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
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_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 ], cost: 1
     28: f5 -> f6 : arg1'=arg1P_29, arg2'=arg2P_29, arg3'=arg3P_29, arg4'=arg4P_29, [ arg3<=arg1 && arg4>=arg2 && arg1==arg1P_29 && arg2==arg2P_29 && arg3==arg3P_29 && arg4==arg4P_29 ], cost: 1
     29: f5 -> f6 : arg1'=arg1P_30, arg2'=arg2P_30, arg3'=arg3P_30, arg4'=arg4P_30, [ arg3>=arg1 && arg4>=arg2 && arg1==arg1P_30 && arg2==arg2P_30 && arg3==arg3P_30 && arg4==arg4P_30 ], cost: 1
     30: f5 -> f6 : arg1'=arg1P_31, arg2'=arg2P_31, arg3'=arg3P_31, arg4'=arg4P_31, [ arg3>=arg1 && arg4<=arg2 && arg1==arg1P_31 && arg2==arg2P_31 && arg3==arg3P_31 && arg4==arg4P_31 ], cost: 1
     32: f5 -> f23 : arg1'=arg1P_33, arg2'=arg2P_33, arg3'=arg3P_33, arg4'=arg4P_33, [ arg3<arg1 && arg3<arg1 && arg3>arg1 && arg1==arg1P_33 && arg2==arg2P_33 && arg3==arg3P_33 && arg4==arg4P_33 ], cost: 1
     33: f5 -> f23 : arg1'=arg1P_34, arg2'=arg2P_34, arg3'=arg3P_34, arg4'=arg4P_34, [ arg3<arg1 && arg3<arg1 && arg4<arg2 && arg1==arg1P_34 && arg2==arg2P_34 && arg3==arg3P_34 && arg4==arg4P_34 ], cost: 1
     34: f5 -> f23 : arg1'=arg1P_35, arg2'=arg2P_35, arg3'=arg3P_35, arg4'=arg4P_35, [ arg3<arg1 && arg4>arg2 && arg3>arg1 && arg1==arg1P_35 && arg2==arg2P_35 && arg3==arg3P_35 && arg4==arg4P_35 ], cost: 1
     35: f5 -> f23 : arg1'=arg1P_36, arg2'=arg2P_36, arg3'=arg3P_36, arg4'=arg4P_36, [ arg3<arg1 && arg4>arg2 && arg4<arg2 && arg1==arg1P_36 && arg2==arg2P_36 && arg3==arg3P_36 && arg4==arg4P_36 ], cost: 1
     36: f5 -> f23 : arg1'=arg1P_37, arg2'=arg2P_37, arg3'=arg3P_37, arg4'=arg4P_37, [ arg4<arg2 && arg3<arg1 && arg3>arg1 && arg1==arg1P_37 && arg2==arg2P_37 && arg3==arg3P_37 && arg4==arg4P_37 ], cost: 1
     37: f5 -> f23 : arg1'=arg1P_38, arg2'=arg2P_38, arg3'=arg3P_38, arg4'=arg4P_38, [ arg4<arg2 && arg3<arg1 && arg4<arg2 && arg1==arg1P_38 && arg2==arg2P_38 && arg3==arg3P_38 && arg4==arg4P_38 ], cost: 1
     38: f5 -> f23 : arg1'=arg1P_39, arg2'=arg2P_39, arg3'=arg3P_39, arg4'=arg4P_39, [ arg4<arg2 && arg4>arg2 && arg3>arg1 && arg1==arg1P_39 && arg2==arg2P_39 && arg3==arg3P_39 && arg4==arg4P_39 ], cost: 1
     39: f5 -> f23 : arg1'=arg1P_40, arg2'=arg2P_40, arg3'=arg3P_40, arg4'=arg4P_40, [ arg4<arg2 && arg4>arg2 && arg4<arg2 && arg1==arg1P_40 && arg2==arg2P_40 && arg3==arg3P_40 && arg4==arg4P_40 ], cost: 1
      4: f10 -> f13 : 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
      9: f13 -> f12 : 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
      5: f11 -> f14 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg1P_6==1+arg1 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
     10: f14 -> f12 : 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
      6: f7 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ x27_1<0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      7: f7 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ x118_1>0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      8: f7 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ x32_1==0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
     26: f12 -> f9 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, [ arg1==arg1P_27 && arg2==arg2P_27 && arg3==arg3P_27 && arg4==arg4P_27 ], cost: 1
