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: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [length1](x0) = [0 0 0]x0 [1 0 0] , [0] [0] = [0] [0], [1 0 0] [length](x0) = [0 0 0]x0 [1 0 0] , [0] [nil] = [0] [1], [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 0] [1] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 1] [s](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [active](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1] [from](x0) = [0 0 0]x0 + [0] [1 0 1] [1] orientation: [2 0 2] [2] [2 0 2] [2] active(from(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(cons(X,from(s(X)))) [0 0 0] [0] [0 0 0] [0] [0] [0] active(length(nil())) = [0] >= [0] = mark(0()) [0] [0] [2 0 2] [2 0 0] [2] [2 0 0] active(length(cons(X,Y))) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]Y = mark(s(length1(Y))) [0 0 0] [0 0 0] [0] [0 0 0] [2 0 0] [2 0 0] active(length1(X)) = [0 0 0]X >= [0 0 0]X = mark(length(X)) [0 0 0] [0 0 0] [2 0 2] [2] [2 0 2] [2] mark(from(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(from(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [0 0 0] [0 0 0] [2 0 0] [2 0 0] mark(length(X)) = [0 0 0]X >= [0 0 0]X = active(length(X)) [0 0 0] [0 0 0] [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [2 0 0] [2 0 0] mark(length1(X)) = [0 0 0]X >= [0 0 0]X = active(length1(X)) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] [1] from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [1 0 1] [1] [1 0 1] [1] [1 1 1] [1] [1 0 1] [1] from(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [1 1 1] [1] [1 0 1] [1] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 0] [1] cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 1 1] [1] [1 0 1] [1 0 0] [1] cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 1] [1 0 1] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] length(mark(X)) = [0 0 0]X >= [0 0 0]X = length(X) [1 0 1] [1 0 0] [1 1 1] [1 0 0] length(active(X)) = [0 0 0]X >= [0 0 0]X = length(X) [1 1 1] [1 0 0] [1 0 1] [1 0 0] length1(mark(X)) = [0 0 0]X >= [0 0 0]X = length1(X) [1 0 1] [1 0 0] [1 1 1] [1 0 0] length1(active(X)) = [0 0 0]X >= [0 0 0]X = length1(X) [1 1 1] [1 0 0] problem: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) 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) 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#(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(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#(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(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: 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) 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) 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(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(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(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(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(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(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(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#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(length1(X)) -> active#(length1(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(0()) -> active#(0()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(nil()) -> active#(nil()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(length(X)) -> active#(length(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> active#(s(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> s#(mark(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> mark#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> from#(mark(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> mark#(X) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(from(X)) -> from#(s(X)) -> from#(active(X)) -> from#(X) active#(from(X)) -> from#(s(X)) -> from#(mark(X)) -> from#(X) active#(from(X)) -> s#(X) -> s#(active(X)) -> s#(X) active#(from(X)) -> s#(X) -> s#(mark(X)) -> s#(X) SCC Processor: #sccs: 6 #rules: 25 #arcs: 177/1024 DPs: mark#(length1(X)) -> active#(length1(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length1(X)) -> mark#(length(X)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> active#(length(X)) mark#(nil()) -> active#(nil()) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) EDG Processor: DPs: mark#(length1(X)) -> active#(length1(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length1(X)) -> mark#(length(X)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> active#(length(X)) mark#(nil()) -> active#(nil()) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) graph: mark#(length1(X)) -> active#(length1(X)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(length1(X)) -> active#(length1(X)) -> active#(length(nil())) -> mark#(0()) mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(length(X)) -> active#(length(X)) -> active#(length(nil())) -> mark#(0()) mark#(length(X)) -> active#(length(X)) -> active#(length1(X)) -> mark#(length(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> active#(length(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length1(X)) -> active#(length1(X)) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(length1(X)) -> mark#(length(X)) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(X)) mark#(s(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(length1(X)) -> active#(length1(X)) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> active#(s(mark(X))) -> active#(length(nil())) -> mark#(0()) mark#(s(X)) -> active#(s(mark(X))) -> active#(length1(X)) -> mark#(length(X)) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(X)) mark#(from(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(length1(X)) -> active#(length1(X)) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> active#(from(mark(X))) -> active#(length(nil())) -> mark#(0()) mark#(from(X)) -> active#(from(mark(X))) -> active#(length1(X)) -> mark#(length(X)) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> mark#(X) active#(length1(X)) -> mark#(length(X)) -> mark#(from(X)) -> active#(from(mark(X))) active#(length1(X)) -> mark#(length(X)) -> mark#(cons(X1,X2)) -> mark#(X1) active#(length1(X)) -> mark#(length(X)) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length1(X)) -> mark#(length(X)) -> mark#(s(X)) -> mark#(X) active#(length1(X)) -> mark#(length(X)) -> mark#(s(X)) -> active#(s(mark(X))) active#(length1(X)) -> mark#(length(X)) -> mark#(length(X)) -> active#(length(X)) active#(length1(X)) -> mark#(length(X)) -> mark#(length1(X)) -> active#(length1(X)) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> mark#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> mark#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> active#(s(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(length(X)) -> active#(length(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(length1(X)) -> active#(length1(X)) CDG Processor: DPs: mark#(length1(X)) -> active#(length1(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(length1(X)) -> mark#(length(X)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> active#(length(X)) mark#(nil()) -> active#(nil()) mark#(0()) -> active#(0()) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) graph: mark#(length1(X)) -> active#(length1(X)) -> active#(length1(X)) -> mark#(length(X)) mark#(length(X)) -> active#(length(X)) -> active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length1(X)) -> active#(length1(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> active#(length(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(length1(X)) -> active#(length1(X)) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(X)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(length1(X)) -> active#(length1(X)) mark#(from(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(from(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(from(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(X)) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) active#(length1(X)) -> mark#(length(X)) -> mark#(length(X)) -> active#(length(X)) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> mark#(X1) SCC Processor: #sccs: 1 #rules: 5 #arcs: 37/169 DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> mark#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Arctic Interpretation Processor: dimension: 1 usable rules: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) 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) interpretation: [mark#](x0) = 4x0, [active#](x0) = 4x0, [length1](x0) = x0, [0] = 0, [length](x0) = x0, [nil] = 1, [mark](x0) = x0, [cons](x0, x1) = x0, [s](x0) = 2x0, [active](x0) = x0, [from](x0) = x0 orientation: mark#(cons(X1,X2)) = 4X1 >= 4X1 = mark#(X1) mark#(from(X)) = 4X >= 4X = mark#(X) mark#(from(X)) = 4X >= 4X = active#(from(mark(X))) active#(from(X)) = 4X >= 4X = mark#(cons(X,from(s(X)))) mark#(s(X)) = 6X >= 4X = mark#(X) active(from(X)) = X >= X = mark(cons(X,from(s(X)))) active(length(nil())) = 1 >= 0 = mark(0()) active(length1(X)) = X >= X = mark(length(X)) mark(from(X)) = X >= X = active(from(mark(X))) mark(cons(X1,X2)) = X1 >= X1 = active(cons(mark(X1),X2)) mark(s(X)) = 2X >= 2X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(X)) mark(nil()) = 1 >= 1 = active(nil()) mark(0()) = 0 >= 0 = active(0()) mark(length1(X)) = X >= X = active(length1(X)) from(mark(X)) = X >= X = from(X) from(active(X)) = X >= X = from(X) cons(mark(X1),X2) = X1 >= X1 = cons(X1,X2) cons(X1,mark(X2)) = X1 >= X1 = cons(X1,X2) cons(active(X1),X2) = X1 >= X1 = cons(X1,X2) cons(X1,active(X2)) = X1 >= X1 = cons(X1,X2) s(mark(X)) = 2X >= 2X = s(X) s(active(X)) = 2X >= 2X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) length1(mark(X)) = X >= X = length1(X) length1(active(X)) = X >= X = length1(X) problem: DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) 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) Restore Modifier: DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) 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) KBO Processor: argument filtering: pi(from) = [0] pi(active) = 0 pi(s) = [] pi(cons) = 0 pi(mark) = 0 pi(nil) = [] pi(length) = 0 pi(0) = [] pi(length1) = 0 pi(active#) = 0 pi(mark#) = 0 usable rules: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) 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) weight function: w0 = 1 w(length1) = w(0) = w(nil) = w(cons) = w(s) = w(active) = 1 w(mark#) = w(active#) = w(length) = w(mark) = w(from) = 0 precedence: cons > nil ~ s ~ from > mark# ~ active# ~ length1 ~ 0 ~ length ~ mark ~ active problem: DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) 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) Restore Modifier: DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> active#(from(mark(X))) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) SCC Processor: #sccs: 1 #rules: 1 #arcs: 14/4 DPs: mark#(cons(X1,X2)) -> mark#(X1) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(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(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(cons#) = 1 problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(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(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(from#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(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(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(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(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(length#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(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(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Subterm Criterion Processor: simple projection: pi(length1#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(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