#938 ⟨a, b, c | aa=b, cbc=b⟩

Properties

Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabb⟩
- Embedding: φ(a) = a, φ(b) = aa, φ(c) = aab

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,cbc=b ac/b - -
caac=aa
caaaa=aaaac
b=aa

10 unique, 112 total

Σ	#	Presentation	Properties	φ
7	366	⟨a, b, c \| aba=b, cbc=1⟩	Grp Inf	93
7	548	⟨a, b, c \| bb=aa, cc=a⟩	Can Inf	1
8	2849	⟨a, b, c \| aaa=b, cac=b⟩	Can Inf	2
8	2851	⟨a, b, c \| aaa=b, cbc=a⟩	Can Inf	3
8	3041	⟨a, b, c \| aba=b, cac=b⟩	Can Inf
8	3042	⟨a, b, c \| aba=b, cbc=a⟩	Can Inf	1
8	3472	⟨a, b, c \| ba=ac, cab=a⟩	Can Inf
8	3501	⟨a, b, c \| bb=ac, aaa=c⟩	Can Inf	2
8	3594	⟨a, b, c \| ba=ac, cb=aa⟩	Can Inf
8	6095	⟨a, b, c \| ab=c, bcc=ca⟩	Can Inf

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

3 total

Σ	#	Presentation	Mapping
8	5257	⟨a, b, c \| aa=b, caac=b⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5764	⟨a, b, c \| aa=b, cbc=aa⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	6065	⟨a, b, c \| ab=c, bac=aa⟩	φ(a) = a, φ(b) = c, φ(c) = ac

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

2 total

Σ	#	Presentation	Mapping
8	3518	⟨a, b, c \| bb=ac, aca=c⟩	φ(a) = c, φ(b) = a, φ(c) = aac
8	3530	⟨a, b, c \| bb=ac, bba=c⟩	φ(a) = c, φ(b) = a, φ(c) = aac