#3497 ⟨a, b, c | bb=aa, ccc=a⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element b has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaaabb⟩
- Embedding: φ(a) = a^-1a^-1a^-1, φ(b) = b, φ(c) = a^-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(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=aa,ccc=a bc/a - -
cbb=bbc
cccccc=bb
a=ccc

5 unique, 27 total

Σ	#	Presentation	Properties	φ
8	1577	⟨a, b, c \| aaa=bb, cac=1⟩	Grp Inf	22
8	2852	⟨a, b, c \| aaa=b, cbc=b⟩	Can Inf
8	5266	⟨a, b, c \| aa=b, cbbc=b⟩	Can Inf
8	5733	⟨a, b, c \| aa=b, bbb=cc⟩	Can Inf
8	5767	⟨a, b, c \| aa=b, cbc=bb⟩	Can Inf