#1639 ⟨a, b | aab=ba, baa=b⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by b is not injective:
- a⁴ ⋅ b = b and 1 ⋅ b = b, however a⁴ ≠ 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.	a⁴b ⇒ b	[2]
2.	ba ⇒ a²b	[1]

# ab:aab=ba,baa=b reversed:a/b - -
aaaab=b
ba=aab

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

3 total

Σ	#	Presentation	Mapping
10	5163	⟨a, b \| aab=ba, aaba=b⟩	φ(a) = a, φ(b) = b
11	14604	⟨a, b \| aaba=b, aaaab=b⟩	φ(a) = a, φ(b) = b
11	15676	⟨a, b \| aab=ba, aaaab=b⟩	φ(a) = a, φ(b) = b