Certificate for #16408 ⟨a, b | aba=ab, baaa=bb⟩

Back:⟨a, b | aba=ab, baaa=bb⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

Referenced by [3], [4].

[2] baaa=bb

Axiom: baaa=bb.

Defines rule #3.

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

[3] abb=ab

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

a ba baaa

Critical pair: abb=abaa.

Reduce RHS:

[1](aba)a
[1]⇒ (aba)
⇒ ab

Defines rule #2.

Referenced by [5].

[4] bbba=bbb

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

baa a aba

Critical pair: baaab=bbba.

Reduce LHS:

[2](baaa)b
⇒ bbb

Flip LHS and RHS.

Defines rule #4.

[5] bbbb=bbb

Overlap of [2] baaa=bb with [3] abb=ab:

baa a abb

Critical pair: baaab=bbbb.

Reduce LHS:

[2](baaa)b
⇒ bbb

Flip LHS and RHS.

Defines rule #5.