#1782 ⟨a, b, c | aab=cc, bbc=1⟩

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element ba has infinite order
Inverses of generators:
- a^-1 = ab⁵
- b^-1 = bc
- c^-1 = b²
Reduced group presentation: ⟨a, b | aaabbaabb⟩
- Isomorphism: φ(a) = b^-1, φ(b) = bbaa, 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(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aab=cc,bbc=1 bc/a - -
cb=bc
bbc=1
cca=babccc
bbba=cabbbbb
aa=bccc

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ	#	Presentation	Mapping
8	1784	⟨a, b, c \| aab=cc, bcb=1⟩	φ(a) = a, φ(b) = abbbbbabbbbbcc, φ(c) = c