#6489 ⟨a, b | aba=b, aaaab=b⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ a⁴ = b and b ⋅ 1 = b, however a⁴ ≠ 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.	ba⁴ ⇒ b	[6]
2.	ab ⇒ ba³	[5]

# ab:aba=b,aaaab=b a/b - -
baaaa=b
ab=baaa

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

2 total

Σ	#	Presentation	Mapping
10	6767	⟨a, b \| aba=b, aaab=ba⟩	φ(a) = a, φ(b) = b
10	6836	⟨a, b \| aba=b, baa=aab⟩	φ(a) = a, φ(b) = b