#5293 ⟨a, b | aba=bb, bbbb=b⟩

Properties

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

# ab:aba=bb,bbbb=b bc/a ba=c morph:2/1
bbb=cc
bcc=b
ccb=b
ccc=c
ab=bbcb
ac=bb
ba=c
ca=cbbc

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

2 total

Σ	#	Presentation	Mapping
11	15926	⟨a, b \| aba=bb, ababb=b⟩	φ(a) = a, φ(b) = b
11	15938	⟨a, b \| aba=bb, babab=b⟩	φ(a) = a, φ(b) = b