#27673 ⟨a, b | aa=1, abbabb=bbb⟩

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 ⋅ b⁶ = b⁴ and b ⋅ b³ = b⁴, however b⁶ ≠ b³
Not right cancellative, because right multiplication by b is not injective:
- b²ab ⋅ b = ab³ and ab² ⋅ b = ab³, however b²ab ≠ ab²

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:aa=1,abbabb=bbb b/a - -
bbbbbbb=bbbb
babbb=abbbbb
bbabb=abbb
aa=1

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

1 total

Σ	#	Presentation	Mapping
11	28282	⟨a, b \| aa=1, bbabb=abbb⟩	φ(a) = a, φ(b) = b