Certificate for #16057 ⟨a, b | aaa=bb, aabb=ab⟩

Back:⟨a, b | aaa=bb, aabb=ab⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

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

[2] ab=aaaaa

Axiom: aabb=ab.

Reduce LHS:

[1]aa(bb)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] baaa=aaaaaaa

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

b b bb

Critical pair: baaa=aaab.

Reduce RHS:

[2]aa(ab)
⇒ aaaaaaa

Defines rule #2.

[4] aaaaaaaaa=aaaa

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

a b bb

Critical pair: aaaa=aaaaab.

Reduce RHS:

[2]aaaa(ab)
⇒ aaaaaaaaa

Flip LHS and RHS.

Defines rule #1.