#3736 ⟨a, b | abaabababa=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(ba)³ = a and a ⋅ 1 = a, however ba²(ba)³ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- aba(ab)³ ⋅ a = a and 1 ⋅ a = a, however aba(ab)³ ≠ 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.	aba² ⇒ a²ba	[4]
2.	a²(ba)⁴ ⇒ a	[3]

# ab:abaabababa=a ab - -
abaa=aaba
aababababa=a

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

1 total

Σ	#	Presentation	Mapping
11	3763	⟨a, b \| ababaababa=a⟩	φ(a) = a, φ(b) = b