Certificate for #19212 ⟨a, b | aba=b, baaaab=a⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [3], [4], [5], [6], [7], [8].

Axiom: baaaab=a.

Referenced by [4], [5], [9], [11], [13].

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

Critical pair: abb=bba.

Referenced by [5], [10].

Overlap of [1] aba=b with [2] baaaab=a:

Critical pair: aa=baaab.

Flip LHS and RHS.

Referenced by [6], [13].

Overlap of [3] abb=bba with [2] baaaab=a:

Critical pair: aba=bbaaaaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [1] aba=b with [4] baaab=aa:

Critical pair: aaa=baab.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aba=b with [6] baab=aaa:

Critical pair: aaaa=bab.

Flip LHS and RHS.

Referenced by [8], [10].

Overlap of [1] aba=b with [7] bab=aaaa:

Critical pair: aaaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9], [10], [11], [12].

Overlap of [2] baaaab=a with [8] bb=aaaaa:

Critical pair: baaaaaaaaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [10], [11], [12], [13].

Overlap of [3] abb=bba with [8] bb=aaaaa:

Critical pair: abaaaaa=bbab.

Reduce LHS:

Reduce RHS:

Referenced by [11].

Overlap of [8] bb=aaaaa with [2] baaaab=a:

Critical pair: ba=aaaaaaaaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Simplify [5] bbaaaaab=b.

Reduce LHS:

Defines rule #2.

Overlap of [2] baaaab=a with [9] ab=baaaaaaaaa:

Critical pair: baaabaaaaaaaaa=a.

Reduce LHS:

Defines rule #1.