#2453 ⟨a, b | aaa=1, bbabb=b⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba² has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab³ = b and b ⋅ 1 = b, however ab³ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- bab² ⋅ b = b and 1 ⋅ b = b, however bab² ≠ 1

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=1,bbabb=b ab - -
aaa=1
bbab=babb
babbb=b

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

1 total

Σ	#	Presentation	Mapping
11	22278	⟨a, b \| aaa=1, abbabb=ab⟩	φ(a) = a, φ(b) = b