diff --git a/src/spttn_cyclops/execute_kernel.cxx b/src/spttn_cyclops/execute_kernel.cxx
index 5ab7ff21..51cb4985 100644
--- a/src/spttn_cyclops/execute_kernel.cxx
+++ b/src/spttn_cyclops/execute_kernel.cxx
@@ -177,6 +177,19 @@ namespace CTF_int {
         }
       }
       break;
+      case SPARSE_xAXPY_OP_NOT_BUFFER: {
+        double * dX = (double *)Bs[term.X];
+        for (int64_t it = tree_pt_st; it < tree_pt_en; it++) {
+          double alpha = A_tree->dt[it].d;
+          int64_t idx_i = A_tree->idx[0][it];
+          double * dY = (double *)((double *)Bs[term.Y] + lda_Bs[term.Y][idx] * idx_i);
+          #pragma omp simd
+          for (int64_t i = 0; i < term.N; i++){
+            dY[i] += alpha * dX[i];
+          }
+        }
+      }
+      break;
       case xAXPY: {
         double * dX = (double *)Bs[term.X];
         double * dY = (double *)Bs[term.Y];
@@ -464,6 +477,9 @@ namespace CTF_int {
     for (int i = 0; i < nterms; i++) {
       if (terms[i].tbuffer_order == -1) continue;
       lda_Bs[nBs+i] = (int64_t *) CTF_int::alloc(sizeof(int64_t) * num_indices);
+      for (int j = 0; j < num_indices; j++) {
+        lda_Bs[nBs+i][j] = 0; // a case where this is queried and the index is not in the buffer; for example, when SPARSE_xAXPY is called with a buffer
+      }
       //(i,a): i is the fastest moving index
       lda_Bs[nBs+i][terms[i].idx_tbuffer[0]] = 1;
       for (int j = 1; j < terms[i].tbuffer_order; j++) {
@@ -513,6 +529,9 @@ namespace CTF_int {
     for (int i = 0; i < nterms; i++) {
       if (terms[i].tbuffer_order == -1) continue;
       lda_Bs[nBs+i] = (int64_t *) CTF_int::alloc(sizeof(int64_t) * num_indices);
+      for (int j = 0; j < num_indices; j++) {
+        lda_Bs[nBs+i][j] = 0; // a case where this is queried and the index is not in the buffer; for example, when SPARSE_xAXPY is called with a buffer
+      }
       //(i,a): i is the fastest moving index
       lda_Bs[nBs+i][terms[i].idx_tbuffer[0]] = 1;
       for (int j = 1; j < terms[i].tbuffer_order; j++) {
diff --git a/src/spttn_cyclops/prepare_kernel.h b/src/spttn_cyclops/prepare_kernel.h
index b9c74b6a..4dcbb66a 100644
--- a/src/spttn_cyclops/prepare_kernel.h
+++ b/src/spttn_cyclops/prepare_kernel.h
@@ -144,7 +144,7 @@ namespace CTF_int {
   };
   
   enum BLAS_OPERANDS {MAIN_TENSOR, PREV_TERM_BUF, CURRENT_TERM_BUF, INP_B, INTERMEDIATE_TENSOR};
-  enum BREAK_REC {NOT_SET, SCALAR, SPARSE, SPARSE_xAXPY, DENSE, DENSE_xAXPY_2D, DENSE_xAXPY_3D, DENSE_STRIDED, DENSE_3D, DENSE_3D_TO_xAXPY, xAXPY, xVEC_MUL, xGER, xGER_TO_xAXPY, xGEMV, RECURSIVE_LOOP};
+  enum BREAK_REC {NOT_SET, SCALAR, SPARSE, SPARSE_xAXPY, SPARSE_xAXPY_OP_NOT_BUFFER, DENSE, DENSE_xAXPY_2D, DENSE_xAXPY_3D, DENSE_STRIDED, DENSE_3D, DENSE_3D_TO_xAXPY, xAXPY, xVEC_MUL, xGER, xGER_TO_xAXPY, xGEMV, RECURSIVE_LOOP};
 
   template <typename dtype>
   const char* enumToStr(BREAK_REC br) {
@@ -153,6 +153,7 @@ namespace CTF_int {
         case SCALAR: return "SCALAR";
         case SPARSE: return "SPARSE";
         case SPARSE_xAXPY: return "SPARSE_xAXPY";
+        case SPARSE_xAXPY_OP_NOT_BUFFER: return "SPARSE_xAXPY_NOT_BUFFER";
         case DENSE: return "DENSE";
         case DENSE_xAXPY_2D: return "DENSE_xAXPY_2D";
         case DENSE_xAXPY_3D: return "DENSE_xAXPY_3D";
@@ -237,12 +238,15 @@ namespace CTF_int {
             }
             if (term.X == -1) {
               IASSERT(term.Bs_in_term[nBs] == true);
-              // interchange
+              // interchange: takes care of the case where the sparse tensor is contracted not in the first term
               term.X = nBs + term.inp_buf_id;
               term.ALPHA = -1;
             }
             if (i == (nterms - 1)) term.Y = nBs - 1;
             else term.Y = nBs + i;
+            if (i == (nterms-1)) {
+              std::cout << "term.X: " << term.X << " term.ALPHA: " << term.ALPHA << " term.Y: " << term.Y << std::endl;
+            }
           }
         }
         break;
@@ -378,18 +382,30 @@ namespace CTF_int {
               break;
             }
           }
-          IASSERT(i != (nterms-1));
           term.ALPHA = -1;
-          term.X = term.blas_B_ids[1];
-          int idx = term.idx_tbuffer[0];
-          term.Y = i + nBs;
-          if (idx_Bs[term.X][0] != term.idx_tbuffer[0]) {
-            term.blas_kernel = RECURSIVE_LOOP;
-            i--;
-            break;
+          int idx = -1;
+          if (i != (nterms-1)) {
+            term.X = term.blas_B_ids[1]; // an input tensor
+            term.Y = nBs + i; // buffer
+            idx = term.idx_tbuffer[0];
+            if (idx_Bs[term.X][0] != term.idx_tbuffer[0]) {
+              term.blas_kernel = RECURSIVE_LOOP;
+              i--;
+              break;
+            }
+          }
+          else {
+            term.blas_kernel = SPARSE_xAXPY_OP_NOT_BUFFER;
+            term.X = nBs + term.inp_buf_id; // an intermediate tensor (one of the other input in the pairwise contraction is the main tensor)
+            term.Y = nBs - 1;
+            idx = idx_Bs[term.Y][0];
+            if (idx != terms[term.inp_buf_id].idx_tbuffer[0]) {
+              term.blas_kernel = RECURSIVE_LOOP;
+              i--;
+              break;
+            }
           }
-          // assert failure: strided access not supported; INCX == 1 and INCY == 1
-          IASSERT(idx_Bs[term.X][0] == term.idx_tbuffer[0]);
+          IASSERT(idx != -1);
           term.INCX = lda_Bs[term.X][idx];
           term.INCY = lda_Bs[term.Y][idx];
           IASSERT(term.INCX == 1 && term.INCY == 1);