#12699 ⟨a, b | aba=aab, aabbb=1⟩

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 a is not injective:
- a ⋅ bab²a = a and a ⋅ 1 = a, however bab²a ≠ 1
Not right cancellative, because right multiplication by bab² is not injective:
- bab²a ⋅ bab² = bab² and 1 ⋅ bab² = bab², however bab²a ≠ 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:aba=aab,aabbb=1 ba - -
aab=aba
ababb=1
ababab=a

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

1 total

Σ	#	Presentation	Mapping
11	12703	⟨a, b \| aba=aab, ababb=1⟩	φ(a) = a, φ(b) = b