#15932 ⟨a, b | aba=bb, abbbb=b⟩

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative commutative monoid
Commutative Gröbner basis: ⟨a, b | b⁸=b, ab=b⁵⟩
Not cancellative, because multiplication by b⁵ is not injective:
- a² ≠ b
- b⁵ ⋅ a² = b⁶
- b⁵ ⋅ b = b⁶
- Cancellative quotient is isomorphic to ℤ₇
Grothendieck group is isomorphic to ℤ₇
Group of units is isomorphic to ℤ₁
3 Archimedian components:
- 1, a, b

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

# ab:aba=bb,abbbb=b b/a
bbbbbbbb=b
ab=bbbbb
ba=bbbbb

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

2 total

Σ	#	Presentation	Mapping
11	15940	⟨a, b \| aba=bb, babbb=b⟩	φ(a) = a, φ(b) = b
11	15942	⟨a, b \| aba=bb, bbabb=b⟩	φ(a) = a, φ(b) = b

Up:	Monoids with two generators and two relations
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Next:	#15933 ⟨a, b \| aba=bb, baaab=a⟩