Certificate for #4776 ⟨a, b | abaaabba=aab⟩

Completion settings:

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

Axiom: abaaabba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #1.

Referenced by [3], [4], [5], [6], [8].

Simplify [1] abaaabba=aab.

Reduce RHS:

Referenced by [4].

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

Critical pair: abacba=c.

Defines rule #5.

Referenced by [5], [6], [7], [9], [10], [16].

Overlap of [2] aab=c with [4] abacba=c:

Critical pair: ac=cacba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [11].

Overlap of [4] abacba=c with [2] aab=c:

Critical pair: abacbc=cab.

Defines rule #6.

Referenced by [7], [9], [12], [13], [17].

Overlap of [4] abacba=c with [4] abacba=c:

Critical pair: abacbc=cbacba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [10], [11], [12], [13], [14], [15].

Overlap of [5] cacba=ac with [2] aab=c:

Critical pair: cacbc=acab.

Defines rule #3.

Overlap of [4] abacba=c with [6] abacbc=cab:

Critical pair: abacbcab=cbacbc.

Reduce LHS:

Defines rule #9.

Referenced by [12].

Overlap of [4] abacba=c with [7] cbacba=cab:

Critical pair: abacab=ccba.

Defines rule #7.

Referenced by [15], [16], [17], [18].

Overlap of [5] cacba=ac with [7] cbacba=cab:

Critical pair: cacab=accba.

Defines rule #4.

Overlap of [6] abacbc=cab with [7] cbacba=cab:

Critical pair: abacbcab=cabbacba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [7] cbacba=cab with [6] abacbc=cab:

Critical pair: cbacbcab=cabbacbc.

Flip LHS and RHS.

Defines rule #15.

Overlap of [7] cbacba=cab with [7] cbacba=cab:

Critical pair: cbacab=cabcba.

Flip LHS and RHS.

Defines rule #10.

Overlap of [7] cbacba=cab with [10] abacab=ccba:

Critical pair: cbacbccba=cabbacab.

Flip LHS and RHS.

Defines rule #16.

Overlap of [10] abacab=ccba with [4] abacba=c:

Critical pair: abacc=ccbaacba.

Flip LHS and RHS.

Defines rule #11.

Overlap of [10] abacab=ccba with [6] abacbc=cab:

Critical pair: abaccab=ccbaacbc.

Flip LHS and RHS.

Defines rule #12.

Overlap of [10] abacab=ccba with [10] abacab=ccba:

Critical pair: abacccba=ccbaacab.

Flip LHS and RHS.

Defines rule #13.