Certificate for #14519 ⟨a, b | aaab=b, babbb=a⟩

Completion settings:

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

Axiom: aaab=b.

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

Axiom: babbb=a.

Referenced by [3], [4], [6], [7], [8], [9], [11].

Overlap of [1] aaab=b with [2] babbb=a:

Critical pair: aaaa=babbb.

Reduce RHS:

Referenced by [10].

Overlap of [2] babbb=a with [2] babbb=a:

Critical pair: babba=aabbb.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aaab=b with [4] aabbb=babba:

Critical pair: ababba=bbb.

Referenced by [6], [7].

Overlap of [5] ababba=bbb with [1] aaab=b:

Critical pair: ababbb=bbbaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [9], [10].

Overlap of [5] ababba=bbb with [2] babbb=a:

Critical pair: ababa=bbbbbb.

Referenced by [10].

Overlap of [2] babbb=a with [6] bbbaab=aa:

Critical pair: baaa=aaab.

Reduce RHS:

Referenced by [12], [13].

Overlap of [2] babbb=a with [6] bbbaab=aa:

Critical pair: babaa=abaab.

Flip LHS and RHS.

Referenced by [10].

Overlap of [6] bbbaab=aa with [9] abaab=babaa:

Critical pair: bbbababaa=aaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11], [13].

Overlap of [2] babbb=a with [10] ab=bbbbbbbbba:

Critical pair: bbbbbbbbbbabb=a.

Reduce LHS:

Defines rule #2.

Referenced by [12], [13].

Overlap of [11] bbbbbbbbbbbbbbbbbbbbbbbbbbbba=a with [8] baaa=b:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbbbbb=aaa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [13].

Overlap of [12] aaa=bbbbbbbbbbbbbbbbbbbbbbbbbbbb with [10] ab=bbbbbbbbba:

Critical pair: aabbbbbbbbba=bbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.