Certificate for #4475 ⟨a, b | aaaabbba=baa⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b
• Auxiliary generators:
  1. bbb=c
  2. caa=d

Axiom: aaaabbba=baa.

Referenced by [4].

Axiom: bbb=c.

Defines rule #10.

Referenced by [4], [5], [6], [8].

Axiom: caa=d.

Defines rule #4.

Referenced by [6], [7], [8], [9], [10], [11].

Overlap of [1] aaaabbba=baa with [2] bbb=c:

Critical pair: aaaaca=baa.

Flip LHS and RHS.

Defines rule #7.

Referenced by [6], [7], [10].

Overlap of [2] bbb=c with [2] bbb=c:

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [7].

Overlap of [2] bbb=c with [4] baa=aaaaca:

Critical pair: bbaaaaca=caa.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [9], [10], [11].

Overlap of [5] cb=bc with [4] baa=aaaaca:

Critical pair: caaaaca=bcaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

Overlap of [2] bbb=c with [7] bd=daaca:

Critical pair: bbdaaca=cd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] caa=d with [6] aaaadadaca=d:

Critical pair: cad=daaadadaca.

Defines rule #5.

Overlap of [4] baa=aaaaca with [6] aaaadadaca=d:

Critical pair: bad=aaaacaaaadadaca.

Reduce RHS:

Defines rule #8.

Overlap of [6] aaaadadaca=d with [3] caa=d:

Critical pair: aaaadadad=da.

Defines rule #1.