Certificate for #6728 ⟨a, b | aba=a, aaaa=bb⟩

Completion settings:

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

Axiom: aba=a.

Defines rule #4.

Referenced by [3], [4].

Axiom: aaaa=bb.

Defines rule #5.

Referenced by [3], [4], [5], [6].

Overlap of [1] aba=a with [2] aaaa=bb:

Critical pair: abbb=aaaa.

Reduce RHS:

Referenced by [6], [10], [11].

Overlap of [2] aaaa=bb with [1] aba=a:

Critical pair: aaaa=bbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] aaaa=bb with [2] aaaa=bb:

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [7], [8], [9], [10], [12].

Overlap of [2] aaaa=bb with [3] abbb=bb:

Critical pair: aaabb=bbbbb.

Referenced by [9].

Simplify [4] bbba=bb.

Reduce LHS:

Referenced by [8].

Overlap of [7] babb=bb with [5] bba=abb:

Critical pair: baabb=bba.

Reduce RHS:

Referenced by [9].

Overlap of [8] baabb=abb with [5] bba=abb:

Critical pair: baaabb=abba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [5] bba=abb with [9] aabb=bbbbbb:

Critical pair: bbbbbbbb=abbabb.

Reduce RHS:

Defines rule #1.

Overlap of [9] aabb=bbbbbb with [3] abbb=bb:

Critical pair: abb=bbbbbbb.

Defines rule #2.

Referenced by [12].

Simplify [5] bba=abb.

Reduce RHS:

Defines rule #3.