Certificate for #5344 ⟨a, b | aaa=bb, aba=bb⟩

Back:⟨a, b | aaa=bb, aba=bb⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [2], [3], [5].

[2] aba=aaa

Axiom: aba=bb.

Reduce RHS:

[1](bb)
⇒ aaa

Defines rule #3.

Referenced by [4], [5].

[3] aaab=baaa

Overlap of [1] bb=aaa with [1] bb=aaa:

b b bb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

[4] baaaa=aaaaa

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

ab a aba

Critical pair: abaaa=aaaba.

Reduce LHS:

[2](aba)aa
⇒ aaaaa

Reduce RHS:

[3](aaab)a
⇒ baaaa

Flip LHS and RHS.

Defines rule #2.

[5] aaaaaaa=aaaaaa

Overlap of [2] aba=aaa with [3] aaab=baaa:

ab a aaab

Critical pair: abbaaa=aaaaab.

Reduce LHS:

[1]a(bb)aaa
⇒ aaaaaaa

Reduce RHS:

[3]aa(aaab)
[2]⇒ a(aba)aa
⇒ aaaaaa

Defines rule #1.