#12170 ⟨a, b | aaaa=ab, aabb=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a⁷ = a and a ⋅ 1 = a, however a⁷ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁷ ⋅ a = a and 1 ⋅ a = a, however a⁷ ≠ 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.	a⁸ ⇒ a	[2]
2.	ab ⇒ a⁴	[1]

# ab:aaaa=ab,aabb=a a/b - -
aaaaaaaa=a
ab=aaaa

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

2 total

Σ	#	Presentation	Mapping
11	12174	⟨a, b \| aaaa=ab, abab=a⟩	φ(a) = a, φ(b) = b
11	12176	⟨a, b \| aaaa=ab, abba=a⟩	φ(a) = a, φ(b) = b