Certificate for #16290 ⟨a, b | aab=bb, abaa=ab⟩

Back:⟨a, b | aab=bb, abaa=ab⟩

Completion settings:

[1] bb=aab

Axiom: aab=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4], [5].

[2] abaa=ab

Axiom: abaa=ab.

Defines rule #1.

Referenced by [4], [5].

[3] baab=aaaab

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

b b bb

Critical pair: baab=aabb.

Reduce RHS:

[1]aa(bb)
⇒ aaaab

Defines rule #4.

Referenced by [4], [5].

[4] baaaab=aaaab

Overlap of [1] bb=aab with [3] baab=aaaab:

b b baab

Critical pair: baaaab=aabaab.

Reduce RHS:

[2]a(abaa)b
[1]⇒ aa(bb)
⇒ aaaab

Defines rule #5.

[5] aaaaab=aaab

Overlap of [2] abaa=ab with [3] baab=aaaab:

a baa baab

Critical pair: aaaaab=abb.

Reduce RHS:

[1]a(bb)
⇒ aaab

Defines rule #2.