#160 ⟨a, b, c | ab=c, bc=a⟩

Properties

Sum of relation sides is 6
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabb⟩
- Embedding: φ(a) = ba^-1b^-1, φ(b) = ba, 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(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:ab=c,bc=a ab/c - -
baa=aab
bab=a
c=ab

3 unique, 306 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
7	913	⟨a, b, c \| aa=b, aca=c⟩	Can Inf	4

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

3 total

Σ	#	Presentation	Mapping
7	934	⟨a, b, c \| aa=b, cac=a⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	2848	⟨a, b, c \| aaa=b, cac=a⟩	φ(a) = a, φ(b) = aaa, φ(c) = b
8	2977	⟨a, b, c \| aab=c, bab=a⟩	φ(a) = a, φ(b) = b, φ(c) = aab