Certificate for #2336 ⟨a, b | ababbba=aab⟩

Completion settings:

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

Axiom: ababbba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #5.

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

Simplify [1] ababbba=aab.

Reduce RHS:

Defines rule #14.

Referenced by [4], [5], [6], [7], [8], [10], [15].

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

Critical pair: ababbbc=cbabbba.

Referenced by [5], [10], [16].

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

Critical pair: ababbbc=cab.

Reduce LHS:

Defines rule #3.

Referenced by [7], [8], [9], [10], [11], [16].

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

Critical pair: ac=cabbba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [12], [13].

Overlap of [6] cabbba=ac with [3] ababbba=c:

Critical pair: cabbbc=acbabbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [10], [11], [12], [13], [14].

Overlap of [5] cbabbba=cab with [3] ababbba=c:

Critical pair: cbabbbc=cabbabbba.

Flip LHS and RHS.

Defines rule #15.

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

Critical pair: cbabbbc=cabab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [10], [14], [15], [17].

Overlap of [3] ababbba=c with [7] acab=cabbbc:

Critical pair: ababbbcabbbc=ccab.

Reduce LHS:

Defines rule #1.

Overlap of [5] cbabbba=cab with [7] acab=cabbbc:

Critical pair: cbabbbcabbbc=cabcab.

Defines rule #13.

Overlap of [6] cabbba=ac with [7] acab=cabbbc:

Critical pair: cabbbcabbbc=accab.

Defines rule #12.

Overlap of [7] acab=cabbbc with [6] cabbba=ac:

Critical pair: aac=cabbbcbba.

Defines rule #8.

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

Critical pair: acbabbbc=cabbbcab.

Defines rule #11.

Overlap of [9] cabab=cbabbbc with [3] ababbba=c:

Critical pair: cc=cbabbbcbba.

Flip LHS and RHS.

Defines rule #4.

Simplify [4] ababbbc=cbabbba.

Reduce RHS:

Defines rule #9.

Referenced by [17].

Overlap of [16] ababbbc=cab with [9] cabab=cbabbbc:

Critical pair: ababbbcbabbbc=cababab.

Reduce LHS:

Reduce RHS:

Defines rule #10.