Certificate for #4683 ⟨a, b | aaab=b, abba=a⟩

Completion settings:

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

Axiom: aaab=b.

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

Axiom: abba=a.

Referenced by [3], [4], [6], [11].

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

Critical pair: aaa=bba.

Referenced by [4], [5], [6], [8], [12].

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

Critical pair: abbb=aaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [5], [10], [12], [13].

Overlap of [1] aaab=b with [3] aaa=bba:

Critical pair: bbab=b.

Reduce LHS:

Referenced by [7], [10], [13], [15].

Overlap of [3] aaa=bba with [3] aaa=bba:

Critical pair: abba=bbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [8], [12].

Overlap of [5] abbb=b with [6] bbaa=a:

Critical pair: aba=baa.

Flip LHS and RHS.

Referenced by [9].

Overlap of [6] bbaa=a with [3] aaa=bba:

Critical pair: bbbba=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9], [11], [12], [13].

Simplify [7] baa=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [9] aba=bbbbba with [5] abbb=b:

Critical pair: abb=bbbbbabbb.

Reduce RHS:

Referenced by [11], [12], [13], [14].

Overlap of [2] abba=a with [8] aa=bbbba:

Critical pair: abbbbbba=aa.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [3] aaa=bba with [8] aa=bbbba:

Critical pair: aabbbba=bbaa.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Overlap of [8] aa=bbbba with [5] abbb=b:

Critical pair: ab=bbbbabbb.

Reduce RHS:

Referenced by [14], [15], [16].

Simplify [10] abb=bbbbbb.

Reduce LHS:

Referenced by [15].

Overlap of [5] abbb=b with [13] ab=bbbbbbbbbbb:

Critical pair: bbbbbbbbbbbbb=b.

Reduce LHS:

Defines rule #1.

Referenced by [16].

Simplify [13] ab=bbbbbbbbbbb.

Reduce RHS:

Defines rule #2.