Certificate for #16079 ⟨a, b | aaa=bb, bbbb=ab⟩

Back:⟨a, b | aaa=bb, bbbb=ab⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

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

[2] ab=aaaaaa

Axiom: bbbb=ab.

Reduce LHS:

[1](bb)bb
[1]⇒ aaa(bb)
⇒ aaaaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] baaa=aaaaaaaa

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

b b bb

Critical pair: baaa=aaab.

Reduce RHS:

[2]aa(ab)
⇒ aaaaaaaa

Defines rule #2.

[4] aaaaaaaaaaa=aaaa

Overlap of [2] ab=aaaaaa with [1] bb=aaa:

a b bb

Critical pair: aaaa=aaaaaab.

Reduce RHS:

[2]aaaaa(ab)
⇒ aaaaaaaaaaa

Flip LHS and RHS.

Defines rule #1.