#2830 ⟨a, b, c | aaa=b, acb=c⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabab^-1⟩
- Embedding: φ(a) = a, φ(b) = aaa, 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:aaa=b,acb=c ac/b - -
acaaa=c
ccaaa=acaac
b=aaa

2 unique, 12 total

Σ	#	Presentation	Properties	φ
8	1585	⟨a, b, c \| aaa=bc, acb=1⟩	Grp Inf	7
8	2970	⟨a, b, c \| aab=c, aca=b⟩	Can Inf	3

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

1 total

Σ	#	Presentation	Mapping
8	5198	⟨a, b, c \| aa=b, acab=c⟩	φ(a) = a, φ(b) = aa, φ(c) = c