Certificate for #6838 ⟨a, b | aba=b, bab=aaa⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [3], [5], [6], [7], [8].

Axiom: bab=aaa.

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

Overlap of [1] aba=b with [2] bab=aaa:

Critical pair: aaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [6].

Overlap of [2] bab=aaa with [3] bb=aaaa:

Critical pair: baaaaa=aaab.

Flip LHS and RHS.

Referenced by [5].

Overlap of [4] aaab=baaaaa with [1] aba=b:

Critical pair: aab=baaaaaa.

Referenced by [6], [7].

Overlap of [1] aba=b with [5] aab=baaaaaa:

Critical pair: abbaaaaaa=bab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [5] aab=baaaaaa with [1] aba=b:

Critical pair: ab=baaaaaaa.

Defines rule #3.

Referenced by [8].

Overlap of [1] aba=b with [7] ab=baaaaaaa:

Critical pair: baaaaaaaa=b.

Defines rule #2.