diff --git a/tc/bench/benchmark.cpp b/tc/bench/benchmark.cpp
index f1a5005..194947f 100644
--- a/tc/bench/benchmark.cpp
+++ b/tc/bench/benchmark.cpp
@@ -8,6 +8,8 @@
 #include <tc/core.hpp>
 #include <tc/groups.hpp>
 
+#define NAMED(x) #x, x
+
 void bench(
     const std::string &group_expr,
     const std::string &symbol,
@@ -34,36 +36,105 @@ void bench(
     fmt::print("{}\n", row);
 }
 
-template<typename ...T>
-tc::Group sch(T ...arg) {
-    std::vector<int> mults{arg...,};
-    return tc::schlafli(mults);
-}
-
 int main(int argc, char *argv[]) {
     std::vector<std::string> args(argv + 1, argv + argc);
 
     fmt::print("{:>24},{:>10},{:>6},{:>9},{:>10}\n", "NAME", "ORDER", "COMPL", "TIME", "COS/S");
 
-    bench("H2", "5", {});
-    bench("H3", "5 3", {});
-    bench("H4", "5 3 3", {});
+    // Finite Groups
     
-    bench("T100", "100 2 100", {});
-    bench("T500", "500 2 500", {});
-    bench("T1000", "1000 2 1000", {});
+    // A_n: 3 * `n-1`           ; n >= 1
+    bench("A_5", "3 * 4", {});
+    bench("A_6", "3 * 5", {});
+    bench("A_7", "3 * 6", {});
+    bench("A_8", "3 * 7", {});
+    // B_n: 4 3 * `n-2`         ; n >= 2
+    bench("B_5", "4 3 * 3", {});
+    bench("B_6", "4 3 * 4", {});
+    bench("B_7", "4 3 * 5", {});
+    bench("B_8", "4 3 * 6", {});
+    // D_n: 3 * [1 1 `n-3`]     ; n >= 4
+    bench("D_5", "3 * [1 1 2]", {});
+    bench("D_6", "3 * [1 1 3]", {});
+    bench("D_7", "3 * [1 1 4]", {});
+    bench("D_8", "3 * [1 1 5]", {});
+    // E_n: 3 * [1 2 `n-4`]     ; n >= 6
+    bench("E_6", "3 * [1 2 2]", {});
+    bench("E_7", "3 * [1 2 3]", {});
+//    bench("E_8", "3 * [1 2 4]", {}); // too big
+    // H_n: 5 3 * `n-2`         ; n >= 2
+    bench("H_3", "5 3 * 0", {});
+    bench("H_4", "5 3 * 1", {});
+    bench("H_5", "5 3 * 2", {});
+    // grid: `p` `q`            ; 2(p+q) > pq
+    // triangle: `p` `q` `r`    ; 1/p + 1/q + 1/r > 1
 
-    bench("E6", "3 * [2 2 1]", {});
-    bench("E7", "3 * [3 2 1]", {});
-//    bench("E8", "3 * [4 2 1]", {});  // too big
+    // Special Finite Groups
+    bench("F_4", "3 4 3", {});
+    bench("G_2", "6", {});
+    // I_2(p): `p`              ; p >= 2
+    bench("I_2(100)", "100", {});
+    bench("I_2(1000)", "1000", {});
+    // "Torus": `p` 2 `q`       ; p, q >= 2
+    bench("T(100)", "100 2 100", {});
+    bench("T(1000)", "1000 2 1000", {});
 
-    bench("B6", "4 3 * 4", {});
-    bench("B7", "4 3 * 5", {});
-    bench("B8", "4 3 * 6", {});
-
-    bench("~A3", "{3 * 4}", {}, 5000000);
-    bench("~A4", "{3 * 5}", {}, 5000000);
-    bench("~I1", "{- * 5}", {}, 5000000);
+    // Affine Groups
+    
+    // ~A_n: {3 * `n+1`}
+    bench("~A_5", "{3 * 6}", {}, 1000000);
+    bench("~A_6", "{3 * 7}", {}, 1000000);
+    bench("~A_7", "{3 * 8}", {}, 1000000);
+    bench("~A_8", "{3 * 9}", {}, 1000000);
+    // ~B_n: 4 3 * `n-3` 3 * [1 1]
+    bench("~B_5", "4 3 * 2 3 * [1 1]", {}, 1000000);
+    bench("~B_6", "4 3 * 3 3 * [1 1]", {}, 1000000);
+    bench("~B_7", "4 3 * 4 3 * [1 1]", {}, 1000000);
+    bench("~B_8", "4 3 * 5 3 * [1 1]", {}, 1000000);
+    // ~B_n: 4 3 * `n-2` 4
+    bench("~C_5", "4 3 * 3 4", {}, 1000000);
+    bench("~C_6", "4 3 * 4 4", {}, 1000000);
+    bench("~C_7", "4 3 * 5 4", {}, 1000000);
+    bench("~C_8", "4 3 * 6 4", {}, 1000000);
+    // ~D_n: 3 * [1 1] 3 * `n-4` 3 * [1 1]
+    bench("~D_5", "3 * [1 1] 3 * 1 3 * [1 1]", {}, 1000000);
+    bench("~D_6", "3 * [1 1] 3 * 2 3 * [1 1]", {}, 1000000);
+    bench("~D_7", "3 * [1 1] 3 * 3 3 * [1 1]", {}, 1000000);
+    bench("~D_8", "3 * [1 1] 3 * 4 3 * [1 1]", {}, 1000000);
+    // grid: `p` `q`            ; 2(p+q) = pq
+    // triangle: `p` `q` `r`    ; 1/p + 1/q + 1/r = 1
+    
+    // Special Affine Groups
+    bench("~I_1", "-", {}, 1000000);
+    bench("~E_6", "3 * [2 2 2]", {}, 1000000);
+    bench("~E_7", "3 * [1 3 3]", {}, 1000000);
+    bench("~E_8", "3 * [1 2 5]", {}, 1000000);
+//    bench("E_9",  "3 * [1 2 5]", {}, 1000000);  // ~E_8 == E_9
+    bench("~F_4", "3 4 3 3", {}, 1000000);
+    bench("~G_2", "6 3", {}, 1000000);
 
