#7837 ⟨a, b, c | ab=1, cac=bba⟩

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 ⋅ d² = a and a ⋅ 1 = a, however d² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- d² ⋅ b = b and 1 ⋅ b = b, however d² ≠ 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 = ac
Reduction order:
- Left-to-right recursive path with deg(d) = 0; deg(b) = deg(c) = 1, b < c; deg(a) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:ab=1,cac=bba d/bc/a ac=d morph:2/0
dddd=dd
ddb=b
cd=bdd
ddc=bd
cb=bdb
add=a
ab=1
ac=d
adc=adbd
ba=dd