     11: f15 -> f18 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1P_12==1+arg1 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     21: f18 -> f17 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, [ arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 ], cost: 1
     12: f19 -> f22 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg2P_13==1+arg2 && arg1==arg1P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     16: f22 -> f21 : 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
     13: f16 -> f19 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg3<=arg1 && arg4>=arg2 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
     14: f16 -> f20 : 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
     15: f16 -> f20 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [ arg4<arg2 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 ], cost: 1
     17: f20 -> f21 : 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
     22: f21 -> f17 : 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
     18: f8 -> f15 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, [ arg3>=arg1 && arg4<=arg2 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 ], cost: 1
     19: f8 -> f16 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, [ arg3<arg1 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 ], cost: 1
     20: f8 -> f16 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [ arg4>arg2 && arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 && arg4==arg4P_21 ], cost: 1
     27: f17 -> f9 : 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
     23: f6 -> f7 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, [ arg3>=arg1 && arg4>=arg2 && arg1==arg1P_24 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 ], cost: 1
     24: f6 -> f8 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, [ arg3<arg1 && arg1==arg1P_25 && arg2==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 ], cost: 1
     25: f6 -> f8 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, [ arg4<arg2 && arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 ], cost: 1
     31: f9 -> f5 : 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
     40: __init -> f1 : arg1'=arg1P_41, arg2'=arg2P_41, arg3'=arg3P_41, arg4'=arg4P_41, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     40: __init -> f1 : arg1'=arg1P_41, arg2'=arg2P_41, arg3'=arg3P_41, arg4'=arg4P_41, [], 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
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_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 ], cost: 1
     28: f5 -> f6 : arg1'=arg1P_29, arg2'=arg2P_29, arg3'=arg3P_29, arg4'=arg4P_29, [ arg3<=arg1 && arg4>=arg2 && arg1==arg1P_29 && arg2==arg2P_29 && arg3==arg3P_29 && arg4==arg4P_29 ], cost: 1
     29: f5 -> f6 : arg1'=arg1P_30, arg2'=arg2P_30, arg3'=arg3P_30, arg4'=arg4P_30, [ arg3>=arg1 && arg4>=arg2 && arg1==arg1P_30 && arg2==arg2P_30 && arg3==arg3P_30 && arg4==arg4P_30 ], cost: 1
     30: f5 -> f6 : arg1'=arg1P_31, arg2'=arg2P_31, arg3'=arg3P_31, arg4'=arg4P_31, [ arg3>=arg1 && arg4<=arg2 && arg1==arg1P_31 && arg2==arg2P_31 && arg3==arg3P_31 && arg4==arg4P_31 ], cost: 1
      4: f10 -> f13 : 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
      9: f13 -> f12 : 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
      5: f11 -> f14 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg1P_6==1+arg1 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
