Certificate for #20181 ⟨a, b | aba=a, aaaa=bbb⟩

Completion settings:

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

Axiom: aba=a.

Defines rule #4.

Referenced by [3], [4].

Axiom: aaaa=bbb.

Defines rule #5.

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

Overlap of [1] aba=a with [2] aaaa=bbb:

Critical pair: abbbb=aaaa.

Reduce RHS:

Referenced by [6], [10], [11].

Overlap of [2] aaaa=bbb with [1] aba=a:

Critical pair: aaaa=bbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] aaaa=bbb with [2] aaaa=bbb:

Critical pair: abbb=bbba.

Flip LHS and RHS.

Referenced by [7], [8], [9], [12].

Overlap of [2] aaaa=bbb with [3] abbbb=bbb:

Critical pair: aaabbb=bbbbbbb.

Referenced by [9].

Simplify [4] bbbba=bbb.

Reduce LHS:

Referenced by [8].

Overlap of [7] babbb=bbb with [5] bbba=abbb:

Critical pair: baabbb=bbba.

Reduce RHS:

Referenced by [9].

Overlap of [8] baabbb=abbb with [5] bbba=abbb:

Critical pair: baaabbb=abbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [9] aabbb=bbbbbbbb with [3] abbbb=bbb:

Critical pair: abbb=bbbbbbbbb.

Defines rule #2.

Referenced by [11], [12].

Overlap of [3] abbbb=bbb with [10] abbb=bbbbbbbbb:

Critical pair: bbbbbbbbbb=bbb.

Defines rule #1.

Simplify [5] bbba=abbb.

Reduce RHS:

Defines rule #3.