#879 ⟨a, b | ab=a, bbbbb=1⟩

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

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.	b⁵ ⇒ 1	[2]

# ab:ab=a,bbbbb=1 ab - -
ab=a
bbbbb=1

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

2 total

Σ	#	Presentation	Mapping
10	4970	⟨a, b \| aba=ab, aaaaa=1⟩	φ(a) = b, φ(b) = a
11	11584	⟨a, b \| abbbb=a, bbbbb=1⟩	φ(a) = a, φ(b) = b