Certificate for #20051 ⟨a, b | aab=b, aaaa=abb⟩

Back:⟨a, b | aab=b, aaaa=abb⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

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

[2] aaaa=abb

Axiom: aaaa=abb.

Defines rule #4.

Referenced by [3], [4].

[3] abbb=b

Overlap of [2] aaaa=abb with [1] aab=b:

aa aa aab

Critical pair: aab=abbb.

Reduce LHS:

[1](aab)
⇒ b

Flip LHS and RHS.

Referenced by [5], [7].

[4] abba=bb

Overlap of [2] aaaa=abb with [2] aaaa=abb:

a aaa aaaa

Critical pair: aabb=abba.

Reduce LHS:

[1](aab)b
⇒ bb

Flip LHS and RHS.

Referenced by [7].

[5] bbb=ab

Overlap of [1] aab=b with [3] abbb=b:

a ab abbb

Critical pair: ab=bbb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7].

[6] bab=abb

Overlap of [5] bbb=ab with [5] bbb=ab:

b bb bbb

Critical pair: bab=abb.

Referenced by [7].

[7] ba=ab

Overlap of [6] bab=abb with [4] abba=bb:

b ab abba

Critical pair: bbb=abbba.

Reduce LHS:

[5](bbb)
⇒ ab

Reduce RHS:

[3](abbb)a
⇒ ba

Flip LHS and RHS.

Defines rule #1.