#1024 ⟨a, b, c | ab=c, aca=b⟩

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) = bab^-1, φ(b) = b, φ(c) = ba

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(b) = deg(a) = 0, b < a; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:ab=c,aca=b ba/c - -
aabb=baba
aaba=b
c=ab

2 unique, 44 total

Σ	#	Presentation	Properties	φ
7	500	⟨a, b, c \| bb=ac, bca=1⟩	Grp Inf	40
7	916	⟨a, b, c \| aa=b, acb=c⟩	Can Inf	2

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

3 total

Σ	#	Presentation	Mapping
7	1037	⟨a, b, c \| ab=c, bbc=a⟩	φ(a) = b, φ(b) = a, φ(c) = ba
8	5171	⟨a, b, c \| aa=b, aaca=c⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	5495	⟨a, b, c \| ab=c, aaba=b⟩	φ(a) = a, φ(b) = b, φ(c) = ab