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, [ 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 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1 30: f3 -> f4 : arg1'=arg1P_31, arg2'=arg2P_31, arg3'=arg3P_31, arg4'=arg4P_31, [ arg2>0 && arg1>0 && arg1==arg1P_31 && arg2==arg2P_31 && arg3==arg3P_31 && arg4==arg4P_31 ], cost: 1 32: f3 -> f27 : arg1'=arg1P_33, arg2'=arg2P_33, arg3'=arg3P_33, arg4'=arg4P_33, [ arg2<=0 && arg1==arg1P_33 && arg2==arg2P_33 && arg3==arg3P_33 && arg4==arg4P_33 ], cost: 1 33: f3 -> f27 : arg1'=arg1P_34, arg2'=arg2P_34, arg3'=arg3P_34, arg4'=arg4P_34, [ arg1<=0 && arg1==arg1P_34 && arg2==arg2P_34 && arg3==arg3P_34 && arg4==arg4P_34 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg2==arg3P_3 && arg4==arg4P_3 ], cost: 1 3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg1==arg4P_4 ], cost: 1 10: f6 -> f7 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2==0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1 11: f6 -> f8 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1 12: f6 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg2>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1 4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 13: f10 -> f9 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1 5: f11 -> f14 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4P_6==-arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1 8: f14 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1 6: f8 -> f11 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg2<0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1 7: f8 -> f12 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2>=0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 9: f12 -> f13 : 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 14: f13 -> f9 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 ], cost: 1 25: f9 -> f15 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, [ arg4>0 && arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 ], cost: 1 26: f9 -> f16 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, [ arg4<=0 && arg1==arg1P_27 && arg2==arg2P_27 && arg3==arg3P_27 && arg4==arg4P_27 ], cost: 1 15: f18 -> f19 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [ arg4P_16==-arg2+arg4 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1 17: f19 -> f15 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 ], cost: 1 16: f15 -> f18 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, [ arg4>=arg2 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 ], cost: 1 18: f15 -> f20 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, [ arg4 f21 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, [ arg1==arg1P_20 && arg4==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 ], cost: 1 27: f21 -> f17 : arg1'=arg1P_28, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, [ arg1==arg1P_28 && arg2==arg2P_28 && arg3==arg3P_28 && arg4==arg4P_28 ], cost: 1 20: f22 -> f23 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [ arg4P_21==-arg2+arg4 && arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 ], cost: 1 22: f23 -> f16 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, [ arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 ], cost: 1 21: f16 -> f22 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, [ arg4<0 && arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 ], cost: 1 23: f16 -> f24 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, [ arg4>=0 && arg1==arg1P_24 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 ], cost: 1 24: f24 -> f25 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, [ arg1==arg1P_25 && arg4==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 ], cost: 1 28: f25 -> f17 : arg1'=arg1P_29, arg2'=arg2P_29, arg3'=arg3P_29, arg4'=arg4P_29, [ arg1==arg1P_29 && arg2==arg2P_29 && arg3==arg3P_29 && arg4==arg4P_29 ], cost: 1 29: f17 -> f26 : arg1'=arg1P_30, arg2'=arg2P_30, arg3'=arg3P_30, arg4'=arg4P_30, [ arg3==arg1P_30 && arg2==arg2P_30 && arg3==arg3P_30 && arg4==arg4P_30 ], cost: 1 31: f26 -> f3 : arg1'=arg1P_32, arg2'=arg2P_32, arg3'=arg3P_32, arg4'=arg4P_32, [ arg1==arg1P_32 && arg2==arg2P_32 && arg3==arg3P_32 && arg4==arg4P_32 ], cost: 1 34: __init -> f1 : arg1'=arg1P_35, arg2'=arg2P_35, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 34: __init -> f1 : arg1'=arg1P_35, arg2'=arg2P_35, arg3'=arg3P_35, arg4'=arg4P_35, [], 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, [ 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 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1 30: f3 -> f4 : arg1'=arg1P_31, arg2'=arg2P_31, arg3'=arg3P_31, arg4'=arg4P_31, [ arg2>0 && arg1>0 && arg1==arg1P_31 && arg2==arg2P_31 && arg3==arg3P_31 && arg4==arg4P_31 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg2==arg3P_3 && arg4==arg4P_3 ], cost: 1 3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg1==arg4P_4 ], cost: 1 10: f6 -> f7 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2==0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1 11: f6 -> f8 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1 12: f6 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg2>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1 4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 13: f10 -> f9 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1 5: f11 -> f14 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4P_6==-arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1 8: f14 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1 6: f8 -> f11 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg2<0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1 7: f8 -> f12 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2>=0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 9: f12 -> f13 : 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 14: f13 -> f9 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 ], cost: 1 25: f9 -> f15 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, [ arg4>0 && arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 ], cost: 1 26: f9 -> f16 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, [ arg4<=0 && arg1==arg1P_27 && arg2==arg2P_27 && arg3==arg3P_27 && arg4==arg4P_27 ], cost: 1 15: f18 -> f19 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [ arg4P_16==-arg2+arg4 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1 17: f19 -> f15 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 ], cost: 1 16: f15 -> f18 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, [ arg4>=arg2 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 ], cost: 1 18: f15 -> f20 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, [ arg4 f21 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, [ arg1==arg1P_20 && arg4==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 ], cost: 1 27: f21 -> f17 : arg1'=arg1P_28, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, [ arg1==arg1P_28 && arg2==arg2P_28 && arg3==arg3P_28 && arg4==arg4P_28 ], cost: 1 20: f22 -> f23 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [ arg4P_21==-arg2+arg4 && arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 ], cost: 1 22: f23 -> f16 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, [ arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 ], cost: 1 21: f16 -> f22 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, [ arg4<0 && arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 ], cost: 1 23: f16 -> f24 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, [ arg4>=0 && arg1==arg1P_24 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 ], cost: 1 24: f24 -> f25 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, [ arg1==arg1P_25 && arg4==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 ], cost: 1 28: f25 -> f17 : arg1'=arg1P_29, arg2'=arg2P_29, arg3'=arg3P_29, arg4'=arg4P_29, [ arg1==arg1P_29 && arg2==arg2P_29 && arg3==arg3P_29 && arg4==arg4P_29 ], cost: 1 29: f17 -> f26 : arg1'=arg1P_30, arg2'=arg2P_30, arg3'=arg3P_30, arg4'=arg4P_30, [ arg3==arg1P_30 && arg2==arg2P_30 && arg3==arg3P_30 && arg4==arg4P_30 ], cost: 1 31: f26 -> f3 : arg1'=arg1P_32, arg2'=arg2P_32, arg3'=arg3P_32, arg4'=arg4P_32, [ arg1==arg1P_32 && arg2==arg2P_32 && arg3==arg3P_32 && arg4==arg4P_32 ], cost: 1 34: __init -> f1 : arg1'=arg1P_35, arg2'=arg2P_35, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1 30: f3 -> f4 : [ arg2>0 && arg1>0 ], cost: 1 2: f4 -> f5 : arg3'=arg2, [], cost: 1 3: f5 -> f6 : arg4'=arg1, [], cost: 1 10: f6 -> f7 : [ arg2==0 ], cost: 1 11: f6 -> f8 : [ arg2<0 ], cost: 1 12: f6 -> f8 : [ arg2>0 ], cost: 1 4: f7 -> f10 : [], cost: 1 13: f10 -> f9 : [], cost: 1 5: f11 -> f14 : arg4'=-arg4, [], cost: 1 8: f14 -> f13 : [], cost: 1 6: f8 -> f11 : [ arg2<0 ], cost: 1 7: f8 -> f12 : [ arg2>=0 ], cost: 1 9: f12 -> f13 : [], cost: 1 14: f13 -> f9 : [], cost: 1 25: f9 -> f15 : [ arg4>0 ], cost: 1 26: f9 -> f16 : [ arg4<=0 ], cost: 1 15: f18 -> f19 : arg4'=-arg2+arg4, [], cost: 1 17: f19 -> f15 : [], cost: 1 16: f15 -> f18 : [ arg4>=arg2 ], cost: 1 18: f15 -> f20 : [ arg4 f21 : arg2'=arg4, [], cost: 1 27: f21 -> f17 : [], cost: 1 20: f22 -> f23 : arg4'=-arg2+arg4, [], cost: 1 22: f23 -> f16 : [], cost: 1 21: f16 -> f22 : [ arg4<0 ], cost: 1 23: f16 -> f24 : [ arg4>=0 ], cost: 1 24: f24 -> f25 : arg2'=arg4, [], cost: 1 28: f25 -> f17 : [], cost: 1 29: f17 -> f26 : arg1'=arg3, [], cost: 1 31: f26 -> f3 : [], cost: 1 34: __init -> f1 : arg1'=arg1P_35, arg2'=arg2P_35, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 38: f3 -> f6 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 3 11: f6 -> f8 : [ arg2<0 ], cost: 1 12: f6 -> f8 : [ arg2>0 ], cost: 1 40: f6 -> f9 : [ arg2==0 ], cost: 3 42: f8 -> f13 : [ arg2>=0 ], cost: 2 43: f8 -> f13 : arg4'=-arg4, [ arg2<0 ], cost: 3 14: f13 -> f9 : [], cost: 1 25: f9 -> f15 : [ arg4>0 ], cost: 1 26: f9 -> f16 : [ arg4<=0 ], cost: 1 46: f15 -> f15 : arg4'=-arg2+arg4, [ arg4>=arg2 ], cost: 3 47: f15 -> f17 : arg2'=arg4, [ arg4 f16 : arg4'=-arg2+arg4, [ arg4<0 ], cost: 3 52: f16 -> f17 : arg2'=arg4, [ arg4>=0 ], cost: 3 48: f17 -> f3 : arg1'=arg3, [], cost: 2 36: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Accelerating simple loops of location 16. Accelerating the following rules: 46: f15 -> f15 : arg4'=-arg2+arg4, [ arg4>=arg2 ], cost: 3 [test] deduced pseudo-invariant arg2<=0, also trying -arg2<=-1 Accelerated rule 46 with non-termination, yielding the new rule 53. Accelerated rule 46 with non-termination, yielding the new rule 54. Accelerated rule 46 with backward acceleration, yielding the new rule 55. Accelerated rule 46 with backward acceleration, yielding the new rule 56. [accelerate] Nesting with 1 inner and 1 outer candidates Also removing duplicate rules: 54. Accelerating simple loops of location 21. Accelerating the following rules: 51: f16 -> f16 : arg4'=-arg2+arg4, [ arg4<0 ], cost: 3 [test] deduced pseudo-invariant -arg2<=0, also trying arg2<=-1 Accelerated rule 51 with non-termination, yielding the new rule 57. Accelerated rule 51 with non-termination, yielding the new rule 58. Accelerated rule 51 with backward acceleration, yielding the new rule 59. Accelerated rule 51 with backward acceleration, yielding the new rule 60. [accelerate] Nesting with 1 inner and 1 outer candidates Also removing duplicate rules: 58. Accelerated all simple loops using metering functions (where possible): Start location: __init 38: f3 -> f6 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 3 11: f6 -> f8 : [ arg2<0 ], cost: 1 12: f6 -> f8 : [ arg2>0 ], cost: 1 40: f6 -> f9 : [ arg2==0 ], cost: 3 42: f8 -> f13 : [ arg2>=0 ], cost: 2 43: f8 -> f13 : arg4'=-arg4, [ arg2<0 ], cost: 3 14: f13 -> f9 : [], cost: 1 25: f9 -> f15 : [ arg4>0 ], cost: 1 26: f9 -> f16 : [ arg4<=0 ], cost: 1 46: f15 -> f15 : arg4'=-arg2+arg4, [ arg4>=arg2 ], cost: 3 47: f15 -> f17 : arg2'=arg4, [ arg4 [28] : [ arg4>=arg2 && arg2==0 && arg4==0 ], cost: NONTERM 55: f15 -> [28] : [ arg4>=arg2 && arg2<=0 ], cost: NONTERM 56: f15 -> f15 : arg4'=-arg2*k+arg4, [ -arg2<=-1 && k>=0 && -arg2*(-1+k)+arg4>=arg2 ], cost: 3*k 51: f16 -> f16 : arg4'=-arg2+arg4, [ arg4<0 ], cost: 3 52: f16 -> f17 : arg2'=arg4, [ arg4>=0 ], cost: 3 57: f16 -> [29] : [ arg2==0 && arg4==-1 ], cost: NONTERM 59: f16 -> [29] : [ arg4<0 && -arg2<=0 ], cost: NONTERM 60: f16 -> f16 : arg4'=arg4-k_2*arg2, [ arg2<=-1 && k_2>=0 && -arg2*(-1+k_2)+arg4<0 ], cost: 3*k_2 48: f17 -> f3 : arg1'=arg3, [], cost: 2 36: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Chained accelerated rules (with incoming rules): Start location: __init 38: f3 -> f6 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 3 11: f6 -> f8 : [ arg2<0 ], cost: 1 12: f6 -> f8 : [ arg2>0 ], cost: 1 40: f6 -> f9 : [ arg2==0 ], cost: 3 42: f8 -> f13 : [ arg2>=0 ], cost: 2 43: f8 -> f13 : arg4'=-arg4, [ arg2<0 ], cost: 3 14: f13 -> f9 : [], cost: 1 25: f9 -> f15 : [ arg4>0 ], cost: 1 26: f9 -> f16 : [ arg4<=0 ], cost: 1 61: f9 -> f15 : arg4'=-arg2+arg4, [ arg4>0 && arg4>=arg2 ], cost: 4 62: f9 -> [28] : [ arg4>0 && arg4>=arg2 && arg2<=0 ], cost: NONTERM 63: f9 -> f15 : arg4'=-arg2*k+arg4, [ arg4>0 && -arg2<=-1 && k>=0 && -arg2*(-1+k)+arg4>=arg2 ], cost: 1+3*k 64: f9 -> f16 : arg4'=-arg2+arg4, [ arg4<0 ], cost: 4 65: f9 -> [29] : [ arg2==0 && arg4==-1 ], cost: NONTERM 66: f9 -> [29] : [ arg4<0 && -arg2<=0 ], cost: NONTERM 67: f9 -> f16 : arg4'=arg4-k_2*arg2, [ arg4<=0 && arg2<=-1 && k_2>=0 && -arg2*(-1+k_2)+arg4<0 ], cost: 1+3*k_2 47: f15 -> f17 : arg2'=arg4, [ arg4 f17 : arg2'=arg4, [ arg4>=0 ], cost: 3 48: f17 -> f3 : arg1'=arg3, [], cost: 2 36: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 68: f3 -> f8 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 4 69: f8 -> f9 : [ arg2>=0 ], cost: 3 70: f8 -> f9 : arg4'=-arg4, [ arg2<0 ], cost: 4 62: f9 -> [28] : [ arg4>0 && arg4>=arg2 && arg2<=0 ], cost: NONTERM 65: f9 -> [29] : [ arg2==0 && arg4==-1 ], cost: NONTERM 66: f9 -> [29] : [ arg4<0 && -arg2<=0 ], cost: NONTERM 71: f9 -> f17 : arg2'=arg4, [ arg4>0 && arg4 f17 : arg2'=-arg2+arg4, arg4'=-arg2+arg4, [ arg4>0 && arg4>=arg2 && -arg2+arg4 f17 : arg2'=-arg2*k+arg4, arg4'=-arg2*k+arg4, [ arg4>0 && -arg2<=-1 && k>=0 && -arg2*(-1+k)+arg4>=arg2 && -arg2*k+arg4 f17 : arg2'=arg4, [ arg4<=0 && arg4>=0 ], cost: 4 75: f9 -> f17 : arg2'=-arg2+arg4, arg4'=-arg2+arg4, [ arg4<0 && -arg2+arg4>=0 ], cost: 7 76: f9 -> f17 : arg2'=arg4-k_2*arg2, arg4'=arg4-k_2*arg2, [ arg4<=0 && arg2<=-1 && k_2>=0 && -arg2*(-1+k_2)+arg4<0 && arg4-k_2*arg2>=0 ], cost: 4+3*k_2 48: f17 -> f3 : arg1'=arg3, [], cost: 2 36: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Applied pruning (of leafs and parallel rules): Start location: __init 68: f3 -> f8 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 4 69: f8 -> f9 : [ arg2>=0 ], cost: 3 70: f8 -> f9 : arg4'=-arg4, [ arg2<0 ], cost: 4 62: f9 -> [28] : [ arg4>0 && arg4>=arg2 && arg2<=0 ], cost: NONTERM 65: f9 -> [29] : [ arg2==0 && arg4==-1 ], cost: NONTERM 66: f9 -> [29] : [ arg4<0 && -arg2<=0 ], cost: NONTERM 71: f9 -> f17 : arg2'=arg4, [ arg4>0 && arg4 f17 : arg2'=-arg2+arg4, arg4'=-arg2+arg4, [ arg4>0 && arg4>=arg2 && -arg2+arg4 f17 : arg2'=-arg2*k+arg4, arg4'=-arg2*k+arg4, [ arg4>0 && -arg2<=-1 && k>=0 && -arg2*(-1+k)+arg4>=arg2 && -arg2*k+arg4 f17 : arg2'=arg4, [ arg4<=0 && arg4>=0 ], cost: 4 76: f9 -> f17 : arg2'=arg4-k_2*arg2, arg4'=arg4-k_2*arg2, [ arg4<=0 && arg2<=-1 && k_2>=0 && -arg2*(-1+k_2)+arg4<0 && arg4-k_2*arg2>=0 ], cost: 4+3*k_2 48: f17 -> f3 : arg1'=arg3, [], cost: 2 36: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 77: f3 -> f9 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 7 62: f9 -> [28] : [ arg4>0 && arg4>=arg2 && arg2<=0 ], cost: NONTERM 65: f9 -> [29] : [ arg2==0 && arg4==-1 ], cost: NONTERM 66: f9 -> [29] : [ arg4<0 && -arg2<=0 ], cost: NONTERM 78: f9 -> f3 : arg1'=arg3, arg2'=arg4, [ arg4>0 && arg4 f3 : arg1'=arg3, arg2'=-arg2+arg4, arg4'=-arg2+arg4, [ arg4>0 && arg4>=arg2 && -arg2+arg4 f3 : arg1'=arg3, arg2'=-arg2*k+arg4, arg4'=-arg2*k+arg4, [ arg4>0 && -arg2<=-1 && k>=0 && -arg2*(-1+k)+arg4>=arg2 && -arg2*k+arg4 f3 : arg1'=arg3, arg2'=arg4, [ arg4<=0 && arg4>=0 ], cost: 6 82: f9 -> f3 : arg1'=arg3, arg2'=arg4-k_2*arg2, arg4'=arg4-k_2*arg2, [ arg4<=0 && arg2<=-1 && k_2>=0 && -arg2*(-1+k_2)+arg4<0 && arg4-k_2*arg2>=0 ], cost: 6+3*k_2 36: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 83: f3 -> f3 : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 && arg1 f3 : arg1'=arg2, arg2'=-arg2+arg1, arg3'=arg2, arg4'=-arg2+arg1, [ arg2>0 && arg1>0 && arg1>=arg2 && -arg2+arg1 f3 : arg1'=arg2, arg2'=-arg2*k+arg1, arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 && -arg2*k+arg1 f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Applied pruning (of leafs and parallel rules): Start location: __init 83: f3 -> f3 : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 && arg1 f3 : arg1'=arg2, arg2'=-arg2+arg1, arg3'=arg2, arg4'=-arg2+arg1, [ arg2>0 && arg1>0 && arg1>=arg2 && -arg2+arg1 f3 : arg1'=arg2, arg2'=-arg2*k+arg1, arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 && -arg2*k+arg1 f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Accelerating simple loops of location 2. Accelerating the following rules: 83: f3 -> f3 : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 && arg1 f3 : arg1'=arg2, arg2'=-arg2+arg1, arg3'=arg2, arg4'=-arg2+arg1, [ arg2>0 && arg1>0 && arg1>=arg2 && -arg2+arg1 f3 : arg1'=arg2, arg2'=-arg2*k+arg1, arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 && -arg2*k+arg1 f3 : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 && arg1 f3 : arg1'=arg2, arg2'=-arg2+arg1, arg3'=arg2, arg4'=-arg2+arg1, [ arg2>0 && arg1>0 && arg1>=arg2 && -arg2+arg1 f3 : arg1'=arg2, arg2'=-arg2*k+arg1, arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 && -arg2*k+arg1 f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 Chained accelerated rules (with incoming rules): Start location: __init 36: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_35, arg4'=arg4P_35, [], cost: 3 86: __init -> f3 : arg1'=arg2P_2, arg2'=arg1P_1, arg3'=arg2P_2, arg4'=arg1P_1, [ arg2P_2>0 && arg1P_1>0 && arg1P_1 f3 : arg1'=arg2P_2, arg2'=-arg2P_2+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2+arg1P_1, [ arg2P_2>0 && arg1P_1>0 && arg1P_1>=arg2P_2 && -arg2P_2+arg1P_1 f3 : arg1'=arg2P_2, arg2'=-arg2P_2*k+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2*k+arg1P_1, [ arg2P_2>0 && arg1P_1>0 && k>=0 && arg1P_1-arg2P_2*(-1+k)>=arg2P_2 && -arg2P_2*k+arg1P_1 f3 : arg1'=arg2P_2, arg2'=-arg2P_2*k+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2*k+arg1P_1, [ arg2P_2>0 && arg1P_1>0 && k>=0 && arg1P_1-arg2P_2*(-1+k)>=arg2P_2 && -arg2P_2*k+arg1P_1 f3 : arg1'=arg2P_2, arg2'=-arg2P_2*k+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2*k+arg1P_1, [ arg2P_2>0 && arg1P_1>0 && k>=0 && arg1P_1-arg2P_2*(-1+k)>=arg2P_2 && -arg2P_2*k+arg1P_1 f3 : arg1'=arg2P_2, arg2'=-arg2P_2*k+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2*k+arg1P_1, [ arg1P_1>0 && k>=0 && arg1P_1-arg2P_2*(-1+k)>=arg2P_2 && -arg2P_2*k+arg1P_1