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

Completion settings:

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

Axiom: aba=b.

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

Axiom: abb=aaa.

Referenced by [3], [5], [6], [10].

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

Critical pair: abb=bba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4], [6], [9].

Overlap of [3] bba=aaa with [1] aba=b:

Critical pair: bbb=aaaba.

Reduce RHS:

Referenced by [5].

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

Critical pair: abaaa=bbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [6], [7], [10].

Overlap of [3] bba=aaa with [2] abb=aaa:

Critical pair: bbaaa=aaabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

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

Critical pair: ab=baaa.

Defines rule #3.

Referenced by [8], [9], [10].

Overlap of [1] aba=b with [7] ab=baaa:

Critical pair: baaaa=b.

Defines rule #2.

Overlap of [1] aba=b with [7] ab=baaa:

Critical pair: abbaaa=bb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] abb=aaa with [7] ab=baaa:

Critical pair: baaab=aaa.

Reduce LHS:

Defines rule #1.