Certificate for #15539 ⟨a, b | aaa=bb, babbb=a⟩

Completion settings:

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

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3], [5], [6], [8], [12].

Axiom: babbb=a.

Reduce LHS:

Referenced by [4].

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

Critical pair: baaa=aaab.

Flip LHS and RHS.

Referenced by [4], [5], [6], [9].

Simplify [2] baaaab=a.

Reduce LHS:

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

Overlap of [1] bb=aaa with [4] babaaa=a:

Critical pair: ba=aaaabaaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [4] babaaa=a with [3] aaab=baaa:

Critical pair: babbaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [8], [9], [11].

Simplify [5] abaaaaaa=ba.

Reduce LHS:

Referenced by [9], [10].

Overlap of [4] babaaa=a with [6] ab=baaaaaaa:

Critical pair: bbaaaaaaaaaa=a.

Reduce LHS:

Referenced by [13].

Overlap of [3] aaab=baaa with [6] ab=baaaaaaa:

Critical pair: aabaaaaaaa=baaa.

Reduce LHS:

Referenced by [10].

Overlap of [7] baaaaaaaaaaaaa=ba with [9] baaaaaaaaa=baaa:

Critical pair: baaaaaaa=ba.

Referenced by [11], [12].

Simplify [6] ab=baaaaaaa.

Reduce RHS:

Defines rule #2.

Overlap of [1] bb=aaa with [10] baaaaaaa=ba:

Critical pair: bba=aaaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Simplify [8] aaaaaaaaaaaaa=a.

Reduce LHS:

Defines rule #1.