Certificate for #7796 ⟨a, b | aaa=1, abbab=bb⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #8.

Referenced by [3], [5], [9].

Axiom: abbab=bb.

Defines rule #6.

Referenced by [3], [4], [6], [10].

Overlap of [1] aaa=1 with [2] abbab=bb:

Critical pair: aabb=bbab.

Defines rule #4.

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

Overlap of [2] abbab=bb with [2] abbab=bb:

Critical pair: abbbb=bbbab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [8].

Overlap of [1] aaa=1 with [3] aabb=bbab:

Critical pair: aabbab=abb.

Reduce LHS:

Defines rule #7.

Referenced by [6], [7], [8], [10].

Overlap of [3] aabb=bbab with [5] bbabab=abb:

Critical pair: aababb=bbabbabab.

Reduce RHS:

Referenced by [9].

Overlap of [4] bbbab=abbbb with [5] bbabab=abb:

Critical pair: babb=abbbbab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [5] bbabab=abb with [4] bbbab=abbbb:

Critical pair: bbabaabbbb=abbbbab.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Overlap of [1] aaa=1 with [6] aababb=babbbb:

Critical pair: aababbbb=ababb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [10].

Overlap of [5] bbabab=abb with [9] ababb=babbbbbb:

Critical pair: bbabbabbbbbb=abbabb.

Reduce LHS:

Reduce RHS:

Defines rule #1.