Certificate for #13131 ⟨a, b | aab=aaa, baa=bb⟩

Back:⟨a, b | aab=aaa, baa=bb⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #3.

Referenced by [3], [4].

[2] bb=baa

Axiom: baa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[3] baaaa=baaa

Overlap of [2] bb=baa with [2] bb=baa:

b b bb

Critical pair: bbaa=baab.

Reduce LHS:

[2](bb)aa
⇒ baaaa

Reduce RHS:

[1]b(aab)
⇒ baaa

Defines rule #2.

[4] aaaaa=aaaa

Overlap of [1] aab=aaa with [2] bb=baa:

aa b bb

Critical pair: aabaa=aaab.

Reduce LHS:

[1](aab)aa
⇒ aaaaa

Reduce RHS:

[1]a(aab)
⇒ aaaa

Defines rule #1.