#3130 ⟨a, b | ab=a, bbba=ba⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- b³ ⋅ a = ba and b ⋅ a = ba, however b³ ≠ 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 ⇒ a	[1]
2.	b³a ⇒ ba	[2]

# ab:ab=a,bbba=ba ab - -
ab=a
bbba=ba

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

5 total

Σ	#	Presentation	Mapping
10	9102	⟨a, b \| ab=a, bbbab=ba⟩	φ(a) = a, φ(b) = b
10	9373	⟨a, b \| ab=a, bbba=bab⟩	φ(a) = a, φ(b) = b
11	25098	⟨a, b \| ab=a, bbbabb=ba⟩	φ(a) = a, φ(b) = b
11	25641	⟨a, b \| ab=a, bbbab=bab⟩	φ(a) = a, φ(b) = b
11	25894	⟨a, b \| ab=a, bbba=babb⟩	φ(a) = a, φ(b) = b