#948 ⟨a, b | ab=a, bbba=a⟩

Properties

Sum of relation sides is 8
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 = a and 1 ⋅ a = a, however b³ ≠ 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.	ab ⇒ a	[1]
2.	b³a ⇒ a	[2]

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

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

12 total

Σ	#	Presentation	Mapping
9	2994	⟨a, b \| ab=a, bbbab=a⟩	φ(a) = a, φ(b) = b
9	3129	⟨a, b \| ab=a, bbba=ab⟩	φ(a) = a, φ(b) = b
10	5245	⟨a, b \| aba=ab, aaab=b⟩	φ(a) = b, φ(b) = a
10	8830	⟨a, b \| ab=a, bbbabb=a⟩	φ(a) = a, φ(b) = b
10	9101	⟨a, b \| ab=a, bbbab=ab⟩	φ(a) = a, φ(b) = b
10	9371	⟨a, b \| ab=a, bbba=abb⟩	φ(a) = a, φ(b) = b
11	14478	⟨a, b \| aaab=b, aaaba=b⟩	φ(a) = b, φ(b) = a
11	15846	⟨a, b \| aba=ab, aaaba=b⟩	φ(a) = b, φ(b) = a
11	24570	⟨a, b \| ab=a, bbbabbb=a⟩	φ(a) = a, φ(b) = b
11	25097	⟨a, b \| ab=a, bbbabb=ab⟩	φ(a) = a, φ(b) = b
11	25639	⟨a, b \| ab=a, bbbab=abb⟩	φ(a) = a, φ(b) = b
11	25890	⟨a, b \| ab=a, bbba=abbb⟩	φ(a) = a, φ(b) = b