#7504 ⟨a, b, c | ab=1, bbaa=cc⟩

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

# abc:ab=1,bbaa=cc da/bc cbb=d morph:3/0
adaadd=daadad
aadaad=1
adaadad=d
b=adaad
cd=daad
aac=aadaa
cc=daadaa