#5205 ⟨a, b | aab=bb, abbb=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 ⋅ b⁵ = b and b ⋅ 1 = b, however b⁵ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b⁵ ⋅ b = b and 1 ⋅ b = b, however b⁵ ≠ 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.	b⁶ ⇒ b	[4]
2.	ab ⇒ b⁴	[3]

# ab:aab=bb,abbb=b b/a - -
bbbbbb=b
ab=bbbb

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

3 total

Σ	#	Presentation	Mapping
11	14581	⟨a, b \| aaba=a, babba=a⟩	φ(a) = b, φ(b) = a
11	15744	⟨a, b \| aab=bb, aaabb=b⟩	φ(a) = a, φ(b) = b
11	15756	⟨a, b \| aab=bb, abaab=b⟩	φ(a) = a, φ(b) = b

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

8 total

Σ	#	Presentation	Mapping
11	12166	⟨a, b \| aaaa=ab, aaab=a⟩	φ(a) = b, φ(b) = a
11	12168	⟨a, b \| aaaa=ab, aaba=a⟩	φ(a) = b, φ(b) = a
11	12172	⟨a, b \| aaaa=ab, abaa=a⟩	φ(a) = b, φ(b) = a
11	14423	⟨a, b \| aaab=a, aabbb=a⟩	φ(a) = b, φ(b) = a
11	14431	⟨a, b \| aaab=a, ababb=a⟩	φ(a) = b, φ(b) = a
11	14435	⟨a, b \| aaab=a, abbab=a⟩	φ(a) = b, φ(b) = a
11	14437	⟨a, b \| aaab=a, abbba=a⟩	φ(a) = b, φ(b) = a
11	14563	⟨a, b \| aaba=a, abbab=a⟩	φ(a) = b, φ(b) = a