#555 ⟨a, b, c | bb=ac, cb=a⟩

Properties

Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element b has infinite order
Submonoid of enveloping group: ⟨a, b | aaabb⟩
- Embedding: φ(a) = a^-1a^-1b^-1a^-1, φ(b) = a^-1, φ(c) = ab

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

# abc:bb=ac,cb=a bc/a - -
cbc=bb
cbbb=bbbc
a=cb

12 unique, 169 total

Σ	#	Presentation	Properties	φ
7	279	⟨a, b, c \| aaa=b, cbc=1⟩	Grp Inf	146
7	543	⟨a, b, c \| ba=ac, cb=a⟩	Can Inf
7	558	⟨a, b, c \| bb=ac, cc=a⟩	Can Inf	2
7	937	⟨a, b, c \| aa=b, cbc=a⟩	Can Inf	2
7	1042	⟨a, b, c \| ab=c, bcc=a⟩	Can Inf	2
8	3045	⟨a, b, c \| aba=c, abc=b⟩	Can Inf	2
8	3051	⟨a, b, c \| aba=c, bab=c⟩	Can Inf
8	3071	⟨a, b, c \| abc=b, bca=c⟩	Can Inf	2
8	3595	⟨a, b, c \| ba=ac, cb=ac⟩	Can Inf
8	5663	⟨a, b, c \| aa=b, aaa=cc⟩	Can Inf	1
8	6019	⟨a, b, c \| ab=c, aba=bc⟩	Can Inf
8	6071	⟨a, b, c \| ab=c, bac=ca⟩	Can Inf

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

2 total

Σ	#	Presentation	Mapping
7	935	⟨a, b, c \| aa=b, cac=b⟩	φ(a) = b, φ(b) = bb, φ(c) = c
8	5758	⟨a, b, c \| aa=b, cac=aa⟩	φ(a) = b, φ(b) = bb, φ(c) = c

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

2 total

Σ	#	Presentation	Mapping
8	5700	⟨a, b, c \| aa=b, aca=cc⟩	φ(a) = c, φ(b) = cc, φ(c) = b
8	6018	⟨a, b, c \| ab=c, aba=bb⟩	φ(a) = c, φ(b) = b, φ(c) = cb