#6413 ⟨a, b | aab=b, abbbb=b⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b⁶ = b and b ⋅ 1 = b, however b⁶ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b⁶ ⋅ b = b and 1 ⋅ b = b, however b⁶ ≠ 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.	b⁷ ⇒ b	[4]
2.	ab ⇒ b⁴	[3]

# ab:aab=b,abbbb=b b/a - -
bbbbbbb=b
ab=bbbb

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

1 total

Σ	#	Presentation	Mapping
10	6723	⟨a, b \| aab=b, bbbb=ab⟩	φ(a) = a, φ(b) = b