#20297 ⟨a, b | aba=b, abbb=bab⟩

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 ⋅ b² = b² and b ⋅ b = b², however b² ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b² ⋅ b = b² and b ⋅ b = b², however b² ≠ 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:aba=b,abbb=bab ab - -
aba=b
bab=abb
bba=abb
bbb=bb
aabb=bb

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

1 total

Σ	#	Presentation	Mapping
11	20311	⟨a, b \| aba=b, babb=bab⟩	φ(a) = a, φ(b) = b