Certificate for #2375 ⟨a, b, c | aab=a, bbcb=1⟩

Completion settings:

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

Axiom: aab=a.

Defines rule #1.

Referenced by [3], [5], [6].

Axiom: bbcb=1.

Referenced by [3], [4], [6], [7], [8].

Overlap of [1] aab=a with [2] bbcb=1:

Critical pair: aa=abcb.

Flip LHS and RHS.

Referenced by [5].

Overlap of [2] bbcb=1 with [2] bbcb=1:

Critical pair: bbc=bcb.

Referenced by [7], [8].

Overlap of [1] aab=a with [3] abcb=aa:

Critical pair: aaa=acb.

Flip LHS and RHS.

Referenced by [6].

Overlap of [5] acb=aaa with [2] bbcb=1:

Critical pair: ac=aaabcb.

Reduce RHS:

Defines rule #3.

Overlap of [2] bbcb=1 with [4] bbc=bcb:

Critical pair: bcbb=1.

Referenced by [8], [9].

Overlap of [2] bbcb=1 with [4] bbc=bcb:

Critical pair: bbcbcb=bc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [9].

Simplify [7] bcbb=1.

Reduce LHS:

Defines rule #2.