#2854 ⟨a, b, c | aaa=b, ccc=b⟩

Properties

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

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

# abc:aaa=b,ccc=b ac/b - -
ccc=aaa
caaa=aaac
b=aaa

4 unique, 30 total

Σ	#	Presentation	Properties	φ
8	2084	⟨a, b, c \| aaab=1, bccc=1⟩	Grp Inf	26
8	2991	⟨a, b, c \| aab=c, bcc=a⟩	Can Inf
8	3602	⟨a, b, c \| bb=ac, cb=aa⟩	Can Inf
8	6089	⟨a, b, c \| ab=c, bcc=aa⟩	Can Inf

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

1 total

Σ	#	Presentation	Mapping
8	5771	⟨a, b, c \| aa=b, ccc=ab⟩	φ(a) = a, φ(b) = aa, φ(c) = c