#3361 ⟨a, b | aaaaabbbaa=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a⁴b³a² = a and a ⋅ 1 = a, however a⁴b³a² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁵b³a ⋅ a = a and 1 ⋅ a = a, however a⁵b³a ≠ 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.	ab³a² ⇒ a²b³a	[5]
2.	a⁶b³a ⇒ a	[6]

# ab:aaaaabbbaa=a ab - -
abbbaa=aabbba
aaaaaabbba=a

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

1 total

Σ	#	Presentation	Mapping
11	3413	⟨a, b \| aaaabbbaaa=a⟩	φ(a) = a, φ(b) = b