#3671 ⟨a, b | aa=1, babb=bab⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab² = bab and b ⋅ ab = bab, however ab² ≠ ab
Not right cancellative, because right multiplication by b is not injective:
- bab ⋅ b = bab and ba ⋅ b = bab, however bab ≠ ba

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.	a² ⇒ 1	[1]
2.	bab² ⇒ bab	[2]

# ab:aa=1,babb=bab ab - -
aa=1
babb=bab

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

5 total

Σ	#	Presentation	Mapping
11	27579	⟨a, b \| aa=1, aababb=bab⟩	φ(a) = a, φ(b) = b
11	27707	⟨a, b \| aa=1, baaabb=bab⟩	φ(a) = a, φ(b) = b
11	28103	⟨a, b \| aa=1, aabab=babb⟩	φ(a) = a, φ(b) = b
11	28171	⟨a, b \| aa=1, ababb=abab⟩	φ(a) = a, φ(b) = b
11	28232	⟨a, b \| aa=1, baaab=babb⟩	φ(a) = a, φ(b) = b

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

4 total

Σ	#	Presentation	Mapping
11	27593	⟨a, b \| aa=1, aabbab=bab⟩	φ(a) = a, φ(b) = b
11	27715	⟨a, b \| aa=1, baabab=bab⟩	φ(a) = a, φ(b) = b
11	28105	⟨a, b \| aa=1, aabab=bbab⟩	φ(a) = a, φ(b) = b
11	28187	⟨a, b \| aa=1, abbab=abab⟩	φ(a) = a, φ(b) = b