Certificate for #1063 ⟨a, b | aabaab=aba⟩

Completion settings:

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

Axiom: aabaab=aba.

Referenced by [3].

Axiom: aba=c.

Defines rule #6.

Referenced by [3], [4], [5], [6], [7], [9].

Simplify [1] aabaab=aba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aabaab=c with [2] aba=c:

Critical pair: acab=c.

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

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

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] aba=c with [4] acab=c:

Critical pair: abc=ccab.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] acab=c with [2] aba=c:

Critical pair: acc=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [10].

Simplify [6] ccab=abc.

Reduce LHS:

Defines rule #2.

Referenced by [9].

Overlap of [2] aba=c with [8] accccb=abc:

Critical pair: ababc=cccccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [4] acab=c with [7] ca=acc:

Critical pair: aaccb=c.

Defines rule #5.