#5409 ⟨a, b | aab=bb, baa=bb⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b = ba² and b ⋅ a² = ba², however b ≠ a²

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

#	Rule	Proof
1.	a²b ⇒ ba²	[2]
2.	b² ⇒ ba²	[3]

# ab:aab=bb,baa=bb a/b - -
aab=baa
bb=baa

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ	#	Presentation	Mapping
11	16520	⟨a, b \| aab=bb, baa=aab⟩	φ(a) = a, φ(b) = b