#2996 ⟨a, b | ab=a, bbbba=a⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- b⁴ ⋅ a = a and 1 ⋅ a = a, however b⁴ ≠ 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.	ab ⇒ a	[1]
2.	b⁴a ⇒ a	[2]

# ab:ab=a,bbbba=a ab - -
ab=a
bbbba=a

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

6 total

Σ	#	Presentation	Mapping
10	8834	⟨a, b \| ab=a, bbbbab=a⟩	φ(a) = a, φ(b) = b
10	9105	⟨a, b \| ab=a, bbbba=ab⟩	φ(a) = a, φ(b) = b
11	15844	⟨a, b \| aba=ab, aaaab=b⟩	φ(a) = b, φ(b) = a
11	24578	⟨a, b \| ab=a, bbbbabb=a⟩	φ(a) = a, φ(b) = b
11	25105	⟨a, b \| ab=a, bbbbab=ab⟩	φ(a) = a, φ(b) = b
11	25647	⟨a, b \| ab=a, bbbba=abb⟩	φ(a) = a, φ(b) = b