diff --git a/example/show_lu_decomp/main.f90 b/example/show_lu_decomp/main.f90
new file mode 100644
index 0000000..df32083
--- /dev/null
+++ b/example/show_lu_decomp/main.f90
@@ -0,0 +1,59 @@
+program show_lu_decomp
+    use dag_m, only: dag_t
+    use iso_varying_string, only: var_str
+    use vertex_m, only: vertex_t
+
+    implicit none
+
+    character(len=*), parameter :: root   = 'shape=circle,fillcolor="white",style=filled'
+    character(len=*), parameter :: branch = 'shape=square,fillcolor="SlateGray1",style=filled'
+    character(len=*), parameter :: leaf   = 'shape=circle,fillcolor="cornsilk",style=filled'
+    type(vertex_t), allocatable :: vertices(:)
+    type(dag_t) :: dag
+    integer :: num_tasks, step, row, matrix_size, latest_matrix, task_base, reconstruction_step, i
+
+    do matrix_size = 1, 5
+        num_tasks = 4 + (matrix_size-1)*2 + sum([((matrix_size-step)*3, step=1,matrix_size-1)])
+        allocate(vertices(num_tasks))
+
+        vertices(1) = vertex_t([integer::], var_str("initial matrix"), var_str(leaf))
+        vertices(2) = vertex_t([1], var_str("print matrix"), var_str(root))
+        do step = 1, matrix_size-1
+            do row = step+1, matrix_size
+                latest_matrix = 1 + sum([(3*(matrix_size-i), i = 1, step-1)]) + 2*(step-1) ! reconstructed matrix from last step
+                task_base = sum([(3*(matrix_size-i), i = 1, step-1)]) + 2*(step-1) + 3*(row-(step+1))
+                vertices(3+task_base) = vertex_t([latest_matrix], var_str("calculate factor"), var_str(branch))
+                vertices(4+task_base) = vertex_t([latest_matrix, 3+task_base], var_str("row multiply"), var_str(branch))
+                vertices(5+task_base) = vertex_t([latest_matrix, 4+task_base], var_str("row subtract"), var_str(branch))
+            end do
+            reconstruction_step = 3 + sum([(3*(matrix_size-i), i = 1, step)]) + 2*(step-1)
+            vertices(reconstruction_step) = vertex_t( &
+                [ 1 + sum([(3*(matrix_size-i), i = 1, step-1)]) + 2*(step-1) &
+                , [(5 + sum([(3*(matrix_size-i), i = 1, step-1)]) + 2*(step-1) + 3*(row-(step+1)) &
+                    , row=step+1, matrix_size)] &
+                ], &
+                var_str("reconstruct matrix"), var_str(branch)) ! depends on previous reconstructed matrix and just subtracted rows
+            ! print the just reconstructed matrix
+            vertices(reconstruction_step+1) = vertex_t([reconstruction_step], var_str("print matrix"), var_str(root))
+        end do
+        vertices(num_tasks-1) = vertex_t( &
+            [([(3 + sum([(3*(matrix_size-i), i = 1, step-1)]) + 2*(step-1) + 3*(row-(step+1)) &
+                , row=step+1, matrix_size)] &
+                , step=1, matrix_size-1)] &
+            , var_str("back substitute"), var_str(branch)) ! depends on all "factors"
+        vertices(num_tasks) = vertex_t([num_tasks-1], var_str("print matrix"), var_str(root))
+
+        dag = dag_t(vertices)
+        deallocate(vertices)
+
+        block
+            character(len=15) :: dotfile_name
+            integer :: funit
+
+            write(dotfile_name, '("lu_decomp_", I1, ".dot")') matrix_size
+            open(newunit = funit, file = dotfile_name, status="replace")
+            write(funit, "(A)") dag%graphviz_digraph()
+            close(funit)
+        end block
+    end do
+end program
\ No newline at end of file
diff --git a/fpm.toml b/fpm.toml
index 467e1bf..7017a0e 100644
--- a/fpm.toml
+++ b/fpm.toml
@@ -26,3 +26,8 @@ main="main.f90"
 name="quadratic_solver"
 source-dir="example/quadratic_solver"
 main="main.f90"
+
+[[example]]
+name="show_lu_decomp"
+source-dir="example/show_lu_decomp"
+main="main.f90"
\ No newline at end of file