⟨a, b, c | aba=a, bccb=1⟩

Up:

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:

Not right cancellative, because right multiplication by a is not injective:

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

# abc:aba=a,bccb=1 ab/dc cb=d morph:2/0 aba=a bbd=dbb cb=d bbc=db dbd=b dbc=1 cdb=1 bcd=1 bcc=cd dcd=c cdd=bdcc ccd=dcc

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

Σ	#	Presentation	Mapping
8	2591	⟨a, b, c \| aba=a, cbbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c

Presentation

Mapping

2591

⟨a, b, c | aba=a, cbbc=1⟩

φ(a) = a, φ(b) = b, φ(c) = c

#2586 ⟨a, b, c | aba=a, bccb=1⟩