Certificate for #19005 ⟨a, b | aab=b, ababba=b⟩

Completion settings:

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

Axiom: aab=b.

Defines rule #1.

Referenced by [3], [5], [8], [9], [11], [12].

Axiom: ababba=b.

Referenced by [3], [4], [6], [10], [13].

Overlap of [1] aab=b with [2] ababba=b:

Critical pair: ab=babba.

Flip LHS and RHS.

Referenced by [4], [5], [7], [14].

Overlap of [2] ababba=b with [3] babba=ab:

Critical pair: ababab=bbba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9], [10], [11], [15].

Overlap of [3] babba=ab with [1] aab=b:

Critical pair: babbb=abab.

Referenced by [6], [7], [8], [9], [10].

Overlap of [2] ababba=b with [5] babbb=abab:

Critical pair: abababab=bbbb.

Referenced by [10].

Overlap of [3] babba=ab with [5] babbb=abab:

Critical pair: bababab=abbbb.

Referenced by [10].

Overlap of [4] bbba=ababab with [5] babbb=abab:

Critical pair: bbabab=abababbbb.

Reduce RHS:

Referenced by [9], [11].

Overlap of [5] babbb=abab with [4] bbba=ababab:

Critical pair: baababab=ababa.

Reduce LHS:

Referenced by [11].

Overlap of [5] babbb=abab with [4] bbba=ababab:

Critical pair: babababab=ababba.

Reduce LHS:

Reduce RHS:

Defines rule #7.

Referenced by [11].

Overlap of [10] bbbbb=b with [4] bbba=ababab:

Critical pair: bbababab=ba.

Reduce LHS:

Referenced by [12], [13], [15].

Overlap of [1] aab=b with [11] ababb=ba:

Critical pair: aba=babb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [14], [15].

Overlap of [2] ababba=b with [11] ababb=ba:

Critical pair: baa=b.

Defines rule #2.

Overlap of [3] babba=ab with [12] babb=aba:

Critical pair: bababa=abbb.

Defines rule #6.

Overlap of [4] bbba=ababab with [12] babb=aba:

Critical pair: bbaba=abababbb.

Reduce RHS:

Defines rule #5.