Certificate for #16325 ⟨a, b | aab=bb, bbab=aa⟩

Back:⟨a, b | aab=bb, bbab=aa⟩

Completion settings:

[1] bb=aab

Axiom: aab=bb.

Flip LHS and RHS.

Defines rule #3.

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

[2] aabab=aa

Axiom: bbab=aa.

Reduce LHS:

[1](bb)ab
⇒ aabab

Defines rule #4.

Referenced by [4], [5], [7].

[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

Referenced by [5].

[4] aabaaab=aab

Overlap of [2] aabab=aa with [1] bb=aab:

aaba b bb

Critical pair: aabaaab=aab.

Referenced by [6].

[5] baa=aaaa

Overlap of [3] baab=aaaab with [2] aabab=aa:

b aab aabab

Critical pair: baa=aaaabab.

Reduce RHS:

[2]aa(aabab)
⇒ aaaa

Defines rule #2.

Referenced by [6].

[6] aaaaaaab=aab

Simplify [4] aabaaab=aab.

Reduce LHS:

[5]aa(baa)ab
⇒ aaaaaaab

Referenced by [7].

[7] aaaaaaa=aa

Overlap of [6] aaaaaaab=aab with [2] aabab=aa:

aaaaa aab aabab

Critical pair: aaaaaaa=aabab.

Reduce RHS:

[2](aabab)
⇒ aa

Defines rule #1.