#2574 ⟨a, b | aaa=1, aabb=bb⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not right cancellative, because right multiplication by b is not injective:
- ab ⋅ b = b² and b ⋅ b = b², however ab ≠ b

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.	a³ ⇒ 1	[1]
2.	ab² ⇒ b²	[3]

# ab:aaa=1,aabb=bb ab - -
aaa=1
abb=bb

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

8 total

Σ	#	Presentation	Mapping
10	8049	⟨a, b \| aaa=1, aabb=abb⟩	φ(a) = a, φ(b) = b
10	8059	⟨a, b \| aaa=1, abab=bab⟩	φ(a) = a, φ(b) = aab
11	22206	⟨a, b \| aaa=1, aaaabb=bb⟩	φ(a) = a, φ(b) = b
11	22253	⟨a, b \| aaa=1, abaaab=bb⟩	φ(a) = a, φ(b) = b
11	22745	⟨a, b \| aaa=1, aaabb=abb⟩	φ(a) = a, φ(b) = b
11	22761	⟨a, b \| aaa=1, aabab=bab⟩	φ(a) = a, φ(b) = aab
11	22770	⟨a, b \| aaa=1, aabba=bba⟩	φ(a) = a, φ(b) = b
11	22827	⟨a, b \| aaa=1, baaab=abb⟩	φ(a) = a, φ(b) = b

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

3 total

Σ	#	Presentation	Mapping
10	8065	⟨a, b \| aaa=1, abba=abb⟩	φ(a) = a, φ(b) = b
11	22218	⟨a, b \| aaa=1, aaabba=bb⟩	φ(a) = a, φ(b) = b
11	22748	⟨a, b \| aaa=1, aaabb=bba⟩	φ(a) = a, φ(b) = b