#4680 ⟨a, b | aaab=b, abaa=b⟩

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 b is not injective:
- b ⋅ a⁶ = b and b ⋅ 1 = b, however a⁶ ≠ 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.	ba⁶ ⇒ b	[5]
2.	ab ⇒ ba⁴	[4]

# ab:aaab=b,abaa=b a/b - -
baaaaaa=b
ab=baaaa

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

1 total

Σ	#	Presentation	Mapping
11	13047	⟨a, b \| baa=aab, aaab=b⟩	φ(a) = a, φ(b) = b