = 1 >= 1 = active#(from(mark(X))) mark#(from(X)) = 1 >= 1 = mark#(X) active(from(X)) = 1 >= 0 = mark(cons(X,from(s(X)))) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(X,Y))) = 1 >= 1 = mark(s(length1(Y))) active(length1(X)) = 1 >= 1 = mark(length(X)) mark(from(X)) = 1 >= 1 = active(from(mark(X))) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(X)) mark(nil()) = 0 >= 0 = active(nil()) mark(0()) = 0 >= 0 = active(0()) mark(length1(X)) = 1 >= 1 = active(length1(X)) from(mark(X)) = 1 >= 1 = from(X) from(active(X)) = 1 >= 1 = from(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) length1(mark(X)) = 1 >= 1 = length1(X) length1(active(X)) = 1 >= 1 = 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)) -> active#(s(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) mark#(from(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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [length1](x0) = 1, [0] = 0, [length](x0) = 1, [nil] = 0, [mark](x0) = 0, [cons](x0, x1) = 1, [s](x0) = 0, [active](x0) = 0, [from](x0) = 1 orientation: mark#(length1(X)) = 1 >= 1 = active#(length1(X)) active#(length1(X)) = 1 >= 1 = mark#(length(X)) mark#(length(X)) = 1 >= 1 = active#(length(X)) active#(length(cons(X,Y))) = 1 >= 1 = mark#(s(length1(Y))) mark#(s(X)) = 1 >= 0 = active#(s(mark(X))) active#(from(X)) = 1 >= 1 = mark#(cons(X,from(s(X)))) mark#(s(X)) = 1 >= 1 = mark#(X) mark#(cons(X1,X2)) = 1 >= 1 = mark#(X1) mark#(from(X)) = 1 >= 1 = active#(from(mark(X))) mark#(from(X)) = 1 >= 1 = mark#(X) active(from(X)) = 0 >= 0 = mark(cons(X,from(s(X)))) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(X,Y))) = 0 >= 0 = mark(s(length1(Y))) active(length1(X)) = 0 >= 0 = mark(length(X)) mark(from(X)) = 0 >= 0 = active(from(mark(X))) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(X)) mark(nil()) = 0 >= 0 = active(nil()) mark(0()) = 0 >= 0 = active(0()) mark(length1(X)) = 0 >= 0 = active(length1(X)) from(mark(X)) = 1 >= 1 = from(X) from(active(X)) = 1 >= 1 = from(X) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) length1(mark(X)) = 1 >= 1 = length1(X) length1(active(X)) = 1 >= 1 = 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))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) mark#(from(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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [length1](x0) = 1, [0] = 0, [length](x0) = 1, [nil] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + 1, [s](x0) = x0, [active](x0) = x0, [from](x0) = x0 + 1 orientation: mark#(length1(X)) = 1 >= 1 = active#(length1(X)) active#(length1(X)) = 1 >= 1 = mark#(length(X)) mark#(length(X)) = 1 >= 1 = active#(length(X)) active#(length(cons(X,Y))) = 1 >= 1 = mark#(s(length1(Y))) active#(from(X)) = X + 1 >= X + 1 = mark#(cons(X,from(s(X)))) mark#(s(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(from(X)) = X + 1 >= X + 1 = active#(from(mark(X))) mark#(from(X)) = X + 1 >= X = mark#(X) active(from(X)) = X + 1 >= X + 1 = mark(cons(X,from(s(X)))) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(X,Y))) = 1 >= 1 = mark(s(length1(Y))) active(length1(X)) = 1 >= 1 = mark(length(X)) mark(from(X)) = X + 1 >= X + 1 = active(from(mark(X))) mark(cons(X1,X2)) = X1 + 1 >= X1 + 1 = active(cons(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(X)) mark(nil()) = 0 >= 0 = active(nil()) mark(0()) = 0 >= 0 = active(0()) mark(length1(X)) = 1 >= 1 = active(length1(X)) from(mark(X)) = X + 1 >= X + 1 = from(X) from(active(X)) = X + 1 >= X + 1 = from(X) cons(mark(X1),X2) = X1 + 1 >= X1 + 1 = cons(X1,X2) cons(X1,mark(X2)) = X1 + 1 >= X1 + 1 = cons(X1,X2) cons(active(X1),X2) = X1 + 1 >= X1 + 1 = cons(X1,X2) cons(X1,active(X2)) = X1 + 1 >= X1 + 1 = cons(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) length1(mark(X)) = 1 >= 1 = length1(X) length1(active(X)) = 1 >= 1 = 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))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(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) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [length1](x0) = 0, [0] = 0, [length](x0) = 0, [nil] = 0, [mark](x0) = x0, [cons](x0, x1) = 0, [s](x0) = x0, [active](x0) = x0, [from](x0) = 1 orientation: mark#(length1(X)) = 0 >= 0 = active#(length1(X)) active#(length1(X)) = 0 >= 0 = mark#(length(X)) mark#(length(X)) = 