Certificate for #14501 ⟨a, b | aaab=b, abbba=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], [7].

Axiom: abbba=a.

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

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

Critical pair: aaa=bbba.

Referenced by [4], [5], [6], [9], [14].

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

Critical pair: abbbb=aaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [5], [11], [12], [14], [15].

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

Critical pair: bbbab=b.

Reduce LHS:

Referenced by [7], [8], [11], [15], [16].

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

Critical pair: abbba=bbbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [9], [13], [14].

Overlap of [1] aaab=b with [5] abbbb=b:

Critical pair: aab=bbbb.

Referenced by [12].

Overlap of [5] abbbb=b with [6] bbbaa=a:

Critical pair: aba=baa.

Flip LHS and RHS.

Referenced by [10].

Overlap of [6] bbbaa=a with [3] aaa=bbba:

Critical pair: bbbbbba=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [12], [14], [15].

Simplify [8] baa=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [10] aba=bbbbbbba with [5] abbbb=b:

Critical pair: abb=bbbbbbbabbbb.

Reduce RHS:

Referenced by [12], [14], [15].

Simplify [7] aab=bbbb.

Reduce LHS:

Referenced by [13], [15].

Overlap of [12] bbbbbbbbbbbbb=bbbb with [6] bbbaa=a:

Critical pair: bbbbbbbbbba=bbbbaa.

Reduce RHS:

Referenced by [14].

Overlap of [3] aaa=bbba with [9] aa=bbbbbba:

Critical pair: aabbbbbba=bbbaa.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Overlap of [9] aa=bbbbbba with [5] abbbb=b:

Critical pair: ab=bbbbbbabbbb.

Reduce RHS:

Defines rule #2.

Referenced by [16].

Overlap of [5] abbbb=b with [15] ab=bbbbbbb:

Critical pair: bbbbbbbbbb=b.

Defines rule #1.