#1283 ⟨a, b | aba=aaa, bbb=1⟩

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 a is not injective:
- a ⋅ ba = a³ and a ⋅ a² = a³, however ba ≠ a²
Not right cancellative, because right multiplication by a is not injective:
- ab ⋅ a = a³ and a² ⋅ a = a³, however ab ≠ a²

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.	aba ⇒ a³	[1]
2.	b³ ⇒ 1	[2]

# ab:aba=aaa,bbb=1 ab - -
aba=aaa
bbb=1

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

1 total

Σ	#	Presentation	Mapping
11	23288	⟨a, b \| aaa=1, abbb=abab⟩	φ(a) = b, φ(b) = a