#4345 ⟨a, b, c | aab=1, ccac=a⟩

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 ⋅ aba = a and a ⋅ 1 = a, however aba ≠ 1
Not right cancellative, because right multiplication by ab is not injective:
- aba ⋅ ab = ab and 1 ⋅ ab = ab, however aba ≠ 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

Reduction order:
- Right-to-left recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aab=1,ccac=a reversed:bc/a - -
ccac=a
aab=1
aac=ccccaa
acac=ccaa