#5286 ⟨a, b | aba=bb, abbb=a⟩

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 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:
- b³ ⋅ a = a and 1 ⋅ a = a, however b³ ≠ 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:aba=bb,abbb=a ab - -
aba=bb
abbb=a
bbba=a
bbbbb=bb

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

2 total

Σ	#	Presentation	Mapping
11	15915	⟨a, b \| aba=bb, aabab=a⟩	φ(a) = a, φ(b) = b
11	15923	⟨a, b \| aba=bb, ababa=a⟩	φ(a) = a, φ(b) = b