#5401 ⟨a, b | aab=ba, bab=bb⟩

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 b is not injective:
- a²b ⋅ b = b² and b ⋅ b = b², however a²b ≠ b

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.	ba ⇒ a²b	[1]
2.	a²b² ⇒ b²	[2]

# ab:aab=ba,bab=bb reversed:a/b - -
ba=aab
aabb=bb

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

1 total

Σ	#	Presentation	Mapping
11	16224	⟨a, b \| aab=ba, aabb=bb⟩	φ(a) = a, φ(b) = b