Certificate for #6834 ⟨a, b | aba=b, abb=aaa⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [3], [4], [5], [6], [7], [8], [9].

Axiom: abb=aaa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

Overlap of [1] aba=b with [1] aba=b:

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [5], [7], [9].

Overlap of [1] aba=b with [2] aaa=abb:

Critical pair: ababb=baa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [2] aaa=abb with [1] aba=b:

Critical pair: aab=abbba.

Reduce RHS:

Defines rule #3.

Referenced by [6], [7].

Overlap of [1] aba=b with [5] aab=bbb:

Critical pair: abbbb=bab.

Flip LHS and RHS.

Referenced by [7].

Overlap of [5] aab=bbb with [1] aba=b:

Critical pair: ab=bbba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [1] aba=b with [4] baa=bbb:

Critical pair: abbb=ba.

Flip LHS and RHS.

Defines rule #2.

Overlap of [7] abbbbb=ab with [3] bba=abb:

Critical pair: abbbabb=aba.

Reduce LHS:

Reduce RHS:

Defines rule #1.