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, arg5'=arg5P_1, [ 10==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 && arg5==arg5P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1==arg1P_2 && 0==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg5==arg5P_2 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && 0==arg3P_3 && arg4==arg4P_3 && arg5==arg5P_3 ], cost: 1 3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && 0==arg4P_4 && arg5==arg5P_4 ], cost: 1 35: f5 -> f6 : arg1'=arg1P_36, arg2'=arg2P_36, arg3'=arg3P_36, arg4'=arg4P_36, arg5'=arg5P_36, [ arg4 f28 : arg1'=arg1P_38, arg2'=arg2P_38, arg3'=arg3P_38, arg4'=arg4P_38, arg5'=arg5P_38, [ arg4>=arg1 && arg1==arg1P_38 && arg2==arg2P_38 && arg3==arg3P_38 && arg4==arg4P_38 && arg5==arg5P_38 ], cost: 1 4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg4P_5==1+arg4 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg5==arg5P_5 ], cost: 1 5: f7 -> f8 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1 30: f8 -> f9 : arg1'=arg1P_31, arg2'=arg2P_31, arg3'=arg3P_31, arg4'=arg4P_31, arg5'=arg5P_31, [ arg5>=0 && arg5<=3 && arg1==arg1P_31 && arg2==arg2P_31 && arg3==arg3P_31 && arg4==arg4P_31 && arg5==arg5P_31 ], cost: 1 31: f8 -> f10 : arg1'=arg1P_32, arg2'=arg2P_32, arg3'=arg3P_32, arg4'=arg4P_32, arg5'=arg5P_32, [ arg5<0 && arg1==arg1P_32 && arg2==arg2P_32 && arg3==arg3P_32 && arg4==arg4P_32 && arg5==arg5P_32 ], cost: 1 32: f8 -> f10 : arg1'=arg1P_33, arg2'=arg2P_33, arg3'=arg3P_33, arg4'=arg4P_33, arg5'=arg5P_33, [ arg5>3 && arg1==arg1P_33 && arg2==arg2P_33 && arg3==arg3P_33 && arg4==arg4P_33 && arg5==arg5P_33 ], cost: 1 6: f12 -> f15 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg2P_7==1+arg2 && arg1==arg1P_7 && arg3==arg3P_7 && arg4==arg4P_7 && arg5==arg5P_7 ], cost: 1 28: f15 -> f14 : arg1'=arg1P_29, arg2'=arg2P_29, arg3'=arg3P_29, arg4'=arg4P_29, arg5'=arg5P_29, [ arg1==arg1P_29 && arg2==arg2P_29 && arg3==arg3P_29 && arg4==arg4P_29 && arg5==arg5P_29 ], cost: 1 7: f16 -> f19 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg2P_8==-1+arg2 && arg1==arg1P_8 && arg3==arg3P_8 && arg4==arg4P_8 && arg5==arg5P_8 ], cost: 1 23: f19 -> f18 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, [ arg1==arg1P_24 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 && arg5==arg5P_24 ], cost: 1 8: f20 -> f23 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [ arg3P_9==1+arg3 && arg1==arg1P_9 && arg2==arg2P_9 && arg4==arg4P_9 && arg5==arg5P_9 ], cost: 1 18: f23 -> f22 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, arg5'=arg5P_19, [ arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 && arg5==arg5P_19 ], cost: 1 9: f24 -> f27 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, [ arg3P_10==-1+arg3 && arg1==arg1P_10 && arg2==arg2P_10 && arg4==arg4P_10 && arg5==arg5P_10 ], cost: 1 13: f27 -> f26 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 ], cost: 1 10: f21 -> f24 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ arg5==3 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 ], cost: 1 11: f21 -> f25 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg5<3 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 && arg5==arg5P_12 ], cost: 1 12: f21 -> f25 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [ arg5>3 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 && arg5==arg5P_13 ], cost: 1 14: f25 -> f26 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 && arg5==arg5P_15 ], cost: 1 19: f26 -> f22 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, arg5'=arg5P_20, [ arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 && arg5==arg5P_20 ], cost: 1 15: f17 -> f20 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, arg5'=arg5P_16, [ arg5==2 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 && arg5==arg5P_16 ], cost: 1 16: f17 -> f21 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, arg5'=arg5P_17, [ arg5<2 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 && arg5==arg5P_17 ], cost: 1 17: f17 -> f21 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, arg5'=arg5P_18, [ arg5>2 && arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 && arg5==arg5P_18 ], cost: 1 24: f22 -> f18 