Certificate for #19844 ⟨a, b | aaa=a, bbbb=aba⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #8.

Referenced by [3], [4].

Axiom: bbbb=aba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [3], [4], [5], [6], [7], [8].

Overlap of [1] aaa=a with [2] aba=bbbb:

Critical pair: aabbbb=aba.

Reduce RHS:

Defines rule #5.

Referenced by [6], [7], [8].

Overlap of [2] aba=bbbb with [1] aaa=a:

Critical pair: aba=bbbbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [2] aba=bbbb with [2] aba=bbbb:

Critical pair: abbbbb=bbbbba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8].

Overlap of [2] aba=bbbb with [3] aabbbb=bbbb:

Critical pair: abbbbb=bbbbabbbb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [3] aabbbb=bbbb with [5] bbbbba=abbbbb:

Critical pair: aababbbbb=bbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [6] bbbbabbbb=abbbbb with [5] bbbbba=abbbbb:

Critical pair: bbbbabbbabbbbb=abbbbbbbbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.