Certificate for #15737 ⟨a, b | aab=bb, aaaaa=a⟩

Back:⟨a, b | aab=bb, aaaaa=a⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #1.

Referenced by [3], [4].

[2] aaaaa=a

Axiom: aaaaa=a.

Defines rule #4.

Referenced by [3].

[3] abbb=ab

Overlap of [2] aaaaa=a with [1] aab=bb:

aaa aa aab

Critical pair: aaabb=ab.

Reduce LHS:

[1]a(aab)b
⇒ abbb

Defines rule #2.

Referenced by [4].

[4] bbbb=bb

Overlap of [1] aab=bb with [3] abbb=ab:

a ab abbb

Critical pair: aab=bbbb.

Reduce LHS:

[1](aab)
⇒ bb

Flip LHS and RHS.

Defines rule #3.