Certificate for #1782 ⟨a, b, c | aab=cc, bbc=1⟩

Completion settings:

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

Axiom: aab=cc.

Referenced by [3], [4].

Axiom: bbc=1.

Defines rule #2.

Referenced by [3], [6], [7], [10], [11], [15], [17].

Overlap of [1] aab=cc with [2] bbc=1:

Critical pair: aa=ccbc.

Referenced by [4], [5], [13].

Overlap of [1] aab=cc with [3] aa=ccbc:

Critical pair: ccbcb=cc.

Referenced by [6].

Overlap of [3] aa=ccbc with [3] aa=ccbc:

Critical pair: accbc=ccbca.

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] bbc=1 with [4] ccbcb=cc:

Critical pair: bbcc=cbcb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [2] bbc=1 with [6] cbcb=c:

Critical pair: bbc=bcb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [12].

Overlap of [7] bcb=1 with [6] cbcb=c:

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [9], [12], [13], [14], [15], [16], [17].

Simplify [5] ccbca=accbc.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [2] bbc=1 with [9] bccca=abccc:

Critical pair: babccc=cca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [2] bbc=1 with [10] cca=babccc:

Critical pair: bbbabccc=ca.

Referenced by [12].

Overlap of [11] bbbabccc=ca with [8] cb=bc:

Critical pair: bbbabccbc=cab.

Reduce LHS:

Referenced by [14].

Simplify [3] aa=ccbc.

Reduce RHS:

Defines rule #5.

Overlap of [12] bbbacc=cab with [8] cb=bc:

Critical pair: bbbacbc=cabb.

Reduce LHS:

Referenced by [15].

Overlap of [14] bbbabcc=cabb with [8] cb=bc:

Critical pair: bbbabcbc=cabbb.

Reduce LHS:

Referenced by [16].

Overlap of [15] bbbac=cabbb with [8] cb=bc:

Critical pair: bbbabc=cabbbb.

Referenced by [17].

Overlap of [16] bbbabc=cabbbb with [8] cb=bc:

Critical pair: bbbabbc=cabbbbb.

Reduce LHS:

Defines rule #4.