#10303 ⟨a, b | aa=1, abbbb=bbb⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab³ = b³ and b ⋅ b² = b³, however ab³ ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- bab² ⋅ b = b³ and b² ⋅ b = b³, however bab² ≠ b²

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,abbbb=bbb ab - -
aa=1
bbbb=abbb
babbb=bbb

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

1 total

Σ	#	Presentation	Mapping
10	10535	⟨a, b \| aa=1, bbbb=abbb⟩	φ(a) = a, φ(b) = b