Certificate for #4667 ⟨a, b | aaab=a, babb=a⟩

Completion settings:

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

Axiom: aaab=a.

Referenced by [4], [5], [12].

Axiom: babb=a.

Referenced by [3], [6], [7], [10].

Overlap of [2] babb=a with [2] babb=a:

Critical pair: baba=aabb.

Flip LHS and RHS.

Referenced by [4].

Overlap of [1] aaab=a with [3] aabb=baba:

Critical pair: ababa=ab.

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

Overlap of [1] aaab=a with [4] ababa=ab:

Critical pair: aaab=aaba.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [4] ababa=ab with [2] babb=a:

Critical pair: abaa=abbb.

Referenced by [9].

Overlap of [5] aaba=a with [2] babb=a:

Critical pair: aaa=abb.

Referenced by [11].

Overlap of [5] aaba=a with [4] ababa=ab:

Critical pair: aab=aba.

Referenced by [9].

Overlap of [5] aaba=a with [8] aab=aba:

Critical pair: abaa=a.

Reduce LHS:

Referenced by [10].

Overlap of [2] babb=a with [9] abbb=a:

Critical pair: ba=ab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [11], [12].

Simplify [7] aaa=abb.

Reduce RHS:

Defines rule #2.

Referenced by [12].

Overlap of [1] aaab=a with [11] aaa=bba:

Critical pair: bbab=a.

Reduce LHS:

Defines rule #3.