Certificate for #19706 ⟨a, b | aba=b, aaaaa=bb⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [4], [5], [6], [7], [8], [9].

Axiom: aaaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [9].

Overlap of [2] bb=aaaaa with [2] bb=aaaaa:

Critical pair: baaaaa=aaaaab.

Flip LHS and RHS.

Referenced by [4].

Overlap of [3] aaaaab=baaaaa with [1] aba=b:

Critical pair: aaaab=baaaaaa.

Referenced by [5].

Overlap of [4] aaaab=baaaaaa with [1] aba=b:

Critical pair: aaab=baaaaaaa.

Referenced by [6].

Overlap of [5] aaab=baaaaaaa with [1] aba=b:

Critical pair: aab=baaaaaaaa.

Referenced by [7].

Overlap of [6] aab=baaaaaaaa with [1] aba=b:

Critical pair: ab=baaaaaaaaa.

Defines rule #3.

Referenced by [8], [9].

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

Critical pair: baaaaaaaaaa=b.

Defines rule #2.

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

Critical pair: abbaaaaaaaaa=bb.

Reduce LHS:

Reduce RHS:

Defines rule #1.