Certificate for #13119 ⟨a, b | bbb=aaa, abba=b⟩

Completion settings:

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

Axiom: bbb=aaa.

Referenced by [3], [4], [7].

Axiom: abba=b.

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

Overlap of [1] bbb=aaa with [1] bbb=aaa:

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [7], [8].

Overlap of [2] abba=b with [3] aaab=baaa:

Critical pair: abbbaaa=baab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [5], [7].

Overlap of [2] abba=b with [4] baab=aaaaaaa:

Critical pair: abaaaaaaa=bab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [6].

Overlap of [2] abba=b with [5] bab=abaaaaaaa:

Critical pair: ababaaaaaaa=bb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8].

Overlap of [1] bbb=aaa with [6] bb=aabaaaaaaaaaaaaaa:

Critical pair: aabaaaaaaaaaaaaaab=aaa.

Reduce LHS:

Defines rule #1.

Overlap of [2] abba=b with [6] bb=aabaaaaaaaaaaaaaa:

Critical pair: aaabaaaaaaaaaaaaaaa=b.

Reduce LHS:

Defines rule #2.