#1891 ⟨a, b, c | aba=cc, acb=1⟩

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 ⋅ cba = a and a ⋅ 1 = a, however cba ≠ 1
Not right cancellative, because right multiplication by cb is not injective:
- cba ⋅ cb = cb and 1 ⋅ cb = cb, however cba ≠ 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:
- Left-to-right recursive path with deg(c) = deg(b) = 0, c < b; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aba=cc,acb=1 cb/a - -
ccccbcc=cc
ccbcccb=cccbccb
ab=cccb
acb=1
ccba=cccbcc