#5351 ⟨a, b | aaa=bb, bab=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 ⋅ ab = b² and b ⋅ b = b², however ab ≠ b
Not right cancellative, because right multiplication by b is not injective:
- ba ⋅ b = b² and b ⋅ b = b², however ba ≠ 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,bab=bb ab - -
aaa=bb
bab=bb
bba=abb
abbb=bbb
baabb=bbb
bbbbb=bbb

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

1 total

Σ	#	Presentation	Mapping
11	16488	⟨a, b \| aaa=bb, bab=aaa⟩	φ(a) = a, φ(b) = b