#5631 ⟨a, b, c | aa=a, abc=ca⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a ⋅ a = a and 1 ⋅ a = a, however a ≠ 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 = bcb
Reduction order:
- Right-to-left recursive path with deg(a) = deg(b) = deg(d) = 0, a < b < d; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:aa=a,abc=ca reversed:abd/c bcb=d morph:3/0
aa=a
abad=ad
ababc=abc
adabc=adc
ca=abc
bcb=d
adcb=adad
bcd=dcb
adcd=adadad