#1635 ⟨a, b | aab=ba, aba=b⟩

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 b is not injective:
- b ⋅ a³ = b and b ⋅ 1 = b, however a³ ≠ 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.	ba³ ⇒ b	[4]
2.	ab ⇒ ba²	[3]

# ab:aab=ba,aba=b a/b - -
baaa=b
ab=baa

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

8 total

Σ	#	Presentation	Mapping
9	2107	⟨a, b \| aba=b, aaab=b⟩	φ(a) = a, φ(b) = b
10	5161	⟨a, b \| aab=ba, aaab=b⟩	φ(a) = a, φ(b) = b
11	12495	⟨a, b \| abaa=ba, baaa=b⟩	φ(a) = a, φ(b) = b
11	19165	⟨a, b \| aba=b, aaaaba=b⟩	φ(a) = a, φ(b) = b
11	19708	⟨a, b \| aba=b, aaaab=ab⟩	φ(a) = a, φ(b) = b
11	19713	⟨a, b \| aba=b, aaaba=ba⟩	φ(a) = a, φ(b) = b
11	20256	⟨a, b \| aba=b, aaab=aba⟩	φ(a) = a, φ(b) = b
11	20266	⟨a, b \| aba=b, aaba=baa⟩	φ(a) = a, φ(b) = b