#54 ⟨a, b | ab=a, bbb=1⟩

Properties

Sum of relation sides is 6
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

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.	b³ ⇒ 1	[2]

# ab:ab=a,bbb=1 ab - -
ab=a
bbb=1

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

12 total

Σ	#	Presentation	Mapping
7	139	⟨a, b \| abb=a, bbb=1⟩	φ(a) = a, φ(b) = b
8	447	⟨a, b \| abb=ab, bbb=1⟩	φ(a) = a, φ(b) = b
9	2421	⟨a, b \| aaa=1, aaaba=b⟩	φ(a) = b, φ(b) = a
9	2565	⟨a, b \| aaa=1, aaab=ba⟩	φ(a) = b, φ(b) = a
10	7489	⟨a, b \| aaa=1, aaabaa=b⟩	φ(a) = b, φ(b) = a
10	8034	⟨a, b \| aaa=1, aaab=baa⟩	φ(a) = b, φ(b) = a
10	8039	⟨a, b \| aaa=1, aaba=aab⟩	φ(a) = b, φ(b) = a
11	22200	⟨a, b \| aaa=1, aaaaba=ab⟩	φ(a) = b, φ(b) = a
11	22209	⟨a, b \| aaa=1, aaabaa=ba⟩	φ(a) = b, φ(b) = a
11	22728	⟨a, b \| aaa=1, aaaab=aba⟩	φ(a) = b, φ(b) = a
11	22738	⟨a, b \| aaa=1, aaaba=baa⟩	φ(a) = b, φ(b) = a
11	22751	⟨a, b \| aaa=1, aabaa=aab⟩	φ(a) = b, φ(b) = a