#5733 ⟨a, b, c | aa=b, bbb=cc⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a⁴ca has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaaabb⟩
- Embedding: φ(a) = a, φ(b) = aa, 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

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:aa=b,bbb=cc ac/b - -
cca=acc
aaaaaa=cc
b=aa

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	3497	⟨a, b, c \| bb=aa, ccc=a⟩	Can Inf
8	5266	⟨a, b, c \| aa=b, cbbc=b⟩	Can Inf
8	5767	⟨a, b, c \| aa=b, cbc=bb⟩	Can Inf