#4731 ⟨a, b | aabb=a, abab=a⟩

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 ⋅ ab² = a and a ⋅ 1 = a, however ab² ≠ 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	[3]
2.	a²b² ⇒ a	[1]

# ab:aabb=a,abab=a ab - -
aba=aab
aabb=a

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

2 total

Σ	#	Presentation	Mapping
11	12938	⟨a, b \| aba=aab, aabb=a⟩	φ(a) = a, φ(b) = b
11	12942	⟨a, b \| aba=aab, abab=a⟩	φ(a) = a, φ(b) = b