#2726 ⟨a, b, c | abc=a, bccb=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 ⋅ bc = a and a ⋅ 1 = a, however bc ≠ 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 = cc
Reduction order:
- Left-to-right 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:abc=a,bccb=1 abd/c cc=d morph:2/0
db=bd
bbd=1
ac=abd
dc=cd
abc=a
bbc=cbb
cc=d

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

1 total

Σ	#	Presentation	Mapping
8	2742	⟨a, b, c \| abc=a, cbbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c