#3864 ⟨a, b | aaaaabaaa=aa⟩

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 ⋅ a⁴ba³ = a² and a ⋅ a = a², however a⁴ba³ ≠ a
Not right cancellative, because right multiplication by a is not injective:
- a⁵ba² ⋅ a = a² and a ⋅ a = a², however a⁵ba² ≠ a

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.	a²ba³ ⇒ a³ba²	[4]
2.	a⁶ba² ⇒ a²	[3]

# ab:aaaaabaaa=aa ab - -
aabaaa=aaabaa
aaaaaabaa=aa

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

1 total

Σ	#	Presentation	Mapping
11	3896	⟨a, b \| aaaabaaaa=aa⟩	φ(a) = a, φ(b) = b