#4163 ⟨a, b | abb=aab, bbb=b⟩

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 ⋅ b² = b and b ⋅ 1 = b, however b² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b² ⋅ b = b and 1 ⋅ b = b, however b² ≠ 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.	b³ ⇒ b	[2]
2.	a²b ⇒ ab²	[1]

# ab:abb=aab,bbb=b ba - -
bbb=b
aab=abb

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

1 total

Σ	#	Presentation	Mapping
10	6538	⟨a, b \| aaa=a, aabb=ab⟩	φ(a) = b, φ(b) = a