#16455 ⟨a, b | aba=bb, abab=bb⟩

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=bb,abab=bb ab - -
aba=bb
bba=abb
bbb=bb
aabb=bb
babb=abb

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

1 total

Σ	#	Presentation	Mapping
11	16552	⟨a, b \| aba=bb, bbb=aba⟩	φ(a) = a, φ(b) = b