Certificate for #4872 ⟨a, b | abbabbba=aab⟩

Completion settings:

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

Axiom: abbabbba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #1.

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

Simplify [1] abbabbba=aab.

Reduce RHS:

Defines rule #7.

Referenced by [4], [5], [6], [7], [8].

Overlap of [3] abbabbba=c with [3] abbabbba=c:

Critical pair: abbabbbc=cbbabbba.

Referenced by [5], [13].

Overlap of [3] abbabbba=c with [2] aab=c:

Critical pair: abbabbbc=cab.

Reduce LHS:

Defines rule #4.

Referenced by [7], [8], [9], [10], [13].

Overlap of [2] aab=c with [3] abbabbba=c:

Critical pair: ac=cbabbba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [11].

Overlap of [6] cbabbba=ac with [3] abbabbba=c:

Critical pair: cbabbbc=acbbabbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [10], [11], [12].

Overlap of [5] cbbabbba=cab with [3] abbabbba=c:

Critical pair: cbbabbbc=cabbbabbba.

Flip LHS and RHS.

Defines rule #9.

Overlap of [5] cbbabbba=cab with [2] aab=c:

Critical pair: cbbabbbc=cabab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [12], [14].

Overlap of [5] cbbabbba=cab with [7] acab=cbabbbc:

Critical pair: cbbabbbcbabbbc=cabcab.

Defines rule #12.

Overlap of [6] cbabbba=ac with [7] acab=cbabbbc:

Critical pair: cbabbbcbabbbc=accab.

Defines rule #11.

Overlap of [7] acab=cbabbbc with [9] cabab=cbbabbbc:

Critical pair: acbbabbbc=cbabbbcab.

Defines rule #10.

Simplify [4] abbabbbc=cbbabbba.

Reduce RHS:

Defines rule #6.

Referenced by [14].

Overlap of [13] abbabbbc=cab with [9] cabab=cbbabbbc:

Critical pair: abbabbbcbbabbbc=cababab.

Reduce LHS:

Reduce RHS:

Defines rule #8.