Certificate for #4165 ⟨a, b | abb=aba, baa=b⟩

Back:⟨a, b | abb=aba, baa=b⟩

Completion settings:

[1] abb=aba

Axiom: abb=aba.

Defines rule #1.

Referenced by [3], [4].

[2] baa=b

Axiom: baa=b.

Defines rule #2.

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

[3] bbb=bba

Overlap of [2] baa=b with [1] abb=aba:

ba a abb

Critical pair: baaba=bbb.

Reduce LHS:

[2](baa)ba
⇒ bba

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[4] abab=ab

Overlap of [1] abb=aba with [3] bbb=bba:

a bb bbb

Critical pair: abba=abab.

Reduce LHS:

[1](abb)a
[2]⇒ a(baa)
⇒ ab

Flip LHS and RHS.

Defines rule #4.

[5] bbab=bb

Overlap of [3] bbb=bba with [3] bbb=bba:

b bb bbb

Critical pair: bbba=bbab.

Reduce LHS:

[3](bbb)a
[2]⇒ b(baa)
⇒ bb

Flip LHS and RHS.

Defines rule #5.