#5348 ⟨a, b | aaa=bb, abb=bb⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ba = b² and b ⋅ b = b², however ba ≠ b
Not right cancellative, because right multiplication by b is not injective:
- ab ⋅ b = b² and b ⋅ b = b², however ab ≠ 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:aaa=bb,abb=bb ab - -
aaa=bb
abb=bb
bba=bb
bbbb=bb

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

2 total

Σ	#	Presentation	Mapping
11	16047	⟨a, b \| aaa=bb, aaaa=bb⟩	φ(a) = a, φ(b) = b
11	16487	⟨a, b \| aaa=bb, abb=aaa⟩	φ(a) = a, φ(b) = b