Certificate for #20304 ⟨a, b | aba=b, baab=bab⟩

Back:⟨a, b | aba=b, baab=bab⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Defines rule #1.

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

[2] baab=bab

Axiom: baab=bab.

Referenced by [4], [5], [6].

[3] bba=abb

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

ab a aba

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [5], [7].

[4] bab=bb

Overlap of [1] aba=b with [2] baab=bab:

a ba baab

Critical pair: abab=bab.

Reduce LHS:

[1](aba)b
⇒ bb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

[5] abb=bb

Overlap of [2] baab=bab with [1] aba=b:

ba ab aba

Critical pair: bab=baba.

Reduce LHS:

[4](bab)
⇒ bb

Reduce RHS:

[4](bab)a
[3]⇒ (bba)
⇒ abb

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[6] baab=bb

Simplify [2] baab=bab.

Reduce RHS:

[4](bab)
⇒ bb

Defines rule #5.

[7] bba=bb

Simplify [3] bba=abb.

Reduce RHS:

[5](abb)
⇒ bb

Defines rule #4.