Certificate for #16078 ⟨a, b | aaa=bb, bbbb=aa⟩

Back:⟨a, b | aaa=bb, bbbb=aa⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3].

[2] aaaaaa=aa

Axiom: bbbb=aa.

Reduce LHS:

[1](bb)bb
[1]⇒ aaa(bb)
⇒ aaaaaa

Defines rule #1.

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.

Referenced by [4], [5].

[4] aab=baa

Overlap of [2] aaaaaa=aa with [3] aaab=baaa:

aaa aaa aaab

Critical pair: aaabaaa=aab.

Reduce LHS:

[3](aaab)aaa
[2]⇒ b(aaaaaa)
⇒ baa

Flip LHS and RHS.

Defines rule #3.

[5] abaa=baaa

Overlap of [2] aaaaaa=aa with [3] aaab=baaa:

aaaa aa aaab

Critical pair: aaaabaaa=aaab.

Reduce LHS:

[3]a(aaab)aaa
[2]⇒ ab(aaaaaa)
⇒ abaa

Reduce RHS:

[3](aaab)
⇒ baaa

Defines rule #2.