#5252 ⟨a, b, c | aa=b, bccb=c⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabaab^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = aa, φ(c) = b^-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(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aa=b,bccb=c ac/b - -
cccaa=aaccc
aaccaa=c
caccaa=aaccac
b=aa

1 unique, 1 total

Σ	#	Presentation	Properties
8	5748	⟨a, b, c \| aa=b, bcb=cc⟩	Can Inf