Certificate for #27671 ⟨a, b | aa=1, abbabb=bab⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #3.

Referenced by [3], [6].

Axiom: abbabb=bab.

Referenced by [3], [4], [5], [7].

Overlap of [1] aa=1 with [2] abbabb=bab:

Critical pair: abab=bbabb.

Defines rule #4.

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

Overlap of [2] abbabb=bab with [2] abbabb=bab:

Critical pair: abbbab=bababb.

Reduce RHS:

Defines rule #6.

Referenced by [5], [6].

Overlap of [3] abab=bbabb with [2] abbabb=bab:

Critical pair: abbab=bbabbbabb.

Reduce RHS:

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

Overlap of [1] aa=1 with [4] abbbab=bbbabbb:

Critical pair: abbbabbb=bbbab.

Reduce LHS:

Referenced by [7], [9].

Overlap of [2] abbabb=bab with [5] abbab=bbbbbabbbb:

Critical pair: bbbbbabbbbb=bab.

Reduce LHS:

Defines rule #2.

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

Overlap of [5] abbab=bbbbbabbbb with [3] abab=bbabb:

Critical pair: abbbbabb=bbbbbabbbbab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [7] bbbbbab=bab with [6] bbbabbbbb=bbbab:

Critical pair: bbbbbab=babbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [5] abbab=bbbbbabbbb.

Reduce RHS:

Defines rule #5.