#1491 ⟨a, b | aab=aa, bbbb=1⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab = a² and a ⋅ a = a², however ab ≠ a

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.	a²b ⇒ a²	[1]
2.	b⁴ ⇒ 1	[2]

# ab:aab=aa,bbbb=1 ab - -
aab=aa
bbbb=1

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

2 total

Σ	#	Presentation	Mapping
11	10909	⟨a, b \| aabb=aab, bbbb=1⟩	φ(a) = a, φ(b) = b
11	10983	⟨a, b \| abab=aba, bbbb=1⟩	φ(a) = abbb, φ(b) = b