Certificate for #4553 ⟨a, b | aaabbaba=baa⟩

Completion settings:

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

Axiom: aaabbaba=baa.

Referenced by [3].

Axiom: aabbab=c.

Defines rule #15.

Referenced by [3], [4], [5], [6], [7], [12], [13].

Overlap of [1] aaabbaba=baa with [2] aabbab=c:

Critical pair: aca=baa.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4], [5], [6], [7], [8], [9], [10], [13], [15], [17], [22].

Overlap of [2] aabbab=c with [3] baa=aca:

Critical pair: aabbaaca=caa.

Reduce LHS:

Referenced by [16].

Overlap of [3] baa=aca with [2] aabbab=c:

Critical pair: bc=acabbab.

Flip LHS and RHS.

Defines rule #16.

Referenced by [8], [9], [10], [11], [14], [15], [20], [21], [22].

Overlap of [3] baa=aca with [2] aabbab=c:

Critical pair: bac=acaabbab.

Reduce RHS:

Defines rule #6.

Referenced by [7], [9], [10], [11], [12], [13], [14], [15], [16], [19], [21], [22].

Overlap of [2] aabbab=c with [6] bac=acc:

Critical pair: aabbaacc=cac.

Reduce LHS:

Defines rule #2.

Referenced by [20].

Overlap of [3] baa=aca with [5] acabbab=bc:

Critical pair: babc=acacabbab.

Reduce RHS:

Defines rule #12.

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

Overlap of [5] acabbab=bc with [3] baa=aca:

Critical pair: acabbaaca=bcaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [5] acabbab=bc with [6] bac=acc:

Critical pair: acabbaacc=bcac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [23].

Overlap of [6] bac=acc with [5] acabbab=bc:

Critical pair: bbc=accabbab.

Flip LHS and RHS.

Defines rule #17.

Referenced by [17], [18], [19], [20], [23].

Overlap of [2] aabbab=c with [8] babc=acbc:

Critical pair: aabacbc=cc.

Reduce LHS:

Defines rule #3.

Overlap of [2] aabbab=c with [8] babc=acbc:

Critical pair: aabbaacbc=cabc.

Reduce LHS:

Defines rule #4.

Overlap of [5] acabbab=bc with [8] babc=acbc:

Critical pair: acabacbc=bcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [5] acabbab=bc with [8] babc=acbc:

Critical pair: acabbaacbc=bcabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Simplify [4] aabacaca=caa.

Reduce LHS:

Defines rule #1.

Referenced by [18].

Overlap of [3] baa=aca with [11] accabbab=bbc:

Critical pair: babbc=acaccabbab.

Reduce RHS:

Defines rule #19.

Referenced by [21], [22].

Overlap of [16] aaaccaca=caa with [11] accabbab=bbc:

Critical pair: aaaccacbbc=caaccabbab.

Reduce RHS:

Defines rule #11.

Overlap of [6] bac=acc with [11] accabbab=bbc:

Critical pair: bbbc=acccabbab.

Defines rule #18.

Overlap of [7] aaaccacc=cac with [11] accabbab=bbc:

Critical pair: aaaccbbc=cacabbab.

Reduce RHS:

Defines rule #10.

Overlap of [5] acabbab=bc with [17] babbc=acbbc:

Critical pair: acabacbbc=bcbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Overlap of [5] acabbab=bc with [17] babbc=acbbc:

Critical pair: acabbaacbbc=bcabbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #21.

Overlap of [10] bcac=acaaccacc with [11] accabbab=bbc:

Critical pair: bcbbc=acaaccacccabbab.

Defines rule #20.