#16067 ⟨a, b | aaa=bb, abbb=aa⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b⁸ = b² and b ⋅ b = b², however b⁸ ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b⁸ ⋅ b = b² and b ⋅ b = b², however b⁸ ≠ 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,abbb=aa b/a - -
bbbbbbbbb=bb
abb=bbbbb
bba=bbbbb
aa=bbbbbb

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

1 total

Σ	#	Presentation	Mapping
11	16074	⟨a, b \| aaa=bb, babb=aa⟩	φ(a) = a, φ(b) = b