#1018 ⟨a, b | ab=a, bba=ba⟩

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:
- b² ⋅ a = ba and b ⋅ a = ba, however b² ≠ 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.	b²a ⇒ ba	[2]

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

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

9 total

Σ	#	Presentation	Mapping
9	3126	⟨a, b \| ab=a, bbab=ba⟩	φ(a) = a, φ(b) = b
9	3192	⟨a, b \| ab=a, bba=bab⟩	φ(a) = a, φ(b) = b
10	9094	⟨a, b \| ab=a, bbabb=ba⟩	φ(a) = a, φ(b) = b
10	9350	⟨a, b \| ab=a, babb=bba⟩	φ(a) = a, φ(b) = b
10	9365	⟨a, b \| ab=a, bbab=bab⟩	φ(a) = a, φ(b) = b
11	25082	⟨a, b \| ab=a, bbabbb=ba⟩	φ(a) = a, φ(b) = b
11	25594	⟨a, b \| ab=a, babbb=bba⟩	φ(a) = a, φ(b) = b
11	25625	⟨a, b \| ab=a, bbabb=bab⟩	φ(a) = a, φ(b) = b
11	25881	⟨a, b \| ab=a, bbab=babb⟩	φ(a) = a, φ(b) = b