Certificate for #12902 ⟨a, b | aab=aaa, babb=a⟩

Back:⟨a, b | aab=aaa, babb=a⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #1.

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

[2] babb=a

Axiom: babb=a.

Defines rule #4.

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

[3] baba=aaaa

Overlap of [2] babb=a with [2] babb=a:

bab b babb

Critical pair: baba=aabb.

Reduce RHS:

[1](aab)b
[1]⇒ a(aab)
⇒ aaaa

Defines rule #3.

Referenced by [5].

[4] aaaaaa=aaa

Overlap of [1] aab=aaa with [2] babb=a:

aa b babb

Critical pair: aaa=aaaabb.

Reduce RHS:

[1]aa(aab)b
[1]⇒ aaa(aab)
⇒ aaaaaa

Flip LHS and RHS.

Defines rule #5.

Referenced by [5].

[5] baa=aaa

Overlap of [3] baba=aaaa with [2] babb=a:

ba ba babb

Critical pair: baa=aaaabb.

Reduce RHS:

[1]aa(aab)b
[1]⇒ aaa(aab)
[4]⇒ (aaaaaa)
⇒ aaa

Defines rule #2.