#6095 ⟨a, b, c | ab=c, bcc=ca⟩

Properties

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

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

# abc:ab=c,bcc=ca b/dca cc=d morph:2/0
bdb=d
ab=c
bdd=ddb
cd=dc
cbd=da
cc=d
ca=bd
ad=dcb

10 unique, 117 total

Σ	#	Presentation	Properties	φ
7	366	⟨a, b, c \| aba=b, cbc=1⟩	Grp Inf	93
7	548	⟨a, b, c \| bb=aa, cc=a⟩	Can Inf	1
7	938	⟨a, b, c \| aa=b, cbc=b⟩	Can Inf	5
8	2849	⟨a, b, c \| aaa=b, cac=b⟩	Can Inf	2
8	2851	⟨a, b, c \| aaa=b, cbc=a⟩	Can Inf	3
8	3041	⟨a, b, c \| aba=b, cac=b⟩	Can Inf
8	3042	⟨a, b, c \| aba=b, cbc=a⟩	Can Inf	1
8	3472	⟨a, b, c \| ba=ac, cab=a⟩	Can Inf
8	3501	⟨a, b, c \| bb=ac, aaa=c⟩	Can Inf	2
8	3594	⟨a, b, c \| ba=ac, cb=aa⟩	Can Inf