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+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n(1);
+# 
+# S :=  { [i] -> [j] : 1 <= i < j <= 100 && n(j) >= 0};
+# 
+# R := domain S;
+# 
+# S;
+
+{[i] -> [j] : 1 <= i < j <= 100 && 0 <= n(j)}
+
+# 
+# R;
+
+{[i]: 1 <= i <= 99 && UNKNOWN}
+
+# 
+# upper_bound R;
+
+{[i]: 1 <= i <= 99}
+
+# 
+# lower_bound R;
+
+{[i]  : FALSE }
+
+# 
+# 
+# R - {[1:50]};
+
+{[i]: 51 <= i <= 99 && UNKNOWN}
+
+# 
+# {[1:50]} - R;
+
+{[i]: 1 <= i <= 50 && UNKNOWN}
+
+# 
+# {[1:50]} - upper_bound R;
+
+{[i]  : FALSE }
+
+# 
+# {[1:50]} - lower_bound R;
+
+{[i]: 1 <= i <= 50}
+
+# 
+# 
+# R union {[10:30]}  union {[25:100]} union {[1:10]};
+
+{[i]: 1 <= i <= 99 && UNKNOWN} union
+ {[i]: 10 <= i <= 30} union
+ {[i]: 25 <= i <= 100} union
+ {[i]: 1 <= i <= 10}
+
+# 
+# upper_bound (R union {[10:30]}  union {[25:100]} union {[1:10]});
+
+{[i]: 1 <= i <= 99} union
+ {[i]: 25 <= i <= 100}
+
+# 
+# lower_bound (R union {[10:30]}  union {[25:100]} union {[1:10]});
+
+{[i]: 10 <= i <= 30} union
+ {[i]: 25 <= i <= 100} union
+ {[i]: 1 <= i <= 10}
+
+# 
+# 
+# {[101:200]} - R;
+
+{[i]: 101 <= i <= 200}
+
+# 
+# {[1:200]} - R;
+
+{[i]: 1 <= i <= 99 && UNKNOWN} union
+ {[i]: 100 <= i <= 200}
+
+# 
+# {[1:200]} - R - {[10:30]}  - {[25:100]};
+
+{[i]: 1 <= i <= 9 && UNKNOWN} union
+ {[i]: 101 <= i <= 200}
+
+# 
+# {[1:200]} - (R union {[10:30]}  union {[25:100]} union {[1:10]});
+
+{[i]: 101 <= i <= 200}
+
+# 
+# {[1:200]} - R - {[10:30]}  - {[25:100]} - {[1:10]};
+
+{[i]: 101 <= i <= 200}
+
+#