Certificate for #6171 ⟨a, b, c | aa=1, abbccb=1⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [6], [13], [14], [15], [16].

Axiom: abbccb=1.

Referenced by [3], [4], [7], [9], [11].

Overlap of [1] aa=1 with [2] abbccb=1:

Critical pair: a=bbccb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4], [5], [14], [15].

Overlap of [2] abbccb=1 with [3] bbccb=a:

Critical pair: abbcca=bccb.

Referenced by [6], [8].

Overlap of [3] bbccb=a with [3] bbccb=a:

Critical pair: bbcca=abccb.

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] abbcca=bccb with [1] aa=1:

Critical pair: abbcc=bccba.

Defines rule #2.

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

Overlap of [2] abbccb=1 with [6] abbcc=bccba:

Critical pair: bccbab=1.

Referenced by [8], [9].

Overlap of [4] abbcca=bccb with [6] abbcc=bccba:

Critical pair: abbccbccba=bccbbbcc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [2] abbccb=1 with [7] bccbab=1:

Critical pair: abbcc=ccbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [6] abbcc=bccba with [9] ccbab=bccba:

Critical pair: abbcbccba=bccbacbab.

Referenced by [13], [14].

Overlap of [2] abbccb=1 with [8] bccbbbcc=ccba:

Critical pair: abbccccba=ccbbbcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [12].

Overlap of [11] ccbbbcc=bccbaccba with [9] ccbab=bccba:

Critical pair: ccbbbcbccba=bccbaccbacbab.

Referenced by [16].

Overlap of [10] abbcbccba=bccbacbab with [1] aa=1:

Critical pair: abbcbccb=bccbacbaba.

Defines rule #8.

Overlap of [10] abbcbccba=bccbacbab with [9] ccbab=bccba:

Critical pair: abbcbbccba=bccbacbabb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [3] bbccb=a with [14] bccbacbabb=abbc:

Critical pair: babbc=aacbabb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [12] ccbbbcbccba=bccbaccbacbab with [1] aa=1:

Critical pair: ccbbbcbccb=bccbaccbacbaba.

Defines rule #9.