     10: f14 -> f12 : 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
      6: f7 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ x27_1<0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      7: f7 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ x118_1>0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      8: f7 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ x32_1==0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
     26: f12 -> f9 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, [ arg1==arg1P_27 && arg2==arg2P_27 && arg3==arg3P_27 && arg4==arg4P_27 ], cost: 1
     11: f15 -> f18 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1P_12==1+arg1 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     21: f18 -> f17 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, [ arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 ], cost: 1
     12: f19 -> f22 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg2P_13==1+arg2 && arg1==arg1P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     16: f22 -> f21 : 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
     13: f16 -> f19 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg3<=arg1 && arg4>=arg2 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
     14: f16 -> f20 : 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
     15: f16 -> f20 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [ arg4<arg2 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 ], cost: 1
     17: f20 -> f21 : 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
     22: f21 -> f17 : 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
     18: f8 -> f15 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, [ arg3>=arg1 && arg4<=arg2 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 ], cost: 1
     19: f8 -> f16 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, [ arg3<arg1 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 ], cost: 1
     20: f8 -> f16 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [ arg4>arg2 && arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 && arg4==arg4P_21 ], cost: 1
     27: f17 -> f9 : 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
     23: f6 -> f7 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, [ arg3>=arg1 && arg4>=arg2 && arg1==arg1P_24 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 ], cost: 1
     24: f6 -> f8 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, [ arg3<arg1 && arg1==arg1P_25 && arg2==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 ], cost: 1
     25: f6 -> f8 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, [ arg4<arg2 && arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 ], cost: 1
     31: f9 -> f5 : 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
     40: __init -> f1 : arg1'=arg1P_41, arg2'=arg2P_41, arg3'=arg3P_41, arg4'=arg4P_41, [], 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
      2: f3 -> f4 : arg3'=arg3P_3, [], cost: 1
      3: f4 -> f5 : arg4'=arg4P_4, [], cost: 1
     28: f5 -> f6 : [ arg3<=arg1 && arg4>=arg2 ], cost: 1
     29: f5 -> f6 : [ arg3>=arg1 && arg4>=arg2 ], cost: 1
     30: f5 -> f6 : [ arg3>=arg1 && arg4<=arg2 ], cost: 1
      4: f10 -> f13 : arg2'=1+arg2, [], cost: 1
      9: f13 -> f12 : [], cost: 1
      5: f11 -> f14 : arg1'=1+arg1, [], cost: 1
     10: f14 -> f12 : [], cost: 1
