#1279 ⟨a, b | aab=aaa, bbb=1⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab = a³ and a ⋅ a² = a³, however ab ≠ a²
Not right cancellative, because right multiplication by a is not injective:
- a⁴ ⋅ a = a² and a ⋅ a = a², however a⁴ ≠ a

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

# ab:aab=aaa,bbb=1 ab - -
aab=aaa
bbb=1
aaaaa=aa

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

1 total

Σ	#	Presentation	Mapping
11	23289	⟨a, b \| aaa=1, abbb=abba⟩	φ(a) = b, φ(b) = a