+    // Hyperbolic Groups
+    // grid: `p` `q`            ; 2(p+q) < pq
+    // triangle: `p` `q` `r`    ; 1/p + 1/q + 1/r < 1
+    
+    // Special Hyperbolic Groups
+    bench("-BH_3", "4 3 5", {}, 1000000);
+    bench("-K_3", "5 3 5", {}, 1000000);
+    bench("-J_3", "3 5 3", {}, 1000000);
+//    bench("~H_3", "3 5 3", {}, 1000000);  // -J_3 == ~H_3
+    bench("-DH_3", "5 3 * [1 1]", {}, 1000000);
+    bench("^AB_3", "{3 3 3 4}", {}, 1000000);
+    bench("^AH_3", "{3 3 3 5}", {}, 1000000);
+    bench("^BB_3", "{3 4 3 4}", {}, 1000000);
+    bench("^BH_3", "{3 4 3 5}", {}, 1000000);
+    bench("^HH_3", "{3 5 3 5}", {}, 1000000);
+    bench("-H_4", "5 3 3 3", {}, 1000000);
+//    bench("~H_4", "5 3 3 3", {}, 1000000);  // -H_4 == ~H_4 == H_5 
+//    bench("H_5", "5 3 3 3", {}, 1000000);
+    bench("-BH_4", "4 3 3 5", {}, 1000000);
+    bench("-K_4", "5 3 3 5", {}, 1000000);
+    bench("-DH_4", "5 3 3 * [1 1]", {}, 1000000);
+    bench("^AF_4", "{3 3 3 3 4}", {}, 1000000);
+    
     return EXIT_SUCCESS;
 }
diff --git a/tc/include/tc/groups.hpp b/tc/include/tc/groups.hpp
index d931af8..a1b7806 100644
--- a/tc/include/tc/groups.hpp
+++ b/tc/include/tc/groups.hpp
@@ -9,15 +9,15 @@ namespace tc {
      * Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
      * @param mults: The sequence of multiplicites between adjacent generators.
      */
-    Group schlafli(const std::vector<int> &mults);
+    Group schlafli(const std::vector<unsigned int> &mults);
 
     Group coxeter(const std::string &symbol);
 
-    Group vcoxeter(const std::string &symbol, std::vector<int> &values);
+    Group vcoxeter(const std::string &symbol, std::vector<unsigned int> &values);
 
     template<typename ...Args>
     Group coxeter(const std::string &symbol, const Args &... args) {
-        std::vector<int> values = {{args...}};
+        std::vector<unsigned int> values = {{args...}};
         return vcoxeter(symbol, values);
     }
 }
diff --git a/tc/src/groups.cpp b/tc/src/groups.cpp
index e063867..e9ae9d5 100644
--- a/tc/src/groups.cpp
+++ b/tc/src/groups.cpp
@@ -4,15 +4,15 @@
 #include <fmt/core.h>
 
 namespace tc {
-    Group schlafli(const std::vector<int> &mults) {
+    Group schlafli(const std::vector<unsigned int> &mults) {
         Group res(mults.size() + 1);
-        for (int i = 0; i < mults.size(); ++i) {
+        for (size_t i = 0; i < mults.size(); ++i) {
             res.set(Rel{i, i + 1, mults[i]});
         }
         return res;
     }
 
-    Group v_coxeter(const std::string &symbol, std::vector<int> &values) {
+    Group vcoxeter(const std::string &symbol, std::vector<unsigned int> &values) {
         fmt::dynamic_format_arg_store<fmt::format_context> ds;
 
         for (const auto &value: values) {
diff --git a/tc/src/lang.cpp b/tc/src/lang.cpp
index 68cc207..cd66658 100644
--- a/tc/src/lang.cpp
+++ b/tc/src/lang.cpp
@@ -211,7 +211,7 @@ std::vector<Op> compile(const std::string &source) {
     std::shared_ptr<peg::Ast> ast;
     bool ast_ok = ast_parser.parse(source, ast);
     assert(ast_ok);
-    std::cout << peg::ast_to_s(ast) << std::endl;
+//    std::cout << peg::ast_to_s(ast) << std::endl;
 #endif
 
     static peg::parser parser = build_parser();