      7: f7 -> f10 : [], cost: 1
      8: f7 -> f11 : [], cost: 1
     26: f12 -> f9 : [], cost: 1
     11: f15 -> f18 : arg1'=1+arg1, [], cost: 1
     21: f18 -> f17 : [], cost: 1
     12: f19 -> f22 : arg2'=1+arg2, [], cost: 1
     16: f22 -> f21 : [], cost: 1
     13: f16 -> f19 : [ arg3<=arg1 && arg4>=arg2 ], cost: 1
     14: f16 -> f20 : [ arg3>arg1 ], cost: 1
     15: f16 -> f20 : [ arg4<arg2 ], cost: 1
     17: f20 -> f21 : [], cost: 1
     22: f21 -> f17 : [], cost: 1
     18: f8 -> f15 : [ arg3>=arg1 && arg4<=arg2 ], cost: 1
     19: f8 -> f16 : [ arg3<arg1 ], cost: 1
     20: f8 -> f16 : [ arg4>arg2 ], cost: 1
     27: f17 -> f9 : [], cost: 1
     23: f6 -> f7 : [ arg3>=arg1 && arg4>=arg2 ], cost: 1
     24: f6 -> f8 : [ arg3<arg1 ], cost: 1
     25: f6 -> f8 : [ arg4<arg2 ], cost: 1
     31: f9 -> f5 : [], cost: 1
     40: __init -> f1 : arg1'=arg1P_41, arg2'=arg2P_41, arg3'=arg3P_41, arg4'=arg4P_41, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     28: f5 -> f6 : [ arg3<=arg1 && arg4>=arg2 ], cost: 1
     29: f5 -> f6 : [ arg3>=arg1 && arg4>=arg2 ], cost: 1
     30: f5 -> f6 : [ arg3>=arg1 && arg4<=arg2 ], cost: 1
     47: f7 -> f12 : arg2'=1+arg2, [], cost: 3
     48: f7 -> f12 : arg1'=1+arg1, [], cost: 3
     26: f12 -> f9 : [], cost: 1
     14: f16 -> f20 : [ arg3>arg1 ], cost: 1
     15: f16 -> f20 : [ arg4<arg2 ], cost: 1
     52: f16 -> f21 : arg2'=1+arg2, [ arg3<=arg1 && arg4>=arg2 ], cost: 3
     17: f20 -> f21 : [], cost: 1
     22: f21 -> f17 : [], cost: 1
     19: f8 -> f16 : [ arg3<arg1 ], cost: 1
     20: f8 -> f16 : [ arg4>arg2 ], cost: 1
     50: f8 -> f17 : arg1'=1+arg1, [ arg3>=arg1 && arg4<=arg2 ], cost: 3
     27: f17 -> f9 : [], cost: 1
     23: f6 -> f7 : [ arg3>=arg1 && arg4>=arg2 ], cost: 1
     24: f6 -> f8 : [ arg3<arg1 ], cost: 1
     25: f6 -> f8 : [ arg4<arg2 ], cost: 1
     31: f9 -> f5 : [], cost: 1
     44: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     53: f5 -> f7 : [ arg3<=arg1 && arg4>=arg2 && arg3>=arg1 ], cost: 2
     54: f5 -> f8 : [ arg4>=arg2 && arg3<arg1 ], cost: 2
     55: f5 -> f7 : [ arg3>=arg1 && arg4>=arg2 ], cost: 2
     56: f5 -> f7 : [ arg3>=arg1 && arg4<=arg2 && arg4>=arg2 ], cost: 2
     57: f5 -> f8 : [ arg3>=arg1 && arg4<arg2 ], cost: 2
     58: f7 -> f9 : arg2'=1+arg2, [], cost: 4
     59: f7 -> f9 : arg1'=1+arg1, [], cost: 4
     17: f20 -> f21 : [], cost: 1
     22: f21 -> f17 : [], cost: 1
     50: f8 -> f17 : arg1'=1+arg1, [ arg3>=arg1 && arg4<=arg2 ], cost: 3
     60: f8 -> f20 : [ arg3<arg1 && arg4<arg2 ], cost: 2
     61: f8 -> f21 : arg2'=1+arg2, [ arg3<arg1 && arg4>=arg2 ], cost: 4
     62: f8 -> f20 : [ arg4>arg2 && arg3>arg1 ], cost: 2
     63: f8 -> f21 : arg2'=1+arg2, [ arg4>arg2 && arg3<=arg1 ], cost: 4
     27: f17 -> f9 : [], cost: 1
     31: f9 -> f5 : [], cost: 1
     44: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     64: f5 -> f9 : arg2'=1+arg2, [ arg3<=arg1 && arg4>=arg2 && arg3>=arg1 ], cost: 6
     65: f5 -> f9 : arg1'=1+arg1, [ arg3<=arg1 && arg4>=arg2 && arg3>=arg1 ], cost: 6
     66: f5 -> f9 : arg2'=1+arg2, [ arg3>=arg1 && arg4>=arg2 ], cost: 6
     67: f5 -> f9 : arg1'=1+arg1, [ arg3>=arg1 && arg4>=arg2 ], cost: 6
     68: f5 -> f9 : arg2'=1+arg2, [ arg3>=arg1 && arg4<=arg2 && arg4>=arg2 ], cost: 6
     69: f5 -> f9 : arg1'=1+arg1, [ arg3>=arg1 && arg4<=arg2 && arg4>=arg2 ], cost: 6
     70: f5 -> f21 : arg2'=1+arg2, [ arg4>=arg2 && arg3<arg1 ], cost: 6
