Certificate for #13043 ⟨a, b | abb=aba, bbbb=b⟩

Back:⟨a, b | abb=aba, bbbb=b⟩

Completion settings:

[1] aba=abb

Axiom: abb=aba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3], [4].

[2] bbbb=b

Axiom: bbbb=b.

Defines rule #2.

Referenced by [3], [4].

[3] abbba=ab

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

ab a aba

Critical pair: ababb=abbba.

Reduce LHS:

[1](aba)bb
[2]⇒ a(bbbb)
⇒ ab

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] abba=abbb

Overlap of [1] aba=abb with [3] abbba=ab:

ab a abbba

Critical pair: abab=abbbbba.

Reduce LHS:

[1](aba)b
⇒ abbb

Reduce RHS:

[2]a(bbbb)ba
⇒ abba

Flip LHS and RHS.

Defines rule #3.