Certificate for #5415 ⟨a, b | abbbbba=babb⟩

Completion settings:

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

Axiom: abbbbba=babb.

Referenced by [3].

Axiom: abbbb=c.

Defines rule #11.

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

Overlap of [1] abbbbba=babb with [2] abbbb=c:

Critical pair: cba=babb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5], [6], [7], [9], [10], [12], [13].

Overlap of [2] abbbb=c with [3] babb=cba:

Critical pair: abbbcba=cabb.

Defines rule #12.

Referenced by [12].

Overlap of [3] babb=cba with [2] abbbb=c:

Critical pair: bc=cbabb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [14].

Overlap of [3] babb=cba with [3] babb=cba:

Critical pair: babcba=cbaabb.

Flip LHS and RHS.

Defines rule #6.

Referenced by [18].

Overlap of [5] ccba=bc with [3] babb=cba:

Critical pair: cccba=bcbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [9], [10], [11], [14], [15], [16], [17], [18], [19], [20], [21].

Overlap of [2] abbbb=c with [7] bcbb=cbc:

Critical pair: abbbcbc=ccbb.

Defines rule #13.

Referenced by [13], [14], [15], [16], [17], [18], [19], [20], [21].

Overlap of [3] babb=cba with [7] bcbb=cbc:

Critical pair: babcbc=cbacbb.

Flip LHS and RHS.

Defines rule #7.

Referenced by [19].

Overlap of [7] bcbb=cbc with [3] babb=cba:

Critical pair: bcbcba=cbcabb.

Flip LHS and RHS.

Defines rule #8.

Referenced by [20].

Overlap of [7] bcbb=cbc with [7] bcbb=cbc:

Critical pair: bcbcbc=cbccbb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [21].

Overlap of [3] babb=cba with [4] abbbcba=cabb:

Critical pair: bcabb=cbabcba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [16].

Overlap of [3] babb=cba with [8] abbbcbc=ccbb:

Critical pair: bccbb=cbabcbc.

Flip LHS and RHS.

Defines rule #5.

Referenced by [17].

Overlap of [8] abbbcbc=ccbb with [5] ccba=bc:

Critical pair: abbbcbbc=ccbbcba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Overlap of [8] abbbcbc=ccbb with [7] bcbb=cbc:

Critical pair: abbbccbc=ccbbbb.

Flip LHS and RHS.

Defines rule #14.

Overlap of [8] abbbcbc=ccbb with [12] cbabcba=bcabb:

Critical pair: abbbcbbcabb=ccbbbabcba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Overlap of [8] abbbcbc=ccbb with [13] cbabcbc=bccbb:

Critical pair: abbbcbbccbb=ccbbbabcbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #16.

Overlap of [8] abbbcbc=ccbb with [6] cbaabb=babcba:

Critical pair: abbbcbbabcba=ccbbbaabb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #17.

Overlap of [8] abbbcbc=ccbb with [9] cbacbb=babcbc:

Critical pair: abbbcbbabcbc=ccbbbacbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #18.

Overlap of [8] abbbcbc=ccbb with [10] cbcabb=bcbcba:

Critical pair: abbbcbbcbcba=ccbbbcabb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #19.

Overlap of [8] abbbcbc=ccbb with [11] cbccbb=bcbcbc:

Critical pair: abbbcbbcbcbc=ccbbbccbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #20.