Certificate for #16439 ⟨a, b | aba=bb, aaaa=bb⟩

Back:⟨a, b | aba=bb, aaaa=bb⟩

Completion settings:

[1] bb=aba

Axiom: aba=bb.

Flip LHS and RHS.

Referenced by [2], [3].

[2] aba=aaaa

Axiom: aaaa=bb.

Reduce RHS:

[1](bb)
⇒ aba

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [5].

[3] bb=aaaa

Simplify [1] bb=aba.

Reduce RHS:

[2](aba)
⇒ aaaa

Defines rule #4.

Referenced by [4].

[4] aaaab=baaaa

Overlap of [3] bb=aaaa with [3] bb=aaaa:

b b bb

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] baaaaa=aaaaaaa

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

ab a aba

Critical pair: abaaaa=aaaaba.

Reduce LHS:

[2](aba)aaa
⇒ aaaaaaa

Reduce RHS:

[4](aaaab)a
⇒ baaaaa

Flip LHS and RHS.

Defines rule #1.