Certificate for #15158 ⟨a, b | aab=ba, ababab=1⟩

Completion settings:

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

Axiom: aab=ba.

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

Axiom: ababab=1.

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

Overlap of [1] aab=ba with [2] ababab=1:

Critical pair: a=baabab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [4], [8], [9].

Overlap of [3] bbba=a with [2] ababab=1:

Critical pair: bbb=ababab.

Reduce RHS:

Defines rule #3.

Referenced by [5], [8], [9].

Overlap of [1] aab=ba with [4] bbb=1:

Critical pair: aa=babb.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] ababab=1 with [5] babb=aa:

Critical pair: abaaa=b.

Referenced by [7], [8].

Overlap of [1] aab=ba with [6] abaaa=b:

Critical pair: ab=baaaa.

Defines rule #2.

Referenced by [8].

Overlap of [3] bbba=a with [6] abaaa=b:

Critical pair: bbbb=abaaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [3] bbba=a with [8] baaaaaaa=b:

Critical pair: bbb=aaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.