#15531 ⟨a, b | aaa=bb, abbbb=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b⁴ = a and a ⋅ 1 = a, however b⁴ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b⁵ ⋅ b = b² and b ⋅ b = b², however b⁵ ≠ 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

# ab:aaa=bb,abbbb=a ab - -
aaa=bb
bba=abb
abbbb=a
bbbbbb=bb

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

1 total

Σ	#	Presentation	Mapping
11	15541	⟨a, b \| aaa=bb, bbabb=a⟩	φ(a) = a, φ(b) = b