Certificate for #2842 ⟨a, b, c | aaa=b, bcb=a⟩

Completion settings:

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

Axiom: aaa=b.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2].

Axiom: bcb=a.

Reduce LHS:

Referenced by [3], [4], [5], [6], [7].

Overlap of [2] aaacaaa=a with [2] aaacaaa=a:

Critical pair: aaaca=acaaa.

Flip LHS and RHS.

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

Overlap of [2] aaacaaa=a with [2] aaacaaa=a:

Critical pair: aaacaa=aacaaa.

Reduce RHS:

Referenced by [5], [6].

Overlap of [3] acaaa=aaaca with [2] aaacaaa=a:

Critical pair: aca=aaacacaaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [3] acaaa=aaaca with [2] aaacaaa=a:

Critical pair: acaa=aaacaacaaa.

Reduce RHS:

Defines rule #1.

Referenced by [7].

Overlap of [2] aaacaaa=a with [6] acaa=aaca:

Critical pair: aaaacaa=a.

Reduce LHS:

Defines rule #2.