#2057 ⟨a, b | abababba=ab⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ cda = c and c ⋅ 1 = c, however cda ≠ 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. c = ab
2. d = cb
Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(d) = deg(b) = 1, d < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abababba=ab reversed:ac/db ab=c,cb=d morph:2/0,2/0
ccda=c
ccdc=d
ab=c
cb=d
dda=ccd
dcda=d
ddc=ccccdd
dcdc=ccdd
db=ccdd