#5186 ⟨a, b | aab=ba, bbba=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b³ = a and a ⋅ 1 = a, however b³ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁷ ⋅ a = a and 1 ⋅ a = a, however a⁷ ≠ 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

# ab:aab=ba,bbba=a reversed:a/b - -
aaaaaaaa=a
ba=aab
abbb=a

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

2 total

Σ	#	Presentation	Mapping
11	14486	⟨a, b \| aaab=b, aabba=b⟩	φ(a) = b, φ(b) = a
11	15723	⟨a, b \| aab=ba, bbaab=a⟩	φ(a) = a, φ(b) = b