Certificate for #16551 ⟨a, b | aba=bb, bbb=aaa⟩

Completion settings:

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

Axiom: aba=bb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [2], [3], [4], [5], [6].

Axiom: bbb=aaa.

Reduce LHS:

Defines rule #8.

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

Overlap of [1] bb=aba with [1] bb=aba:

Critical pair: baba=abab.

Reduce RHS:

Defines rule #6.

Referenced by [4].

Overlap of [1] bb=aba with [3] baba=aaa:

Critical pair: baaa=abaaba.

Flip LHS and RHS.

Defines rule #9.

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

Overlap of [2] abab=aaa with [1] bb=aba:

Critical pair: abaaba=aaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [4] abaaba=baaa with [5] aaab=baaa:

Critical pair: abaabbaaa=baaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [7].

Overlap of [5] aaab=baaa with [4] abaaba=baaa:

Critical pair: aabaaa=baaaaaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [9].

Overlap of [4] abaaba=baaa with [7] aabaaaaaaaaa=aabaaa:

Critical pair: abaabaaa=baaaaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [7] aabaaaaaaaaa=aabaaa with [5] aaab=baaa:

Critical pair: aabaaaaaaabaaa=aabaaaab.

Reduce LHS:

Reduce RHS:

Defines rule #1.