#789 ⟨a, b | aabaaaab=a⟩

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 ⋅ aba⁴b = a and a ⋅ 1 = a, however aba⁴b ≠ 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.	a⁵b ⇒ a²ba³	[2]
2.	a²ba⁴b ⇒ a	[1]

# ab:aabaaaab=a ba - -
aaaaab=aabaaa
aabaaaab=a

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

1 total

Σ	#	Presentation	Mapping
11	3734	⟨a, b \| abaababaab=a⟩	φ(a) = aa, φ(b) = b