#146 ⟨a, b, c | aa=b, cc=b⟩

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) = a^-1, φ(b) = a^-1a^-1, 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,cc=b ac/b - -
cc=aa
caa=aac
b=aa

3 unique, 304 total

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

5 total

Σ	#	Presentation	Mapping
7	1053	⟨a, b, c \| aa=b, cc=aa⟩	φ(a) = a, φ(b) = aa, φ(c) = c
7	1061	⟨a, b, c \| ab=c, bb=aa⟩	φ(a) = a, φ(b) = c, φ(c) = ac
8	3477	⟨a, b, c \| bb=aa, aaa=c⟩	φ(a) = a, φ(b) = c, φ(c) = aaa
8	3478	⟨a, b, c \| bb=aa, aab=c⟩	φ(a) = a, φ(b) = c, φ(c) = aac
8	3482	⟨a, b, c \| bb=aa, aba=c⟩	φ(a) = a, φ(b) = c, φ(c) = aca