#4025 ⟨a, b | aba=aab, aabb=1⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab²a = a and a ⋅ 1 = a, however ab²a ≠ 1
Not right cancellative, because right multiplication by ab² is not injective:
- ab²a ⋅ ab² = ab² and 1 ⋅ ab² = ab², however ab²a ≠ 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.	aba ⇒ a²b	[1]
2.	a²b² ⇒ 1	[2]

# ab:aba=aab,aabb=1 ab - -
aba=aab
aabb=1

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

2 total

Σ	#	Presentation	Mapping
10	4027	⟨a, b \| aba=aab, abab=1⟩	φ(a) = a, φ(b) = b
10	5910	⟨a, b \| abab=1, abaab=a⟩	φ(a) = a, φ(b) = b