Certificate for #13156 ⟨a, b | aba=aaa, bbb=ab⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Axiom: aba=aaa.

Flip LHS and RHS.

Referenced by [3].

Axiom: bbb=ab.

Flip LHS and RHS.

Defines rule #2.

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

Simplify [1] aaa=aba.

Reduce RHS:

Defines rule #4.

Referenced by [4], [5].

Overlap of [3] aaa=bbba with [3] aaa=bbba:

Critical pair: abbba=bbbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] aaa=bbba with [2] ab=bbb:

Critical pair: aabbb=bbbab.

Reduce LHS:

Reduce RHS:

Defines rule #1.