WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1000==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && 1==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && 1==arg3P_3 && arg4==arg4P_3 ], cost: 1 3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && 1==arg4P_4 ], cost: 1 17: f5 -> f6 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, [ arg2^3 f6 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 ], cost: 1 20: f5 -> f18 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [ arg2^3==arg3^3+arg4^3 && arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 && arg4==arg4P_21 ], cost: 1 21: f5 -> f18 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, [ arg4>arg1 && arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 ], cost: 1 4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg2P_5==1+arg2 && arg1==arg1P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 7: f7 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2>arg1 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 8: f7 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg2<=arg1 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1 5: f8 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg1==arg1P_6 && 1==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1 6: f11 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3P_7==1+arg3 && arg1==arg1P_7 && arg2==arg2P_7 && arg4==arg4P_7 ], cost: 1 9: f12 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1 10: f9 -> f10 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1 13: f10 -> f13 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg3>arg1 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1 14: f10 -> f14 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [ arg3<=arg1 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 ], cost: 1 11: f13 -> f16 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && 1==arg3P_12 && arg4==arg4P_12 ], cost: 1 12: f16 -> f17 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg4P_13==1+arg4 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1 15: f17 -> f15 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [ arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 ], cost: 1 16: f14 -> f15 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, [ arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 ], cost: 1 19: f15 -> f5 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, [ arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 ], cost: 1 22: __init -> f1 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 22: __init -> f1 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1000==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && 1==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && 1==arg3P_3 && arg4==arg4P_3 ], cost: 1 3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && 1==arg4P_4 ], cost: 1 17: f5 -> f6 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, [ arg2^3 f6 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 ], cost: 1 4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg2P_5==1+arg2 && arg1==arg1P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 7: f7 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2>arg1 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 8: f7 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg2<=arg1 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1 5: f8 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg1==arg1P_6 && 1==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1 6: f11 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3P_7==1+arg3 && arg1==arg1P_7 && arg2==arg2P_7 && arg4==arg4P_7 ], cost: 1 9: f12 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1 10: f9 -> f10 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1 13: f10 -> f13 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg3>arg1 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1 14: f10 -> f14 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [ arg3<=arg1 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 ], cost: 1 11: f13 -> f16 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && 1==arg3P_12 && arg4==arg4P_12 ], cost: 1 12: f16 -> f17 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg4P_13==1+arg4 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1 15: f17 -> f15 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [ arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 ], cost: 1 16: f14 -> f15 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, [ arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 ], cost: 1 19: f15 -> f5 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, [ arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 ], cost: 1 22: __init -> f1 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=1000, [], cost: 1 1: f2 -> f3 : arg2'=1, [], cost: 1 2: f3 -> f4 : arg3'=1, [], cost: 1 3: f4 -> f5 : arg4'=1, [], cost: 1 17: f5 -> f6 : [ arg2^3 f6 : [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 ], cost: 1 4: f6 -> f7 : arg2'=1+arg2, [], cost: 1 7: f7 -> f8 : [ arg2>arg1 ], cost: 1 8: f7 -> f9 : [ arg2<=arg1 ], cost: 1 5: f8 -> f11 : arg2'=1, [], cost: 1 6: f11 -> f12 : arg3'=1+arg3, [], cost: 1 9: f12 -> f10 : [], cost: 1 10: f9 -> f10 : [], cost: 1 13: f10 -> f13 : [ arg3>arg1 ], cost: 1 14: f10 -> f14 : [ arg3<=arg1 ], cost: 1 11: f13 -> f16 : arg3'=1, [], cost: 1 12: f16 -> f17 : arg4'=1+arg4, [], cost: 1 15: f17 -> f15 : [], cost: 1 16: f14 -> f15 : [], cost: 1 19: f15 -> f5 : [], cost: 1 22: __init -> f1 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 17: f5 -> f6 : [ arg2^3 f6 : [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 ], cost: 1 4: f6 -> f7 : arg2'=1+arg2, [], cost: 1 28: f7 -> f10 : [ arg2<=arg1 ], cost: 2 30: