Certificate for #13765 ⟨a, b | abbba=1, aaaaaa=1⟩

Completion settings:

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

Axiom: abbba=1.

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

Axiom: aaaaaa=1.

Defines rule #1.

Referenced by [4], [6], [8], [9].

Overlap of [1] abbba=1 with [1] abbba=1:

Critical pair: abbb=bbba.

Referenced by [4], [5].

Overlap of [1] abbba=1 with [2] aaaaaa=1:

Critical pair: abbb=aaaaa.

Reduce LHS:

Referenced by [5].

Simplify [3] abbb=bbba.

Reduce RHS:

Referenced by [6].

Overlap of [1] abbba=1 with [5] abbb=aaaaa:

Critical pair: abbbaaaaa=bbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

Overlap of [6] bbb=aaaa with [6] bbb=aaaa:

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [2] aaaaaa=1 with [7] aaaab=baaaa:

Critical pair: aabaaaa=b.

Referenced by [9].

Overlap of [7] aaaab=baaaa with [8] aabaaaa=b:

Critical pair: aab=baaaaaaaa.

Reduce RHS:

Defines rule #2.