#916 ⟨a, b, c | aa=b, acb=c⟩

Properties

Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabab^-1⟩
- 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,acb=c ac/b - -
acaa=c
ccaa=acac
b=aa

2 unique, 45 total

Σ	#	Presentation	Properties	φ
7	500	⟨a, b, c \| bb=ac, bca=1⟩	Grp Inf	40
7	1024	⟨a, b, c \| ab=c, aca=b⟩	Can Inf	3

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

2 total

Σ	#	Presentation	Mapping
8	5262	⟨a, b, c \| aa=b, cacc=a⟩	φ(a) = c, φ(b) = cc, φ(c) = a
8	5512	⟨a, b, c \| ab=c, abaa=b⟩	φ(a) = a, φ(b) = c, φ(c) = ac