#1677 ⟨a, b | aba=ba, baa=b⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ a² = b and b ⋅ 1 = b, however a² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- a ⋅ b = b and 1 ⋅ b = b, however a ≠ 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.	ab ⇒ b	[3]
2.	ba² ⇒ b	[2]

# ab:aba=ba,baa=b ab - -
ab=b
baa=b

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

2 total

Σ	#	Presentation	Mapping
10	5135	⟨a, b \| aab=ab, abaa=b⟩	φ(a) = a, φ(b) = b
11	15618	⟨a, b \| aab=ab, aabaa=b⟩	φ(a) = a, φ(b) = b