Certificate for #18727 ⟨a, b | aaa=a, ababba=b⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [3], [4].

Axiom: ababba=b.

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

Overlap of [1] aaa=a with [2] ababba=b:

Critical pair: aab=ababba.

Reduce RHS:

Defines rule #2.

Referenced by [6], [11], [12].

Overlap of [2] ababba=b with [1] aaa=a:

Critical pair: ababba=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [7], [9], [10].

Overlap of [2] ababba=b with [4] baa=b:

Critical pair: ababb=ba.

Referenced by [6], [8], [10].

Overlap of [3] aab=b with [5] ababb=ba:

Critical pair: aba=babb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [10].

Overlap of [6] babb=aba with [6] babb=aba:

Critical pair: bababa=abaabb.

Reduce RHS:

Defines rule #7.

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

Overlap of [2] ababba=b with [7] bababa=abbb:

Critical pair: abababbb=bbaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] bababa=abbb with [4] baa=b:

Critical pair: babab=abbba.

Flip LHS and RHS.

Referenced by [12].

Overlap of [7] bababa=abbb with [5] ababb=ba:

Critical pair: babba=abbbbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [3] aab=b with [10] abbbbb=ab:

Critical pair: aab=bbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [3] aab=b with [9] abbba=babab:

Critical pair: ababab=bbba.

Flip LHS and RHS.

Defines rule #5.