Certificate for #16180 ⟨a, b | aab=ab, baaa=bb⟩

Back:⟨a, b | aab=ab, baaa=bb⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Defines rule #2.

Referenced by [3], [4].

[2] baaa=bb

Axiom: baaa=bb.

Defines rule #4.

Referenced by [3], [4].

[3] bab=bbb

Overlap of [2] baaa=bb with [1] aab=ab:

ba aa aab

Critical pair: baab=bbb.

Reduce LHS:

[1]b(aab)
⇒ bab

Defines rule #1.

Referenced by [4].

[4] bbbb=bbb

Overlap of [2] baaa=bb with [1] aab=ab:

baa a aab

Critical pair: baaab=bbab.

Reduce LHS:

[2](baaa)b
⇒ bbb

Reduce RHS:

[3]b(bab)
⇒ bbbb

Flip LHS and RHS.

Defines rule #3.