#451 ⟨a, b | bab=ab, bbb=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by a is not injective:
- b ⋅ a = a and 1 ⋅ a = 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.	ba ⇒ a	[3]
2.	b³ ⇒ 1	[2]

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

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

10 total

Σ	#	Presentation	Mapping
9	2419	⟨a, b \| aaa=1, aaaab=b⟩	φ(a) = b, φ(b) = a
9	2564	⟨a, b \| aaa=1, aaab=ab⟩	φ(a) = b, φ(b) = a
9	2569	⟨a, b \| aaa=1, aaba=ba⟩	φ(a) = b, φ(b) = a
10	7483	⟨a, b \| aaa=1, aaaaab=b⟩	φ(a) = b, φ(b) = a
10	8031	⟨a, b \| aaa=1, aaab=aab⟩	φ(a) = b, φ(b) = a
10	8040	⟨a, b \| aaa=1, aaba=aba⟩	φ(a) = b, φ(b) = a
11	22196	⟨a, b \| aaa=1, aaaaab=ab⟩	φ(a) = b, φ(b) = a
11	22201	⟨a, b \| aaa=1, aaaaba=ba⟩	φ(a) = b, φ(b) = a
11	22727	⟨a, b \| aaa=1, aaaab=aab⟩	φ(a) = b, φ(b) = a
11	22736	⟨a, b \| aaa=1, aaaba=aba⟩	φ(a) = b, φ(b) = a