#1555 ⟨a, b | aaaaaabaa=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 ⋅ a⁵ba² = a and a ⋅ 1 = a, however a⁵ba² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁶ba ⋅ a = a and 1 ⋅ a = a, however a⁶ba ≠ 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	[5]
2.	a⁷ba ⇒ a	[6]

# ab:aaaaaabaa=a ab - -
abaa=aaba
aaaaaaaba=a

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

2 total

Σ	#	Presentation	Mapping
10	1563	⟨a, b \| aaaaabaaa=a⟩	φ(a) = a, φ(b) = b
10	1579	⟨a, b \| aaaabaaaa=a⟩	φ(a) = a, φ(b) = b