#3535 ⟨a, b, c | bb=ac, bca=c⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabab^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = b^-1aa, φ(b) = a, φ(c) = b

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

# abc:bb=ac,bca=c abd/c abc=d morph:3/3
da=bb
bdbb=dd
adbba=d
ddbba=adbbd
dddbb=bdbdd
c=dbbaa

4 unique, 9 total

Σ	#	Presentation	Properties	φ
8	2988	⟨a, b, c \| aab=c, bcb=a⟩	Can Inf	2
8	3510	⟨a, b, c \| bb=ac, aba=c⟩	Can Inf	2
8	5585	⟨a, b, c \| ab=c, bcac=a⟩	Can Inf
8	6037	⟨a, b, c \| ab=c, aca=bc⟩	Can Inf	1

5 unique, 50 total

Σ	#	Presentation	Properties	φ
8	1714	⟨a, b, c \| aab=bc, cba=1⟩	Grp Inf	38
8	2984	⟨a, b, c \| aab=c, bbc=a⟩	Can Inf	5
8	3474	⟨a, b, c \| ba=ac, cbb=a⟩	Can Inf
8	3524	⟨a, b, c \| bb=ac, baa=c⟩	Can Inf	2
8	5568	⟨a, b, c \| ab=c, bacc=a⟩	Can Inf