#930 ⟨a, b, c | aa=b, bcb=c⟩

Properties

Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabaab^-1⟩
- Embedding: φ(a) = a, φ(b) = aa, 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,bcb=c ac/b - -
ccaa=aacc
aacaa=c
cacaa=aacac
b=aa

2 unique, 17 total

Σ	#	Presentation	Properties	φ
8	2179	⟨a, b, c \| aabb=1, bacc=1⟩	Grp Inf	15
8	3490	⟨a, b, c \| bb=aa, acb=c⟩	Can Inf

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

4 total

Σ	#	Presentation	Mapping
8	2992	⟨a, b, c \| aab=c, caa=b⟩	φ(a) = a, φ(b) = c, φ(c) = aac
8	3047	⟨a, b, c \| aba=c, aca=b⟩	φ(a) = a, φ(b) = c, φ(c) = aca
8	5174	⟨a, b, c \| aa=b, aacb=c⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5535	⟨a, b, c \| ab=c, acaa=b⟩	φ(a) = a, φ(b) = c, φ(c) = ac