#3429 ⟨a, b | aaabaaaaba=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 ⋅ a²ba⁴ba = a and a ⋅ 1 = a, however a²ba⁴ba ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a³ba⁴b ⋅ a = a and 1 ⋅ a = a, however a³ba⁴b ≠ 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.	aba² ⇒ a²ba	[6]
2.	a⁶(ba)² ⇒ a	[3]

# ab:aaabaaaaba=a ab - -
abaa=aaba
aaaaaababa=a

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

2 total

Σ	#	Presentation	Mapping
11	3433	⟨a, b \| aaabaaabaa=a⟩	φ(a) = a, φ(b) = b
11	3539	⟨a, b \| aabaaaabaa=a⟩	φ(a) = a, φ(b) = b