#11074 ⟨a, b | baab=aab, bbbb=1⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by a is not injective:
- ba ⋅ a = a² and a ⋅ a = a², however ba ≠ a

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.	ba² ⇒ a²	[3]
2.	b⁴ ⇒ 1	[2]

# ab:baab=aab,bbbb=1 ab - -
baa=aa
bbbb=1

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

1 total

Σ	#	Presentation	Mapping
11	17630	⟨a, b \| aaaa=1, aaabb=bb⟩	φ(a) = b, φ(b) = a