diff --git a/src/smt/smt_parallel.cpp b/src/smt/smt_parallel.cpp
index d9badd2b1..8a3910590 100644
--- a/src/smt/smt_parallel.cpp
+++ b/src/smt/smt_parallel.cpp
@@ -1696,6 +1696,8 @@ namespace smt {
 
     void parallel::batch_manager::set_canceled() {
         std::scoped_lock lock(mux);
+        if (m_state != state::is_running)
+            return;
         cancel_background_threads();
     }
 
diff --git a/src/solver/parallel_tactical2.cpp b/src/solver/parallel_tactical2.cpp
index 8d341b665..96d9e1c32 100644
--- a/src/solver/parallel_tactical2.cpp
+++ b/src/solver/parallel_tactical2.cpp
@@ -482,6 +482,8 @@ class parallel_solver {
 
         void set_cancel() {
             std::scoped_lock lock(mux);
+            if (m_state != state::is_running)
+                return;
             cancel_workers_unlocked();
         }
 
@@ -926,9 +928,9 @@ class parallel_solver {
         expr_ref_vector const& get_unsat_core() const { return m_unsat_core; }
 
         void collect_statistics(statistics& st) const {
-            st.update("parallel-num_cubes", m_stats.m_num_cubes);
+            st.update("parallel-num-cubes", m_stats.m_num_cubes);
             st.update("parallel-max-cube-size", m_stats.m_max_cube_depth);
-            st.update("bb-backbones-found", m_stats.m_backbones_found);
+            st.update("parallel-backbones-found", m_stats.m_backbones_found);
             st.update("parallel-core-min-jobs-enqueued", m_stats.m_core_min_jobs_enqueued);
             st.update("parallel-core-min-jobs-published", m_stats.m_core_min_jobs_published);
             st.update("parallel-core-min-jobs-skipped", m_stats.m_core_min_jobs_skipped);
@@ -1641,31 +1643,31 @@ class parallel_solver {
         }
 
         void collect_statistics(statistics& st) const {
-            st.update("bb-batches-total", m_stats.m_batches_total);
-            st.update("bb-candidates-total", m_stats.m_candidates_total);
-            st.update("bb-backbones-detected", m_stats.m_backbones_detected);
-            st.update("bb-internal-backbones-found", m_stats.m_internal_backbones_found);
-            st.update("bb-retry-backbones-found", m_stats.m_retry_backbones_found);
-            st.update("bb-retries", m_stats.m_bb_retries);
-            st.update("bb-core-refinement-rounds", m_stats.m_core_refinement_rounds);
-            st.update("bb-singleton-backbones", m_stats.m_singleton_backbones);
-            st.update("bb-fallback-singleton-checks", m_stats.m_fallback_singleton_checks);
-            st.update("bb-fallback-chunk-exhausted", m_stats.m_fallback_reason_chunk_exhausted);
-            st.update("bb-fallback-undef", m_stats.m_fallback_reason_undef);
-            st.update("bb-literals-removed-by-core", m_stats.m_lits_removed_by_core);
-            st.update("bb-num-chunk-increases", m_stats.m_num_chunk_increases);
+            st.update("parallel-bb-batches-total", m_stats.m_batches_total);
+            st.update("parallel-bb-candidates-total", m_stats.m_candidates_total);
+            st.update("parallel-bb-backbones-detected", m_stats.m_backbones_detected);
+            st.update("parallel-bb-internal-backbones-found", m_stats.m_internal_backbones_found);
+            st.update("parallel-bb-retry-backbones-found", m_stats.m_retry_backbones_found);
+            st.update("parallel-bb-retries", m_stats.m_bb_retries);
+            st.update("parallel-bb-core-refinement-rounds", m_stats.m_core_refinement_rounds);
+            st.update("parallel-bb-singleton-backbones", m_stats.m_singleton_backbones);
+            st.update("parallel-bb-fallback-singleton-checks", m_stats.m_fallback_singleton_checks);
+            st.update("parallel-bb-fallback-chunk-exhausted", m_stats.m_fallback_reason_chunk_exhausted);
+            st.update("parallel-bb-fallback-undef", m_stats.m_fallback_reason_undef);
+            st.update("parallel-bb-literals-removed-by-core", m_stats.m_lits_removed_by_core);
+            st.update("parallel-bb-num-chunk-increases", m_stats.m_num_chunk_increases);
 
             auto safe_ratio = [](double num, double den) -> double {
                 return den > 0 ? num / den : 0.0;
             };
 
-            st.update("bb-backbone-yield-pct",
+            st.update("parallel-bb-backbone-yield-pct",
                 100.0 * safe_ratio(m_stats.m_internal_backbones_found, m_stats.m_candidates_total));
-            st.update("bb-avg-backbones-per-batch",
+            st.update("parallel-bb-avg-backbones-per-batch",
                 safe_ratio(m_stats.m_internal_backbones_found, m_stats.m_batches_total));
-            st.update("bb-core-refinement-rounds-per-batch",
+            st.update("parallel-bb-core-refinement-rounds-per-batch",
                 safe_ratio(m_stats.m_core_refinement_rounds, m_stats.m_batches_total));
-            st.update("bb-core-effectiveness-lit-removed-per-round",
+            st.update("parallel-bb-core-effectiveness-lit-removed-per-round",
                 safe_ratio(m_stats.m_lits_removed_by_core, m_stats.m_core_refinement_rounds));
         }