#8606 ⟨a, b | aa=a, ababba=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a ⋅ a = a and 1 ⋅ a = a, however a ≠ 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.	a² ⇒ a	[1]
2.	abab²a ⇒ a	[2]

# ab:aa=a,ababba=a ab - -
aa=a
ababba=a

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

3 total

Σ	#	Presentation	Mapping
11	24086	⟨a, b \| aa=a, aababba=a⟩	φ(a) = a, φ(b) = b
11	24112	⟨a, b \| aa=a, abaabba=a⟩	φ(a) = a, φ(b) = b
11	24661	⟨a, b \| aa=a, ababba=aa⟩	φ(a) = a, φ(b) = b

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

1 total

Σ	#	Presentation	Mapping
11	24092	⟨a, b \| aa=a, aabbaba=a⟩	φ(a) = a, φ(b) = b