#4678 ⟨a, b | aaab=b, aabb=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 ⋅ b³ = b and b ⋅ 1 = b, however b³ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- a ⋅ b = b² and b ⋅ b = b², however a ≠ b

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.	ab ⇒ b²	[3]
2.	b⁴ ⇒ b	[4]

# ab:aaab=b,aabb=b ba - -
ab=bb
bbbb=b

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

3 total

Σ	#	Presentation	Mapping
10	4682	⟨a, b \| aaab=b, abab=b⟩	φ(a) = a, φ(b) = b
10	4708	⟨a, b \| aaba=a, baba=a⟩	φ(a) = b, φ(b) = a
11	12999	⟨a, b \| abb=aab, aaab=b⟩	φ(a) = a, φ(b) = b