#913 ⟨a, b, c | aa=b, aca=c⟩

Properties

Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabb⟩
- Embedding: φ(a) = ba, φ(b) = baba, 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:aa=b,aca=c ac/b - -
aca=c
cca=acc
b=aa

3 unique, 305 total

Σ	#	Presentation	Properties	φ
6	68	⟨a, b, c \| aab=1, bcc=1⟩	Grp Inf	294
6	146	⟨a, b, c \| aa=b, cc=b⟩	Can Inf	5
6	160	⟨a, b, c \| ab=c, bc=a⟩	Can Inf	3

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

4 total

Σ	#	Presentation	Mapping
7	1018	⟨a, b, c \| ab=c, aba=b⟩	φ(a) = a, φ(b) = c, φ(c) = ac
8	2827	⟨a, b, c \| aaa=b, aca=c⟩	φ(a) = a, φ(b) = aaa, φ(c) = c
8	2963	⟨a, b, c \| aab=c, aba=b⟩	φ(a) = a, φ(b) = c, φ(c) = aac
8	3035	⟨a, b, c \| aba=b, bab=c⟩	φ(a) = a, φ(b) = c, φ(c) = cac