#13110 ⟨a, b | bbb=aaa, aaaa=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b³ = a and a ⋅ 1 = a, however b³ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- b³ ⋅ a = a and 1 ⋅ a = a, however b³ ≠ 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

# ab:bbb=aaa,aaaa=a ba - -
aaa=bbb
bbba=a
abbb=a
bbbbbb=bbb

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

1 total

Σ	#	Presentation	Mapping
11	13113	⟨a, b \| bbb=aaa, aaab=b⟩	φ(a) = b, φ(b) = a