#16056 ⟨a, b | aaa=bb, aabb=aa⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ c³ = c and c ⋅ 1 = c, however c³ ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- c³ ⋅ c = c and 1 ⋅ c = c, however c³ ≠ 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 = aa
Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(a) = 1; deg(b) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aaa=bb,aabb=aa c/a/b aa=c morph:2/0
cccc=c
ac=ccc
ca=ccc
aa=c
cbccc=cb
cba=cbcc
cccb=bccc
abc=ccbc
bb=ccc

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

1 total

Σ	#	Presentation	Mapping
11	16064	⟨a, b \| aaa=bb, abba=aa⟩	φ(a) = a, φ(b) = b