#6397 ⟨a, b | aab=b, aabbb=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:
- a² ⋅ b = b and 1 ⋅ b = b, however a² ≠ 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 ⇒ b	[1]
2.	b³ ⇒ b	[2]

# ab:aab=b,aabbb=b ab - -
aab=b
bbb=b

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

4 total

Σ	#	Presentation	Mapping
10	6421	⟨a, b \| aab=b, baabb=b⟩	φ(a) = a, φ(b) = b
10	6433	⟨a, b \| aab=b, bbaab=b⟩	φ(a) = a, φ(b) = b
10	6691	⟨a, b \| aab=b, abbb=ab⟩	φ(a) = a, φ(b) = b
10	6825	⟨a, b \| aab=b, bbb=aab⟩	φ(a) = a, φ(b) = b