#4873 ⟨a, b, c | ab=a, bbccb=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1

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

Auxiliary generators:
1. d = bcc
Reduction order:
- Right-to-left recursive path with deg(a) = deg(b) = deg(d) = 0, a < b < d; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:ab=a,bbccb=1 reversed:abd/c bcc=d morph:3/0
ab=a
ad=a
bd=db
dbb=1
cd=ddbcb
cbbb=bbbc
cc=ddb

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

2 total

Σ	#	Presentation	Mapping
8	4897	⟨a, b, c \| ab=a, bccbb=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	4943	⟨a, b, c \| ab=a, cbbbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c