Certificate for #8060 ⟨a, b | aaa=1, abab=bba⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #1.

Referenced by [3], [4], [6], [8], [10].

Axiom: abab=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [5], [7], [9], [11].

Overlap of [2] bba=abab with [1] aaa=1:

Critical pair: bb=ababaa.

Flip LHS and RHS.

Referenced by [4], [11].

Overlap of [1] aaa=1 with [3] ababaa=bb:

Critical pair: aabb=babaa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

Overlap of [2] bba=abab with [4] babaa=aabb:

Critical pair: baabb=ababbaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aaa=1 with [5] abaababa=baabb:

Critical pair: aabaabb=baababa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [2] bba=abab with [6] baababa=aabaabb:

Critical pair: baabaabb=ababababa.

Flip LHS and RHS.

Referenced by [8].

Overlap of [1] aaa=1 with [7] ababababa=baabaabb:

Critical pair: aabaabaabb=babababa.

Flip LHS and RHS.

Defines rule #5.

Referenced by [9].

Overlap of [2] bba=abab with [8] babababa=aabaabaabb:

Critical pair: baabaabaabb=ababbababa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [1] aaa=1 with [9] abaabaabaabab=baabaabaabb:

Critical pair: aabaabaabaabb=baabaabaabab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

Overlap of [2] bba=abab with [10] baabaabaabab=aabaabaabaabb:

Critical pair: baabaabaabaabb=abababaabaabab.

Reduce RHS:

Defines rule #7.