Certificate for #14342 ⟨a, b | aaaa=a, aabba=b⟩

Completion settings:

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

Axiom: aaaa=a.

Defines rule #4.

Referenced by [3], [4], [9], [10].

Axiom: aabba=b.

Referenced by [3], [4], [5].

Overlap of [1] aaaa=a with [2] aabba=b:

Critical pair: aaab=aabba.

Reduce RHS:

Defines rule #3.

Referenced by [5], [7], [9], [11].

Overlap of [2] aabba=b with [1] aaaa=a:

Critical pair: aabba=baaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [8], [10].

Overlap of [3] aaab=b with [2] aabba=b:

Critical pair: ab=bba.

Flip LHS and RHS.

Referenced by [6], [8], [10].

Overlap of [5] bba=ab with [4] baaa=b:

Critical pair: bb=abaa.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [3] aaab=b with [6] abaa=bb:

Critical pair: aabb=baa.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] baaa=b with [6] abaa=bb:

Critical pair: baabb=bbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [3] aaab=b with [8] aba=aabbbb:

Critical pair: aaaabbbb=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

Overlap of [4] baaa=b with [8] aba=aabbbb:

Critical pair: baaaabbbb=bba.

Reduce LHS:

Reduce RHS:

Referenced by [11].

Overlap of [3] aaab=b with [10] abbbbbbbb=ab:

Critical pair: aaab=bbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.