Certificate for #1665 ⟨a, b, c | aab=ba, bcb=1⟩

Completion settings:

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

Axiom: aab=ba.

Defines rule #1.

Referenced by [5], [6], [14].

Axiom: bcb=1.

Referenced by [3], [4], [7], [12].

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

Critical pair: bc=cb.

Defines rule #4.

Referenced by [4], [5], [7], [8], [10], [12].

Overlap of [2] bcb=1 with [3] bc=cb:

Critical pair: cbb=1.

Defines rule #2.

Referenced by [9], [12], [13], [14].

Overlap of [1] aab=ba with [3] bc=cb:

Critical pair: aacb=bac.

Flip LHS and RHS.

Referenced by [6], [7], [13].

Overlap of [1] aab=ba with [5] bac=aacb:

Critical pair: aaaacb=baac.

Referenced by [11].

Overlap of [2] bcb=1 with [5] bac=aacb:

Critical pair: bcaacb=ac.

Reduce LHS:

Referenced by [8], [9].

Overlap of [7] cbaacb=ac with [3] bc=cb:

Critical pair: cbaaccb=acc.

Referenced by [13].

Overlap of [7] cbaacb=ac with [4] cbb=1:

Critical pair: cbaa=acb.

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [9] acb=cbaa with [3] bc=cb:

Critical pair: accb=cbaac.

Referenced by [13].

Simplify [6] aaaacb=baac.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [2] bcb=1 with [11] baac=cbaaaaaaaa:

Critical pair: bccbaaaaaaaa=aac.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Simplify [8] cbaaccb=acc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [13] acc=ccaaaaaaaaaaaaaaaa with [4] cbb=1:

Critical pair: ac=ccaaaaaaaaaaaaaaaabb.

Reduce RHS:

Defines rule #3.