#1577 ⟨a, b | aaa=aa, aab=b⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a² = a² and a ⋅ a = a², however a² ≠ a
Not right cancellative, because right multiplication by b is not injective:
- a ⋅ b = b and 1 ⋅ b = b, however a ≠ 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 ⇒ b	[3]
2.	a³ ⇒ a²	[1]

# ab:aaa=aa,aab=b ab - -
ab=b
aaa=aa

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

2 total

Σ	#	Presentation	Mapping
10	5025	⟨a, b \| aaa=aa, aaab=b⟩	φ(a) = a, φ(b) = b
11	15404	⟨a, b \| aaa=aa, aaaab=b⟩	φ(a) = a, φ(b) = b