Certificate for #19718 ⟨a, b | aba=b, aaabb=bb⟩

Back:⟨a, b | aba=b, aaabb=bb⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Defines rule #1.

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

[2] aaabb=bb

Axiom: aaabb=bb.

Defines rule #3.

Referenced by [4], [5].

[3] bba=abb

Overlap of [1] aba=b with [1] aba=b:

ab a aba

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[4] baabb=abbb

Overlap of [1] aba=b with [2] aaabb=bb:

ab a aaabb

Critical pair: abbb=baabb.

Flip LHS and RHS.

Defines rule #5.

[5] aabbb=babb

Overlap of [2] aaabb=bb with [3] bba=abb:

aaab b bba

Critical pair: aaababb=bbba.

Reduce LHS:

[1]aa(aba)bb
⇒ aabbb

Reduce RHS:

[3]b(bba)
⇒ babb

Defines rule #4.