Certificate for #2300 ⟨a, b | aaa=1, ababbb=1⟩

Completion settings:

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

Axiom: aaa=1.

Referenced by [3], [4], [8], [10].

Axiom: ababbb=1.

Referenced by [3], [6], [7], [11].

Overlap of [1] aaa=1 with [2] ababbb=1:

Critical pair: aa=babbb.

Defines rule #3.

Referenced by [4], [8], [9], [10].

Overlap of [1] aaa=1 with [3] aa=babbb:

Critical pair: babbba=1.

Referenced by [5], [8], [10].

Overlap of [4] babbba=1 with [4] babbba=1:

Critical pair: babb=bbba.

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [2] ababbb=1 with [5] bbba=babb:

Critical pair: abababb=a.

Referenced by [8].

Overlap of [2] ababbb=1 with [5] bbba=babb:

Critical pair: ababbbabb=bba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [1] aaa=1 with [6] abababb=a:

Critical pair: aaa=bababb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [8] bababb=1 with [7] bba=abb:

Critical pair: babaabb=a.

Reduce LHS:

Referenced by [10], [11].

Overlap of [1] aaa=1 with [9] abbbbbbbbbbbb=a:

Critical pair: aaa=bbbbbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] ababbb=1 with [9] abbbbbbbbbbbb=a:

Critical pair: aba=bbbbbbbbb.

Defines rule #4.