     71: f5 -> f21 : arg2'=1+arg2, [ arg3<arg1 && arg4>arg2 ], cost: 6
     72: f5 -> f17 : arg1'=1+arg1, [ arg3>=arg1 && arg4<arg2 ], cost: 5
     17: f20 -> f21 : [], cost: 1
     22: f21 -> f17 : [], cost: 1
     27: f17 -> f9 : [], cost: 1
     31: f9 -> f5 : [], cost: 1
     44: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     64: f5 -> f9 : arg2'=1+arg2, [ arg3<=arg1 && arg4>=arg2 && arg3>=arg1 ], cost: 6
     65: f5 -> f9 : arg1'=1+arg1, [ arg3<=arg1 && arg4>=arg2 && arg3>=arg1 ], cost: 6
     66: f5 -> f9 : arg2'=1+arg2, [ arg3>=arg1 && arg4>=arg2 ], cost: 6
     67: f5 -> f9 : arg1'=1+arg1, [ arg3>=arg1 && arg4>=arg2 ], cost: 6
     68: f5 -> f9 : arg2'=1+arg2, [ arg3>=arg1 && arg4<=arg2 && arg4>=arg2 ], cost: 6
     69: f5 -> f9 : arg1'=1+arg1, [ arg3>=arg1 && arg4<=arg2 && arg4>=arg2 ], cost: 6
     70: f5 -> f21 : arg2'=1+arg2, [ arg4>=arg2 && arg3<arg1 ], cost: 6
     71: f5 -> f21 : arg2'=1+arg2, [ arg3<arg1 && arg4>arg2 ], cost: 6
     72: f5 -> f17 : arg1'=1+arg1, [ arg3>=arg1 && arg4<arg2 ], cost: 5
     22: f21 -> f17 : [], cost: 1
     27: f17 -> f9 : [], cost: 1
     31: f9 -> f5 : [], cost: 1
     44: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     78: f5 -> f5 : arg2'=1+arg2, [ arg3<=arg1 && arg4>=arg2 && arg3>=arg1 ], cost: 7
     79: f5 -> f5 : arg1'=1+arg1, [ arg3<=arg1 && arg4>=arg2 && arg3>=arg1 ], cost: 7
     80: f5 -> f5 : arg2'=1+arg2, [ arg3>=arg1 && arg4>=arg2 ], cost: 7
     81: f5 -> f5 : arg1'=1+arg1, [ arg3>=arg1 && arg4>=arg2 ], cost: 7
     82: f5 -> f5 : arg2'=1+arg2, [ arg3>=arg1 && arg4<=arg2 && arg4>=arg2 ], cost: 7
     83: f5 -> f5 : arg1'=1+arg1, [ arg3>=arg1 && arg4<=arg2 && arg4>=arg2 ], cost: 7
     84: f5 -> f5 : arg1'=1+arg1, [ arg3>=arg1 && arg4<arg2 ], cost: 7
     85: f5 -> f5 : arg2'=1+arg2, [ arg4>=arg2 && arg3<arg1 ], cost: 9
     86: f5 -> f5 : arg2'=1+arg2, [ arg3<arg1 && arg4>arg2 ], cost: 9
     44: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Accelerating simple loops of location 4.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     78: f5 -> f5 : arg2'=1+arg2, [ arg3-arg1==0 && arg4>=arg2 ], cost: 7
     79: f5 -> f5 : arg1'=1+arg1, [ arg3-arg1==0 && arg4>=arg2 ], cost: 7
     80: f5 -> f5 : arg2'=1+arg2, [ arg3>=arg1 && arg4>=arg2 ], cost: 7
     81: f5 -> f5 : arg1'=1+arg1, [ arg3>=arg1 && arg4>=arg2 ], cost: 7
     82: f5 -> f5 : arg2'=1+arg2, [ arg3>=arg1 && -arg2+arg4==0 ], cost: 7
     83: f5 -> f5 : arg1'=1+arg1, [ arg3>=arg1 && -arg2+arg4==0 ], cost: 7
     84: f5 -> f5 : arg1'=1+arg1, [ arg3>=arg1 && arg4<arg2 ], cost: 7
     85: f5 -> f5 : arg2'=1+arg2, [ arg4>=arg2 && arg3<arg1 ], cost: 9
     86: f5 -> f5 : arg2'=1+arg2, [ arg3<arg1 && arg4>arg2 ], cost: 9

   Accelerated rule 78 with backward acceleration, yielding the new rule 87.
   Failed to prove monotonicity of the guard of rule 79.
   Accelerated rule 80 with backward acceleration, yielding the new rule 88.
   Accelerated rule 81 with backward acceleration, yielding the new rule 89.
   Failed to prove monotonicity of the guard of rule 82.
   Accelerated rule 83 with backward acceleration, yielding the new rule 90.
   Accelerated rule 84 with backward acceleration, yielding the new rule 91.
   Accelerated rule 85 with backward acceleration, yielding the new rule 92.
   Accelerated rule 86 with backward acceleration, yielding the new rule 93.