f7 -> f10 : arg2'=1, arg3'=1+arg3, [ arg2>arg1 ], cost: 4 32: f10 -> f15 : [ arg3<=arg1 ], cost: 2 34: f10 -> f15 : arg3'=1, arg4'=1+arg4, [ arg3>arg1 ], cost: 4 19: f15 -> f5 : [], cost: 1 26: __init -> f5 : arg1'=1000, arg2'=1, arg3'=1, arg4'=1, [], cost: 5 Eliminated locations (on tree-shaped paths): Start location: __init 35: f5 -> f7 : arg2'=1+arg2, [ arg2^3 f7 : arg2'=1+arg2, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 ], cost: 2 37: f7 -> f15 : [ arg2<=arg1 && arg3<=arg1 ], cost: 4 38: f7 -> f15 : arg3'=1, arg4'=1+arg4, [ arg2<=arg1 && arg3>arg1 ], cost: 6 39: f7 -> f15 : arg2'=1, arg3'=1+arg3, [ arg2>arg1 && 1+arg3<=arg1 ], cost: 6 40: f7 -> f15 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2>arg1 && 1+arg3>arg1 ], cost: 8 19: f15 -> f5 : [], cost: 1 26: __init -> f5 : arg1'=1000, arg2'=1, arg3'=1, arg4'=1, [], cost: 5 Eliminated locations (on tree-shaped paths): Start location: __init 41: f5 -> f15 : arg2'=1+arg2, [ arg2^3 f15 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 ], cost: 8 43: f5 -> f15 : arg2'=1, arg3'=1+arg3, [ arg2^3arg1 && 1+arg3<=arg1 ], cost: 8 44: f5 -> f15 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 && 1+arg3>arg1 ], cost: 10 45: f5 -> f15 : arg2'=1+arg2, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3<=arg1 ], cost: 6 46: f5 -> f15 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3>arg1 ], cost: 8 47: f5 -> f15 : arg2'=1, arg3'=1+arg3, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3<=arg1 ], cost: 8 48: f5 -> f15 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3>arg1 ], cost: 10 19: f15 -> f5 : [], cost: 1 26: __init -> f5 : arg1'=1000, arg2'=1, arg3'=1, arg4'=1, [], cost: 5 Eliminated locations (on tree-shaped paths): Start location: __init 49: f5 -> f5 : arg2'=1+arg2, [ arg2^3 f5 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 ], cost: 9 51: f5 -> f5 : arg2'=1, arg3'=1+arg3, [ arg2^3arg1 && 1+arg3<=arg1 ], cost: 9 52: f5 -> f5 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 && 1+arg3>arg1 ], cost: 11 53: f5 -> f5 : arg2'=1+arg2, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3<=arg1 ], cost: 7 54: f5 -> f5 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3>arg1 ], cost: 9 55: f5 -> f5 : arg2'=1, arg3'=1+arg3, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3<=arg1 ], cost: 9 56: f5 -> f5 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3>arg1 ], cost: 11 26: __init -> f5 : arg1'=1000, arg2'=1, arg3'=1, arg4'=1, [], cost: 5 Accelerating simple loops of location 4. Accelerating the following rules: 49: f5 -> f5 : arg2'=1+arg2, [ arg2^3 f5 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 ], cost: 9 51: f5 -> f5 : arg2'=1, arg3'=1+arg3, [ arg2^3arg1 && 1+arg3<=arg1 ], cost: 9 52: f5 -> f5 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 && 1+arg3>arg1 ], cost: 11 53: f5 -> f5 : arg2'=1+arg2, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3<=arg1 ], cost: 7 54: f5 -> f5 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3>arg1 ], cost: 9 55: f5 -> f5 : arg2'=1, arg3'=1+arg3, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3<=arg1 ], cost: 9 56: f5 -> f5 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3>arg1 ], cost: 11 Accelerated rule 49 with backward acceleration, yielding the new rule 57. Failed to prove monotonicity of the guard of rule 50. Failed to prove monotonicity of the guard of rule 51. Failed to prove monotonicity of the guard of rule 52. Failed to prove monotonicity of the guard of rule 53. Failed to prove monotonicity of the guard of rule 54. Failed to prove monotonicity of the guard of rule 55. Failed to prove monotonicity of the guard of rule 56. [accelerate] Nesting with 8 inner and 8 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 49: f5 -> f5 : arg2'=1+arg2, [ arg2^3 f5 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 ], cost: 9 51: f5 -> f5 : arg2'=1, arg3'=1+arg3, [ arg2^3arg1 && 1+arg3<=arg1 ], cost: 9 52: f5 -> f5 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 && 1+arg3>arg1 ], cost: 11 53: f5 -> f5 : arg2'=1+arg2, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3<=arg1 ], cost: 7 54: f5 -> f5 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3>arg1 ], cost: 9 55: f5 -> f5 : arg2'=1, arg3'=1+arg3, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3<=arg1 ], cost: 9 56: f5 -> f5 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3>arg1 ], cost: 11 57: f5 -> f5 : arg2'=arg1, [ arg4<=arg1 && arg3<=arg1 && -arg2+arg1>=0 && (-1+arg1)^3 f5 : arg1'=1000, arg2'=1, arg3'=1, arg4'=1, [], cost: 5 Aborted due to lack of remaining time ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 49: f5 -> f5 : arg2'=1+arg2, [ arg2^3 f5 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 ], cost: 9 51: f5 -> f5 : arg2'=1, arg3'=1+arg3, [ arg2^3arg1 && 1+arg3<=arg1 ], cost: 9 52: f5 -> f5 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3arg1 && 1+arg3>arg1 ], cost: 11 53: f5 -> f5 : arg2'=1+arg2, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3<=arg1 ], cost: 7 54: f5 -> f5 : arg2'=1+arg2, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2<=arg1 && arg3>arg1 ], cost: 9 55: f5 -> f5 : arg2'=1, arg3'=1+arg3, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3<=arg1 ], cost: 9 56: f5 -> f5 : arg2'=1, arg3'=1, arg4'=1+arg4, [ arg2^3>arg3^3+arg4^3 && arg4<=arg1 && 1+arg2>arg1 && 1+arg3>arg1 ], cost: 11 57: f5 -> f5 : arg2'=arg1, [ arg4<=arg1 && arg3<=arg1 && -arg2+arg1>=0 && (-1+arg1)^3 f5 : arg1'=1000, arg2'=1, arg3'=1, arg4'=1, [], cost: 5 This is only a partial result (probably due to a timeout). Trying to find the maximal complexity that has already been derived. Performed chaining from the start location: Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [] WORST_CASE(Omega(1),?)