Certificate for #16512 ⟨a, b | aab=ba, bab=aaa⟩

Back:⟨a, b | aab=ba, bab=aaa⟩

Completion settings:

[1] ba=aab

Axiom: aab=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3], [4].

[2] aabb=aaa

Axiom: bab=aaa.

Reduce LHS:

[1](ba)b
⇒ aabb

Defines rule #3.

Referenced by [3], [4], [6].

[3] aaaaaab=aaaaab

Overlap of [1] ba=aab with [2] aabb=aaa:

b a aabb

Critical pair: baaa=aababb.

Reduce LHS:

[1](ba)aa
[1]⇒ aa(ba)a
[1]⇒ aaaa(ba)
⇒ aaaaaab

Reduce RHS:

[1]aa(ba)bb
[2]⇒ aa(aabb)b
⇒ aaaaab

Referenced by [4], [5].

[4] aaaaaa=aaaa

Overlap of [2] aabb=aaa with [1] ba=aab:

aab b ba

Critical pair: aabaab=aaaa.

Reduce LHS:

[1]aa(ba)ab
[1]⇒ aaaa(ba)b
[3]⇒ (aaaaaab)b
[2]⇒ aaa(aabb)
⇒ aaaaaa

Referenced by [5], [6].

[5] aaaaab=aaaab

Simplify [3] aaaaaab=aaaaab.

Reduce LHS:

[4](aaaaaa)b
⇒ aaaab

Flip LHS and RHS.

Referenced by [6].

[6] aaaaa=aaaa

Overlap of [5] aaaaab=aaaab with [2] aabb=aaa:

aaa aab aabb

Critical pair: aaaaaa=aaaabb.

Reduce LHS:

[4](aaaaaa)
⇒ aaaa

Reduce RHS:

[2]aa(aabb)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #1.