#5370 ⟨a, b | aab=aa, bba=ab⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by a is not injective:
- b⁴a ⋅ a = a² and a ⋅ a = a², however b⁴a ≠ 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.	ab ⇒ b²a	[2]
2.	b⁴a² ⇒ a²	[3]

# ab:aab=aa,bba=ab reversed:b/a - -
ab=bba
bbbbaa=aa

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

1 total

Σ	#	Presentation	Mapping
11	16248	⟨a, b \| aab=ba, baab=bb⟩	φ(a) = b, φ(b) = a