Certificate for #4770 ⟨a, b | abaaabab=abb⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(a) = 0; deg(c) = deg(b) = 1, c < b
• Auxiliary generators:
  1. abb=c

Axiom: abaaabab=abb.

Referenced by [3].

Axiom: abb=c.

Defines rule #1.

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

Simplify [1] abaaabab=abb.

Reduce RHS:

Defines rule #5.

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

Overlap of [3] abaaabab=c with [3] abaaabab=c:

Critical pair: abaaabc=caaabab.

Referenced by [5], [8].

Overlap of [3] abaaabab=c with [2] abb=c:

Critical pair: abaaabc=cb.

Reduce LHS:

Defines rule #3.

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

Overlap of [5] caaabab=cb with [3] abaaabab=c:

Critical pair: caaabc=cbaaabab.

Flip LHS and RHS.

Defines rule #7.

Overlap of [5] caaabab=cb with [2] abb=c:

Critical pair: caaabc=cbb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Simplify [4] abaaabc=caaabab.

Reduce RHS:

Defines rule #4.

Referenced by [9].

Overlap of [8] abaaabc=cb with [7] cbb=caaabc:

Critical pair: abaaabcaaabc=cbbb.

Reduce LHS:

Reduce RHS:

Defines rule #6.