#554 ⟨a, b, c | bb=ac, ca=b⟩

Properties

Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaba^-1b^-1⟩
- Embedding: φ(a) = aab, φ(b) = a, φ(c) = b^-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

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

# abc:bb=ac,ca=b ab/c - -
bba=ab
ca=b
ac=bb
bc=cbb

6 unique, 23 total

Σ	#	Presentation	Properties	φ
7	417	⟨a, b, c \| abc=b, cba=1⟩	Grp Inf	10
7	537	⟨a, b, c \| ba=ac, bb=c⟩	Can Inf	4
7	1041	⟨a, b, c \| ab=c, bca=c⟩	Can Inf	2
8	5567	⟨a, b, c \| ab=c, baca=c⟩	Can Inf
8	5675	⟨a, b, c \| aa=b, aac=ca⟩	Can Inf	1
8	6101	⟨a, b, c \| ab=c, cac=ba⟩	Can Inf

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

3 total

Σ	#	Presentation	Mapping
8	3454	⟨a, b, c \| ba=ac, acb=c⟩	φ(a) = c, φ(b) = a, φ(c) = ab
8	3460	⟨a, b, c \| ba=ac, bab=c⟩	φ(a) = c, φ(b) = a, φ(c) = ab
8	6026	⟨a, b, c \| ab=c, abc=ba⟩	φ(a) = c, φ(b) = a, φ(c) = b