#5736 ⟨a, b | aaab=1, aaaab=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²ba = a and a ⋅ 1 = a, however a²ba ≠ 1
Not right cancellative, because right multiplication by a²b is not injective:
- a²ba ⋅ a²b = a²b and 1 ⋅ a²b = a²b, however a²ba ≠ 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

#	Rule	Proof
1.	a³b ⇒ 1	[1]

# ab:aaab=1,aaaab=a ab - -
aaab=1

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

3 total

Σ	#	Presentation	Mapping
10	5738	⟨a, b \| aaab=1, aaaba=a⟩	φ(a) = a, φ(b) = b
10	5741	⟨a, b \| aaab=1, aaabb=b⟩	φ(a) = a, φ(b) = b
10	5769	⟨a, b \| aaab=1, baaab=b⟩	φ(a) = a, φ(b) = b