Certificate for #4012 ⟨a, b | aaabbaaab=ba⟩

Completion settings:

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

Axiom: aaabbaaab=ba.

Referenced by [3].

Axiom: baaab=c.

Referenced by [3], [4], [5], [6], [10], [11].

Overlap of [1] aaabbaaab=ba with [2] baaab=c:

Critical pair: aaabc=ba.

Referenced by [5], [7].

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

Critical pair: baaac=caaab.

Referenced by [8].

Overlap of [2] baaab=c with [3] aaabc=ba:

Critical pair: bba=cc.

Referenced by [6], [9].

Overlap of [5] bba=cc with [2] baaab=c:

Critical pair: bc=ccaab.

Defines rule #3.

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

Overlap of [3] aaabc=ba with [6] bc=ccaab:

Critical pair: aaaccaab=ba.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [4] baaac=caaab with [7] ba=aaaccaab:

Critical pair: aaaccaabaac=caaab.

Reduce LHS:

Referenced by [9], [11].

Overlap of [5] bba=cc with [7] ba=aaaccaab:

Critical pair: baaaccaab=cc.

Reduce LHS:

Referenced by [11].

Overlap of [2] baaab=c with [7] ba=aaaccaab:

Critical pair: aaaccaabaab=c.

Reduce LHS:

Defines rule #4.

Overlap of [2] baaab=c with [7] ba=aaaccaab:

Critical pair: baaaaaaccaab=ca.

Reduce LHS:

Defines rule #1.