Certificate for #12461 ⟨a, b | aabb=ab, baaa=a⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b

Axiom: aabb=ab.

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

Axiom: baaa=a.

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

Overlap of [1] aabb=ab with [2] baaa=a:

Critical pair: aaba=abaaa.

Reduce RHS:

Referenced by [5].

Overlap of [2] baaa=a with [1] aabb=ab:

Critical pair: baab=abb.

Referenced by [9].

Overlap of [2] baaa=a with [3] aaba=aa:

Critical pair: baaa=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [10].

Overlap of [5] aba=a with [2] baaa=a:

Critical pair: aa=aaa.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [2] baaa=a with [6] aaa=aa:

Critical pair: baaa=aa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [9].

Overlap of [6] aaa=aa with [1] aabb=ab:

Critical pair: aab=aabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [9].

Simplify [4] baab=abb.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [9] bab=ab with [5] aba=a:

Critical pair: ba=aba.

Reduce RHS:

Defines rule #2.