#17654 ⟨a, b | aaaa=1, ababb=ab⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element aba² has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab² = b and b ⋅ 1 = b, however ab² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- bab ⋅ b = b and 1 ⋅ b = b, however bab ≠ 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.	a⁴ ⇒ 1	[1]
2.	bab² ⇒ b	[3]

# ab:aaaa=1,ababb=ab ab - -
aaaa=1
babb=b

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

1 total

Σ	#	Presentation	Mapping
11	17658	⟨a, b \| aaaa=1, abbab=ab⟩	φ(a) = a, φ(b) = b