#8075 ⟨a, b | aaa=1, abbb=bbb⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not right cancellative, because right multiplication by b is not injective:
- ab² ⋅ b = b³ and b² ⋅ b = b³, however ab² ≠ b²

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.	a³ ⇒ 1	[1]
2.	ab³ ⇒ b³	[2]

# ab:aaa=1,abbb=bbb ab - -
aaa=1
abbb=bbb

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

1 total

Σ	#	Presentation	Mapping
11	22779	⟨a, b \| aaa=1, aabbb=bbb⟩	φ(a) = a, φ(b) = b