Certificate for #4242 ⟨a, b | abaaabaab=ba⟩

Completion settings:

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

Axiom: abaaabaab=ba.

Referenced by [3].

Axiom: baa=c.

Referenced by [3], [4].

Overlap of [1] abaaabaab=ba with [2] baa=c:

Critical pair: acabaab=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [2] baa=c with [3] ba=acacb:

Critical pair: acacba=c.

Reduce LHS:

Defines rule #2.

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

Overlap of [3] ba=acacb with [4] acacacacb=c:

Critical pair: bc=acacbcacacacb.

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] acacacacb=c with [3] ba=acacb:

Critical pair: acacacacacacb=ca.

Reduce LHS:

Defines rule #1.

Referenced by [7].

Overlap of [3] ba=acacb with [6] acacc=ca:

Critical pair: bca=acacbcacc.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] acacacacb=c with [7] acacbcacc=bca:

Critical pair: acacbca=ccacc.

Referenced by [9].

Simplify [5] acacbcacacacb=bc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.