#3678 ⟨a, b | aa=1, bbbb=bab⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab = b⁴ and b ⋅ b³ = b⁴, however ab ≠ b³
Not right cancellative, because right multiplication by b is not injective:
- ba ⋅ b = b⁴ and b³ ⋅ b = b⁴, however ba ≠ b³

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.	bab ⇒ b⁴	[2]
2.	a² ⇒ 1	[1]

# ab:aa=1,bbbb=bab b/a - -
bab=bbbb
aa=1

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

6 total

Σ	#	Presentation	Mapping
11	27609	⟨a, b \| aa=1, aabbbb=bab⟩	φ(a) = a, φ(b) = b
11	27723	⟨a, b \| aa=1, baabbb=bab⟩	φ(a) = a, φ(b) = b
11	27752	⟨a, b \| aa=1, bbaabb=bab⟩	φ(a) = a, φ(b) = b
11	28107	⟨a, b \| aa=1, aabab=bbbb⟩	φ(a) = a, φ(b) = b
11	28213	⟨a, b \| aa=1, abbbb=abab⟩	φ(a) = a, φ(b) = b
11	28233	⟨a, b \| aa=1, baaab=bbbb⟩	φ(a) = a, φ(b) = b