#5108 ⟨a, b | aab=aa, abbb=a⟩

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 a is not injective:
- a ⋅ b³ = a and a ⋅ 1 = a, however b³ ≠ 1

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 ⇒ a²	[1]
2.	ab³ ⇒ a	[2]

# ab:aab=aa,abbb=a ab - -
aab=aa
abbb=a

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

1 total

Σ	#	Presentation	Mapping
11	12436	⟨a, b \| aabb=aa, abbb=a⟩	φ(a) = a, φ(b) = b