#3631 ⟨a, b | aabbaaabba=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 ⋅ ab²a³b²a = a and a ⋅ 1 = a, however ab²a³b²a ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a²b²a³b² ⋅ a = a and 1 ⋅ a = a, however a²b²a³b² ≠ 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.	ab²a² ⇒ a²b²a	[5]
2.	a⁴(b²a)² ⇒ a	[3]

# ab:aabbaaabba=a ab - -
abbaa=aabba
aaaabbabba=a

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

1 total

Σ	#	Presentation	Mapping
11	3637	⟨a, b \| aabbaabbaa=a⟩	φ(a) = a, φ(b) = b