#5567 ⟨a, b, c | ab=c, baca=c⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaba^-1b^-1⟩
- Embedding: φ(a) = ba, φ(b) = a^-1b^-1b^-1, 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

Auxiliary generators:
1. d = ac
Reduction order:
- Right-to-left recursive path with deg(c) = deg(b) = deg(d) = 0, c < b < d; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:ab=c,baca=c reversed:cbd/a ac=d morph:2/0
cdc=db
bdc=cb
cdd=dc
bdd=cc
cda=d
bda=c
ac=d
ab=c
ad=dda

6 unique, 26 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	554	⟨a, b, c \| bb=ac, ca=b⟩	Can Inf	3
7	1041	⟨a, b, c \| ab=c, bca=c⟩	Can Inf	2
8	5675	⟨a, b, c \| aa=b, aac=ca⟩	Can Inf	1
8	6101	⟨a, b, c \| ab=c, cac=ba⟩	Can Inf