Certificate for #12512 ⟨a, b | abab=aa, bbab=a⟩

Back:⟨a, b | abab=aa, bbab=a⟩

Completion settings:

[1] abab=aa

Axiom: abab=aa.

Defines rule #3.

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

[2] bbab=a

Axiom: bbab=a.

Defines rule #5.

Referenced by [3], [5].

[3] bbaa=aa

Overlap of [2] bbab=a with [2] bbab=a:

bba b bbab

Critical pair: bbaa=abab.

Reduce RHS:

[1](abab)
⇒ aa

Defines rule #4.

Referenced by [5].

[4] abaa=aaab

Overlap of [1] abab=aa with [1] abab=aa:

ab ab abab

Critical pair: abaa=aaab.

Referenced by [6].

[5] aab=aa

Overlap of [2] bbab=a with [1] abab=aa:

bb ab abab

Critical pair: bbaa=aab.

Reduce LHS:

[3](bbaa)
⇒ aa

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

[6] abaa=aaa

Simplify [4] abaa=aaab.

Reduce RHS:

[5]a(aab)
⇒ aaa

Defines rule #2.