0 >= 0 = active#(length(X)) active#(length(cons(X,Y))) = 0 >= 0 = mark#(s(length1(Y))) active#(from(X)) = 0 >= 0 = mark#(cons(X,from(s(X)))) mark#(s(X)) = X >= X = mark#(X) mark#(from(X)) = 1 >= 0 = active#(from(mark(X))) active(from(X)) = 1 >= 0 = mark(cons(X,from(s(X)))) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(X,Y))) = 0 >= 0 = mark(s(length1(Y))) active(length1(X)) = 0 >= 0 = mark(length(X)) mark(from(X)) = 1 >= 1 = active(from(mark(X))) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(X)) mark(nil()) = 0 >= 0 = active(nil()) mark(0()) = 0 >= 0 = active(0()) mark(length1(X)) = 0 >= 0 = active(length1(X)) from(mark(X)) = 1 >= 1 = from(X) from(active(X)) = 1 >= 1 = from(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) length1(mark(X)) = 0 >= 0 = length1(X) length1(active(X)) = 0 >= 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))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(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: dimension: 1 interpretation: [mark#](x0) = 0, [active#](x0) = x0, [length1](x0) = 0, [0] = 0, [length](x0) = 0, [nil] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [s](x0) = 0, [active](x0) = 0, [from](x0) = 1 orientation: mark#(length1(X)) = 0 >= 0 = active#(length1(X)) active#(length1(X)) = 0 >= 0 = mark#(length(X)) mark#(length(X)) = 0 >= 0 = active#(length(X)) active#(length(cons(X,Y))) = 0 >= 0 = mark#(s(length1(Y))) active#(from(X)) = 1 >= 0 = mark#(cons(X,from(s(X)))) mark#(s(X)) = 0 >= 0 = mark#(X) active(from(X)) = 0 >= 0 = mark(cons(X,from(s(X)))) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(X,Y))) = 0 >= 0 = mark(s(length1(Y))) active(length1(X)) = 0 >= 0 = mark(length(X)) mark(from(X)) = 0 >= 0 = active(from(mark(X))) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(X)) mark(nil()) = 0 >= 0 = active(nil()) mark(0()) = 0 >= 0 = active(0()) mark(length1(X)) = 0 >= 0 = active(length1(X)) from(mark(X)) = 1 >= 1 = from(X) from(active(X)) = 1 >= 1 = from(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = 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)) = 0 >= 0 = length1(X) length1(active(X)) = 0 >= 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) Open DPs: from#(active(X)) -> from#(X) from#(mark(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) Matrix Interpretation Processor: dimension: 1 interpretation: [from#](x0) = x0 + 1, [length1](x0) = 0, [0] = 0, [length](x0) = 0, [nil] = 1, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [s](x0) = 0, [active](x0) = x0 + 1, [from](x0) = 1 orientation: from#(active(X)) = X + 2 >= X + 1 = from#(X) from#(mark(X)) = X + 2 >= X + 1 = from#(X) active(from(X)) = 2 >= 2 = 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)) = 1 >= 1 = mark(length(X)) mark(from(X)) = 2 >= 2 = active(from(mark(X))) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(X)) mark(nil()) = 2 >= 2 = active(nil()) mark(0()) = 1 >= 1 = active(0()) mark(length1(X)) = 1 >= 1 = active(length1(X)) from(mark(X)) = 1 >= 1 = from(X) from(active(X)) = 1 >= 1 = from(X) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = 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)) = 0 >= 0 = length1(X) length1(active(X)) = 0 >= 0 = 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#(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) 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: dimension: 1 interpretation: [cons#](x0, x1) = x1, [length1](x0) = 0, [0] = 0, [length](x0) = 0, [nil] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [s](x0) = 0, [active](x0) = x0 + 1, [from](x0) = 0 orientation: cons#(active(X1),X2) = X2 >= X2 = cons#(X1,X2) cons#(X1,active(X2)) = X2 + 1 >= X2 = cons#(X1,X2) cons#(X1,mark(X2)) = X2 + 1 >= X2 = cons#(X1,X2) cons#(mark(X1),X2) = X2 >= 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)) = 1 >= 1 = mark(length(X)) mark(from(X)) = 1 >= 1 = active(from(mark(X))) mark(cons(X1,X2)) = 1 >= 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()) = 1 >= 1 = active(nil()) mark(0()) = 1 >= 1 = active(0()) mark(length1(X)) = 1 >= 1 = active(length1(X)) from(mark(X)) = 0 >= 0 = from(X) from(active(X)) = 0 >= 0 = from(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = 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)) = 0 >= 0 = length1(X) length1(active(X)) = 0 >= 0 = length1(X) problem: DPs: cons#(active(X1),X2) -> cons#(X1,X2) cons#(mark(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) Matrix Interpretation Processor: dimension: 1 interpretation: [cons#](x0, x1) = x0 + 1, [length1](x0) = x0, [0] = 0, [length](x0) = x0, [nil] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [s](x0) = 1, [active](x0) = x0 + 1, [from](x0) = 1 orientation: cons#(active(X1),X2) = X1 + 2 >= X1 + 1 = cons#(X1,X2) cons#(mark(X1),X2) = X1 + 2 >= X1 + 1 = cons#(X1,X2) active(from(X)) = 2 >= 2 = mark(cons(X,from(s(X)))) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(X,Y))) = 2 >= 2 = mark(s(length1(Y))) active(length1(X)) = X + 1 >= X + 1 = mark(length(X)) mark(from(X)) = 2 >= 2 = active(from(mark(X))) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = X + 1 >= X + 1 = active(length(X)) mark(nil()) = 1 >= 1 = active(nil()) mark(0()) = 1 >= 1 = active(0()) mark(length1(X)) = X + 1 >= X + 1 = active(length1(X)) from(mark(X)) = 1 >= 1 = from(X) from(active(X)) = 1 >= 1 = from(X) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = X + 1 >= X = length(X) length(active(X)) = X + 1 >= X = length(X) length1(mark(X)) = X + 1 >= X = length1(X) length1(active(X)) = X + 1 >= X = 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#(active(X)) -> s#(X) s#(mark(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) Matrix Interpretation Processor: dimension: 1 interpretation: [s#](x0) = x0 + 1, [length1](x0) = 0, [0] = 0, [length](x0) = 0, [nil] = 1, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [s](x0) = 0, [active](x0) = x0 + 1, [from](x0) = 1 orientation: s#(active(X)) = X + 2 >= X + 1 = s#(X) s#(mark(X)) = X + 2 >= X + 1 = s#(X) active(from(X)) = 2 >= 2 = 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)) = 1 >= 1 = mark(length(X)) mark(from(X)) = 2 >= 2 = active(from(mark(X))) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(X)) mark(nil()) = 2 >= 2 = active(nil()) mark(0()) = 1 >= 1 = active(0()) mark(length1(X)) = 1 >= 1 = active(length1(X)) from(mark(X)) = 1 >= 1 = from(X) from(active(X)) = 1 >= 1 = from(X) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = 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)) = 0 >= 0 = length1(X) length1(active(X)) = 0 >= 0 = 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: 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) Matrix Interpretation Processor: dimension: 1 interpretation: [length1#](x0) = x0 + 1, [length1](x0) = 0, [0] = 0, [length](x0) = 0, [nil] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [s](x0) = 0, [active](x0) = x0 + 1, [from](x0) = 0 orientation: length1#(mark(X)) = X + 2 >= X + 1 = length1#(X) length1#(active(X)) = X + 2 >= X + 1 = length1#(X) 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)) = 1 >= 1 = mark(length(X)) mark(from(X)) = 1 >= 1 = active(from(mark(X))) mark(cons(X1,X2)) = 1 >= 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()) = 1 >= 1 = active(nil()) mark(0()) = 1 >= 1 = active(0()) mark(length1(X)) = 1 >= 1 = active(length1(X)) from(mark(X)) = 0 >= 0 = from(X) from(active(X)) = 0 >= 0 = from(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = 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)) = 0 >= 0 = length1(X) length1(active(X)) = 0 >= 0 = 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: 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) Matrix Interpretation Processor: dimension: 1 interpretation: [length#](x0) = x0 + 1, [length1](x0) = 0, [0] = 0, [length](x0) = 0, [nil] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [s](x0) = 0, [active](x0) = x0 + 1, [from](x0) = 0 orientation: length#(mark(X)) = X + 2 >= X + 1 = length#(X) length#(active(X)) = X + 2 >= X + 1 = length#(X) 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)) = 1 >= 1 = mark(length(X)) mark(from(X)) = 1 >= 1 = active(from(mark(X))) mark(cons(X1,X2)) = 1 >= 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()) = 1 >= 1 = active(nil()) mark(0()) = 1 >= 1 = active(0()) mark(length1(X)) = 1 >= 1 = active(length1(X)) from(mark(X)) = 0 >= 0 = from(X) from(active(X)) = 0 >= 0 = from(X) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = 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)) = 0 >= 0 = length1(X) length1(active(X)) = 0 >= 0 = 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