Certificate for #19550 ⟨a, b | aab=b, ababb=ba⟩

Completion settings:

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

Axiom: aab=b.

Defines rule #4.

Referenced by [3], [4], [6], [8], [9].

Axiom: ababb=ba.

Referenced by [3], [6], [9].

Overlap of [1] aab=b with [2] ababb=ba:

Critical pair: aba=babb.

Defines rule #5.

Referenced by [4], [5], [6], [7], [9], [10], [11].

Overlap of [1] aab=b with [3] aba=babb:

Critical pair: ababb=ba.

Reduce LHS:

Defines rule #2.

Referenced by [6], [9], [11].

Overlap of [3] aba=babb with [3] aba=babb:

Critical pair: abbabb=babbba.

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [2] ababb=ba with [4] babbbb=ba:

Critical pair: ababba=baabbbb.

Reduce LHS:

Reduce RHS:

Defines rule #8.

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

Overlap of [3] aba=babb with [6] baa=bbbbb:

Critical pair: abbbbb=babba.

Flip LHS and RHS.

Referenced by [9], [10], [11], [12].

Overlap of [6] baa=bbbbb with [1] aab=b:

Critical pair: bb=bbbbbb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [10], [11], [12].

Overlap of [2] ababb=ba with [7] babba=abbbbb:

Critical pair: abababbbbb=baabba.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [7] babba=abbbbb with [3] aba=babb:

Critical pair: babbbabb=abbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] babba=abbbbb with [7] babba=abbbbb:

Critical pair: bababbbbb=abbbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [12].

Overlap of [6] baa=bbbbb with [11] abbba=bbabbb:

Critical pair: babbabbb=bbbbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.