#16330 ⟨a, b | aab=bb, bbba=ab⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b³ = b² and b ⋅ b = b², however b³ ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b³ ⋅ b = b² and b ⋅ b = b², however b³ ≠ b

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=bb,bbba=ab reversed:b/a - -
bbbb=bb
ab=bbba
bbaa=bbb

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

1 total

Σ	#	Presentation	Mapping
11	16460	⟨a, b \| aba=bb, abbb=ab⟩	φ(a) = a, φ(b) = b

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

2 total

Σ	#	Presentation	Mapping
11	16461	⟨a, b \| aba=bb, abbb=ba⟩	φ(a) = a, φ(b) = b
11	16468	⟨a, b \| aba=bb, babb=ba⟩	φ(a) = a, φ(b) = b