Certificate for #20252 ⟨a, b | aba=b, aaaa=bab⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [3], [4], [6], [7], [8], [9], [10].

Axiom: aaaa=bab.

Flip LHS and RHS.

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

Overlap of [1] aba=b with [1] aba=b:

Critical pair: abb=bba.

Referenced by [8].

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

Critical pair: aaaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [8].

Overlap of [2] bab=aaaa with [4] bb=aaaaa:

Critical pair: baaaaaa=aaaab.

Flip LHS and RHS.

Referenced by [6].

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

Critical pair: aaab=baaaaaaa.

Referenced by [7].

Overlap of [6] aaab=baaaaaaa with [1] aba=b:

Critical pair: aab=baaaaaaaa.

Referenced by [8], [9].

Overlap of [1] aba=b with [7] aab=baaaaaaaa:

Critical pair: abbaaaaaaaa=bab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [7] aab=baaaaaaaa with [1] aba=b:

Critical pair: ab=baaaaaaaaa.

Defines rule #3.

Referenced by [10].

Overlap of [1] aba=b with [9] ab=baaaaaaaaa:

Critical pair: baaaaaaaaaa=b.

Defines rule #2.