#6154 ⟨a, b, c | aa=1, abaccb=1⟩

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element ab has infinite order
Inverses of generators:
- a^-1 = a
- b^-1 = adba
- c^-1 = (ba)²c
- d^-1 = (ba)²

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

# abc:aa=1,abaccb=1 reversed:bad/c cc=d morph:2/0
aa=1
bad=dba
dbab=a
cd=dc
cbab=babaca
cc=d

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

1 total

Σ	#	Presentation	Mapping
8	6732	⟨a, b, c \| aa=1, baccb=a⟩	φ(a) = a, φ(b) = b, φ(c) = c