#13020 ⟨a, b | abb=aba, abaa=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba² = a and a ⋅ 1 = a, however ba² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- aba ⋅ a = a and 1 ⋅ a = a, however aba ≠ 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

#	Rule	Proof
1.	ab² ⇒ aba	[1]
2.	aba² ⇒ a	[2]

# ab:abb=aba,abaa=a ab - -
abb=aba
abaa=a

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

1 total

Σ	#	Presentation	Mapping
11	13024	⟨a, b \| abb=aba, abba=a⟩	φ(a) = a, φ(b) = b