Certificate for #1438 ⟨a, b, c | ab=1, aaa=cb⟩

Completion settings:

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

Axiom: ab=1.

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

Axiom: aaa=cb.

Referenced by [3], [4].

Overlap of [2] aaa=cb with [1] ab=1:

Critical pair: aa=cbb.

Referenced by [5].

Overlap of [2] aaa=cb with [2] aaa=cb:

Critical pair: acb=cba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] aa=cbb with [1] ab=1:

Critical pair: a=cbbb.

Defines rule #4.

Referenced by [6], [7].

Overlap of [1] ab=1 with [5] a=cbbb:

Critical pair: cbbbb=1.

Defines rule #2.

Referenced by [8].

Simplify [4] cba=acb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [7] cbbbcb=cbcbbb with [7] cbbbcb=cbcbbb:

Critical pair: cbbbcbcbbb=cbcbbbbbcb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.