#5269 ⟨a, b, c | aa=b, cbcc=b⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabbab^-1b^-1⟩
- Embedding: φ(a) = b^-1, φ(b) = b^-1b^-1, φ(c) = a

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(a) = 0, c < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aa=b,cbcc=b ca/b - -
caacc=aa
aaaacc=caacaa
b=aa

1 unique, 1 total

Σ	#	Presentation	Properties
8	4476	⟨a, b, c \| aba=1, cbcc=b⟩	Grp Inf