Certificate for #3486 ⟨a, b, c | bb=aa, aca=a⟩

Completion settings:

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

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #7.

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

Axiom: aca=a.

Defines rule #8.

Referenced by [4], [5].

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

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aa=bb with [2] aca=a:

Critical pair: aa=bbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [2] aca=a with [1] aa=bb:

Critical pair: acbb=aa.

Reduce RHS:

Defines rule #4.

Referenced by [6].

Overlap of [1] aa=bb with [5] acbb=bb:

Critical pair: abb=bbcbb.

Defines rule #3.

Referenced by [7], [9].

Simplify [3] bba=abb.

Reduce RHS:

Defines rule #5.

Referenced by [8], [9].

Overlap of [7] bba=bbcbb with [1] aa=bb:

Critical pair: bbbb=bbcbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [7] bba=bbcbb with [6] abb=bbcbb:

Critical pair: bbbbcbb=bbcbbbb.

Flip LHS and RHS.

Defines rule #1.