Changes

| <math>S_0\!</math>

| <math>S_0\!</math>

| <math>=\!</math>

| <math>=\!</math>

| <math>\{ \ominus, \vert \} = \{</math>[[Image:Cactus Node Big Fat.jpg|16px]], [[Image:Cactus Spike Big Fat.jpg|12px]]<math>\}\!</math>

| <math>\{ \ominus, \vert \} = \{</math>[[Image:Rooted Node.jpg|16px]], [[Image:Rooted Edge.jpg|12px]]<math>\}\!</math>

|}

|}

Simple intuition, or a simple inductive proof, assures us that any rooted tree can be reduced by way of the arithmetic initials either to a root node [[Image:Cactus Node Big Fat.jpg|16px]] or else to a rooted edge [[Image:Cactus Spike Big Fat.jpg|12px]]&nbsp;.

Simple intuition, or a simple inductive proof, assures us that any rooted tree can be reduced by way of the arithmetic initials either to a root node [[Image:Rooted Node.jpg|16px]] or else to a rooted edge [[Image:Rooted Edge.jpg|12px]]&nbsp;.

For example, consider the reduction that proceeds as follows:

For example, consider the reduction that proceeds as follows: