#9749 ⟨a, b | aa=1, abbabbb=b⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ac has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ c² = c and c ⋅ 1 = c, however c² ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- c² ⋅ c = c and 1 ⋅ c = c, however c² ≠ 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. c = bab
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.
Morphocompletion: how the auxiliary generators were found.

# ab:aa=1,abbabbb=b ac/b bab=c morph:3/0
aa=1
ccc=c
ccac=ac
bcc=b
cb=abcacc
cab=bac
bab=c

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

1 total

Σ	#	Presentation	Mapping
10	10058	⟨a, b \| aa=1, bbabbb=ab⟩	φ(a) = a, φ(b) = b