Certificate for #16068 ⟨a, b | aaa=bb, abbb=ab⟩

Back:⟨a, b | aaa=bb, abbb=ab⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [2], [3], [5].

[2] aaaab=ab

Axiom: abbb=ab.

Reduce LHS:

[1]a(bb)b
⇒ aaaab

Referenced by [4].

[3] aaab=baaa

Overlap of [1] bb=aaa with [1] bb=aaa:

b b bb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [6].

[4] abaaa=ab

Simplify [2] aaaab=ab.

Reduce LHS:

[3]a(aaab)
⇒ abaaa

Defines rule #3.

Referenced by [5], [6].

[5] aaaaaaa=aaaa

Overlap of [4] abaaa=ab with [4] abaaa=ab:

abaa a abaaa

Critical pair: abaaab=abbaaa.

Reduce LHS:

[4](abaaa)b
[1]⇒ a(bb)
⇒ aaaa

Reduce RHS:

[1]a(bb)aaa
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #1.

[6] baaaaaa=baaa

Overlap of [3] aaab=baaa with [4] abaaa=ab:

aa ab abaaa

Critical pair: aaab=baaaaaa.

Reduce LHS:

[3](aaab)
⇒ baaa

Flip LHS and RHS.

Defines rule #2.