Certificate for #15760 ⟨a, b | aab=bb, ababb=b⟩

Back:⟨a, b | aab=bb, ababb=b⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #1.

Referenced by [3], [4], [5].

[2] ababb=b

Axiom: ababb=b.

Referenced by [3], [5].

[3] bbabb=ab

Overlap of [1] aab=bb with [2] ababb=b:

a ab ababb

Critical pair: ab=bbabb.

Flip LHS and RHS.

Referenced by [4], [5].

[4] bab=abb

Overlap of [1] aab=bb with [3] bbabb=ab:

aa b bbabb

Critical pair: aaab=bbbabb.

Reduce LHS:

[1]a(aab)
⇒ abb

Reduce RHS:

[3]b(bbabb)
⇒ bab

Flip LHS and RHS.

Defines rule #2.

[5] bbbb=b

Overlap of [3] bbabb=ab with [3] bbabb=ab:

bba bb bbabb

Critical pair: bbaab=ababb.

Reduce LHS:

[1]bb(aab)
⇒ bbbb

Reduce RHS:

[2](ababb)
⇒ b

Defines rule #3.