Certificate for #5345 ⟨a, b | aaa=bb, abb=aa⟩

Back:⟨a, b | aaa=bb, abb=aa⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3].

[2] aaaa=aa

Axiom: abb=aa.

Reduce LHS:

[1]a(bb)
⇒ aaaa

Defines rule #1.

Referenced by [4], [5], [6].

[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=abaaa

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

a aaa aaab

Critical pair: abaaa=aab.

Flip LHS and RHS.

Referenced by [5], [6].

[5] abaa=baaa

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

aa aa aaab

Critical pair: aabaaa=aaab.

Reduce LHS:

[4](aab)aaa
[2]⇒ ab(aaaa)aa
[2]⇒ ab(aaaa)
⇒ abaa

Reduce RHS:

[3](aaab)
⇒ baaa

Defines rule #2.

Referenced by [6].

[6] aab=baa

Simplify [4] aab=abaaa.

Reduce RHS:

[5](abaa)a
[2]⇒ b(aaaa)
⇒ baa

Defines rule #3.