#523 ⟨a, b, c | ac=ab, bb=a⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bc = b³ and b ⋅ b² = b³, however bc ≠ b²

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

Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	b²c ⇒ b³	[4]
2.	a ⇒ b²	[2]

# abc:ac=ab,bb=a bc/a - -
bbc=bbb
a=bb

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

6 total

Σ	#	Presentation	Mapping
7	535	⟨a, b, c \| ba=ac, bb=a⟩	φ(a) = bb, φ(b) = b, φ(c) = c
8	2818	⟨a, b, c \| aaa=b, aac=b⟩	φ(a) = b, φ(b) = bbb, φ(c) = c
8	5662	⟨a, b, c \| aa=b, aaa=bc⟩	φ(a) = b, φ(b) = bb, φ(c) = c
8	5670	⟨a, b, c \| aa=b, aac=ab⟩	φ(a) = b, φ(b) = bb, φ(c) = c
8	5672	⟨a, b, c \| aa=b, aac=ba⟩	φ(a) = b, φ(b) = bb, φ(c) = c
8	5989	⟨a, b, c \| ab=c, aaa=ac⟩	φ(a) = b, φ(b) = c, φ(c) = bc