[accelerate] Nesting with 9 inner and 9 outer candidates
   Removing the simple loops: 78 80 81 83 84 85 86.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     79: f5 -> f5 : arg1'=1+arg1, [ arg3-arg1==0 && arg4>=arg2 ], cost: 7
     82: f5 -> f5 : arg2'=1+arg2, [ arg3>=arg1 && -arg2+arg4==0 ], cost: 7
     87: f5 -> f5 : arg2'=1+arg4, [ arg3-arg1==0 && 1-arg2+arg4>=0 ], cost: 7-7*arg2+7*arg4
     88: f5 -> f5 : arg2'=1+arg4, [ arg3>=arg1 && 1-arg2+arg4>=0 ], cost: 7-7*arg2+7*arg4
     89: f5 -> f5 : arg1'=1+arg3, [ arg4>=arg2 && 1+arg3-arg1>=0 ], cost: 7+7*arg3-7*arg1
     90: f5 -> f5 : arg1'=1+arg3, [ -arg2+arg4==0 && 1+arg3-arg1>=0 ], cost: 7+7*arg3-7*arg1
     91: f5 -> f5 : arg1'=1+arg3, [ arg4<arg2 && 1+arg3-arg1>=0 ], cost: 7+7*arg3-7*arg1
     92: f5 -> f5 : arg2'=1+arg4, [ arg3<arg1 && 1-arg2+arg4>=0 ], cost: 9-9*arg2+9*arg4
     93: f5 -> f5 : arg2'=arg4, [ arg3<arg1 && -arg2+arg4>=0 ], cost: -9*arg2+9*arg4
     44: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Chained accelerated rules (with incoming rules):
   Start location: __init
     44: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5
     94: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [ arg4P_4>=arg2P_2 ], cost: 12
     95: __init -> f5 : arg1'=arg1P_1, arg2'=1+arg2P_2, arg3'=arg3P_3, arg4'=arg2P_2, [ arg3P_3>=arg1P_1 ], cost: 12
     96: __init -> f5 : arg1'=arg3P_3, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ 1+arg4P_4-arg2P_2>=0 ], cost: 12+7*arg4P_4-7*arg2P_2
     97: __init -> f5 : arg1'=arg1P_1, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3>=arg1P_1 && 1+arg4P_4-arg2P_2>=0 ], cost: 12+7*arg4P_4-7*arg2P_2
     98: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [ arg4P_4>=arg2P_2 && 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
     99: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg2P_2, [ 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
    100: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [ arg4P_4<arg2P_2 && 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
    101: __init -> f5 : arg1'=arg1P_1, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3<arg1P_1 && 1+arg4P_4-arg2P_2>=0 ], cost: 14+9*arg4P_4-9*arg2P_2
    102: __init -> f5 : arg1'=arg1P_1, arg2'=arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3<arg1P_1 && arg4P_4-arg2P_2>=0 ], cost: 5+9*arg4P_4-9*arg2P_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     96: __init -> f5 : arg1'=arg3P_3, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ 1+arg4P_4-arg2P_2>=0 ], cost: 12+7*arg4P_4-7*arg2P_2
     97: __init -> f5 : arg1'=arg1P_1, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3>=arg1P_1 && 1+arg4P_4-arg2P_2>=0 ], cost: 12+7*arg4P_4-7*arg2P_2
     98: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [ arg4P_4>=arg2P_2 && 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
     99: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg2P_2, [ 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
    100: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [ arg4P_4<arg2P_2 && 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
    101: __init -> f5 : arg1'=arg1P_1, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3<arg1P_1 && 1+arg4P_4-arg2P_2>=0 ], cost: 14+9*arg4P_4-9*arg2P_2
    102: __init -> f5 : arg1'=arg1P_1, arg2'=arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3<arg1P_1 && arg4P_4-arg2P_2>=0 ], cost: 5+9*arg4P_4-9*arg2P_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     96: __init -> f5 : arg1'=arg3P_3, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ 1+arg4P_4-arg2P_2>=0 ], cost: 12+7*arg4P_4-7*arg2P_2
     97: __init -> f5 : arg1'=arg1P_1, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3>=arg1P_1 && 1+arg4P_4-arg2P_2>=0 ], cost: 12+7*arg4P_4-7*arg2P_2
     98: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [ arg4P_4>=arg2P_2 && 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
     99: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg2P_2, [ 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
    100: __init -> f5 : arg1'=1+arg3P_3, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, [ arg4P_4<arg2P_2 && 1-arg1P_1+arg3P_3>=0 ], cost: 12-7*arg1P_1+7*arg3P_3
    101: __init -> f5 : arg1'=arg1P_1, arg2'=1+arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3<arg1P_1 && 1+arg4P_4-arg2P_2>=0 ], cost: 14+9*arg4P_4-9*arg2P_2
    102: __init -> f5 : arg1'=arg1P_1, arg2'=arg4P_4, arg3'=arg3P_3, arg4'=arg4P_4, [ arg3P_3<arg1P_1 && arg4P_4-arg2P_2>=0 ], cost: 5+9*arg4P_4-9*arg2P_2

Computing asymptotic complexity for rule 96
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 99
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 97
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 98
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 100
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 101
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 102
   Resulting cost 0 has complexity: Unknown

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),?)