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, arg5'=arg5P_25, [ arg1==arg1P_25 && arg2==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 && arg5==arg5P_25 ], cost: 1 20: f13 -> f16 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, arg5'=arg5P_21, [ arg5==1 && arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 && arg4==arg4P_21 && arg5==arg5P_21 ], cost: 1 21: f13 -> f17 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, arg5'=arg5P_22, [ arg5<1 && arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 && arg5==arg5P_22 ], cost: 1 22: f13 -> f17 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, arg5'=arg5P_23, [ arg5>1 && arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 && arg5==arg5P_23 ], cost: 1 29: f18 -> f14 : arg1'=arg1P_30, arg2'=arg2P_30, arg3'=arg3P_30, arg4'=arg4P_30, arg5'=arg5P_30, [ arg1==arg1P_30 && arg2==arg2P_30 && arg3==arg3P_30 && arg4==arg4P_30 && arg5==arg5P_30 ], cost: 1 25: f9 -> f12 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, arg5'=arg5P_26, [ arg5==0 && arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 && arg5==arg5P_26 ], cost: 1 26: f9 -> f13 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, arg5'=arg5P_27, [ arg5<0 && arg1==arg1P_27 && arg2==arg2P_27 && arg3==arg3P_27 && arg4==arg4P_27 && arg5==arg5P_27 ], cost: 1 27: f9 -> f13 : arg1'=arg1P_28, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, [ arg5>0 && arg1==arg1P_28 && arg2==arg2P_28 && arg3==arg3P_28 && arg4==arg4P_28 && arg5==arg5P_28 ], cost: 1 33: f14 -> f11 : arg1'=arg1P_34, arg2'=arg2P_34, arg3'=arg3P_34, arg4'=arg4P_34, arg5'=arg5P_34, [ arg1==arg1P_34 && arg2==arg2P_34 && arg3==arg3P_34 && arg4==arg4P_34 && arg5==arg5P_34 ], cost: 1 34: f10 -> f11 : arg1'=arg1P_35, arg2'=arg2P_35, arg3'=arg3P_35, arg4'=arg4P_35, arg5'=arg5P_35, [ arg1==arg1P_35 && arg2==arg2P_35 && arg3==arg3P_35 && arg4==arg4P_35 && arg5==arg5P_35 ], cost: 1 36: f11 -> f5 : arg1'=arg1P_37, arg2'=arg2P_37, arg3'=arg3P_37, arg4'=arg4P_37, arg5'=arg5P_37, [ arg1==arg1P_37 && arg2==arg2P_37 && arg3==arg3P_37 && arg4==arg4P_37 && arg5==arg5P_37 ], cost: 1 38: __init -> f1 : arg1'=arg1P_39, arg2'=arg2P_39, arg3'=arg3P_39, arg4'=arg4P_39, arg5'=arg5P_39, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 38: __init -> f1 : arg1'=arg1P_39, arg2'=arg2P_39, arg3'=arg3P_39, arg4'=arg4P_39, arg5'=arg5P_39, [], 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, arg5'=arg5P_1, [ 10==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 && arg5==arg5P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1==arg1P_2 && 0==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg5==arg5P_2 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && 0==arg3P_3 && arg4==arg4P_3 && arg5==arg5P_3 ], cost: 1 3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && 0==arg4P_4 && arg5==arg5P_4 ], cost: 1 35: f5 -> f6 : arg1'=arg1P_36, arg2'=arg2P_36, arg3'=arg3P_36, arg4'=arg4P_36, arg5'=arg5P_36, [ arg4 f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg4P_5==1+arg4 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg5==arg5P_5 ], cost: 1 5: f7 -> f8 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1 30: f8 -> f9 : arg1'=arg1P_31, arg2'=arg2P_31, arg3'=arg3P_31, arg4'=arg4P_31, arg5'=arg5P_31, [ arg5>=0 && arg5<=3 && arg1==arg1P_31 && arg2==arg2P_31 && arg3==arg3P_31 && arg4==arg4P_31 && arg5==arg5P_31 ], cost: 1 31: f8 -> f10 : arg1'=arg1P_32, arg2'=arg2P_32, arg3'=arg3P_32, arg4'=arg4P_32, arg5'=arg5P_32, [ arg5<0 && arg1==arg1P_32 && arg2==arg2P_32 && arg3==arg3P_32 && arg4==arg4P_32 && arg5==arg5P_32 ], cost: 1 32: f8 -> f10 : arg1'=arg1P_33, arg2'=arg2P_33, arg3'=arg3P_33, arg4'=arg4P_33, arg5'=arg5P_33, [ arg5>3 && arg1==arg1P_33 && arg2==arg2P_33 && arg3==arg3P_33 && arg4==arg4P_33 && arg5==arg5P_33 ], cost: 1 6: f12 -> f15 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg2P_7==1+arg2 && arg1==arg1P_7 && arg3==arg3P_7 && arg4==arg4P_7 && arg5==arg5P_7 ], cost: 1 28: f15 -> f14 : arg1'=arg1P_29, arg2'=arg2P_29, arg3'=arg3P_29, arg4'=arg4P_29, arg5'=arg5P_29, [ arg1==arg1P_29 && arg2==arg2P_29 && arg3==arg3P_29 && arg4==arg4P_29 && arg5==arg5P_29 ], cost: 1 7: f16 -> f19 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg2P_8==-1+arg2 && arg1==arg1P_8 && arg3==arg3P_8 && arg4==arg4P_8 && arg5==arg5P_8 ], cost: 1 23: f19 -> f18 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, [ arg1==arg1P_24 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 && arg5==arg5P_24 ], cost: 1 8: f20 -> f23 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [ arg3P_9==1+arg3 && arg1==arg1P_9 && arg2==arg2P_9 && arg4==arg4P_9 && arg5==arg5P_9 ], cost: 1 18: f23 -> f22 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, arg5'=arg5P_19, [ arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 && arg5==arg5P_19 ], cost: 1 9: f24 -> f27 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, [ arg3P_10==-1+arg3 && arg1==arg1P_10 && arg2==arg2P_10 && arg4==arg4P_10 && arg5==arg5P_10 ], cost: 1 13: f27 -> f26 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 ], cost: 1 10: f21 -> f24 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ arg5==3 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 ], cost: 1 11: f21 -> f25 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg5<3 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 && arg5==arg5P_12 ], cost: 1 12: f21 -> f25 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [ arg5>3 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 && arg5==arg5P_13 ], cost: 1 14: f25 -> f26 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 && arg5==arg5P_15 ], cost: 1 19: f26 -> f22 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, arg5'=arg5P_20, [ arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 && arg5==arg5P_20 ], cost: 1 15: f17 -> f20 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, arg5'=arg5P_16, [ arg5==2 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 && arg5==arg5P_16 ], cost: 1 16: f17 -> f21 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, arg5'=arg5P_17, [ arg5<2 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 && arg5==arg5P_17 ], cost: 1 17: f17 -> f21 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, arg5'=arg5P_18, [ arg5>2 && arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 && arg5==arg5P_18 ], cost: 1 24: f22 -> f18 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, arg5'=arg5P_25, [ arg1==arg1P_25 && arg2==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 && arg5==arg5P_25 ], cost: 1 20: f13 -> f16 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, arg5'=arg5P_21, [ arg5==1 && arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 && arg4==arg4P_21 && arg5==arg5P_21 ], cost: 1 21: f13 -> f17 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, arg5'=arg5P_22, [ arg5<1 && arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 && arg5==arg5P_22 ], cost: 1 22: f13 -> f17 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, arg5'=arg5P_23, [ arg5>1 && arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 && arg5==arg5P_23 ], cost: 1 29: f18 -> f14 : arg1'=arg1P_30, arg2'=arg2P_30, arg3'=arg3P_30, arg4'=arg4P_30, arg5'=arg5P_30, [ arg1==arg1P_30 && arg2==arg2P_30 && arg3==arg3P_30 && arg4==arg4P_30 && arg5==arg5P_30 ], cost: 1 25: f9 -> f12 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, arg5'=arg5P_26, [ arg5==0 && arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 && arg5==arg5P_26 ], cost: 1 26: f9 -> f13 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, arg5'=arg5P_27, [ arg5<0 && arg1==arg1P_27 && arg2==arg2P_27 && arg3==arg3P_27 && arg4==arg4P_27 && arg5==arg5P_27 ], cost: 1 27: f9 -> f13 : arg1'=arg1P_28, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, [ arg5>0 && arg1==arg1P_28 && arg2==arg2P_28 && arg3==arg3P_28 && arg4==arg4P_28 && arg5==arg5P_28 ], cost: 1 33: f14 -> f11 : arg1'=arg1P_34, arg2'=arg2P_34, arg3'=arg3P_34, arg4'=arg4P_34, arg5'=arg5P_34, [ arg1==arg1P_34 && arg2==arg2P_34 && arg3==arg3P_34 && arg4==arg4P_34 && arg5==arg5P_34 ], cost: 1 34: f10 -> f11 : arg1'=arg1P_35, arg2'=arg2P_35, arg3'=arg3P_35, arg4'=arg4P_35, arg5'=arg5P_35, [ arg1==arg1P_35 && arg2==arg2P_35 && arg3==arg3P_35 && arg4==arg4P_35 && arg5==arg5P_35 ], cost: 1 36: f11 -> f5 : arg1'=arg1P_37, arg2'=arg2P_37, arg3'=arg3P_37, arg4'=arg4P_37, arg5'=arg5P_37, [ arg1==arg1P_37 && arg2==arg2P_37 && arg3==arg3P_37 && arg4==arg4P_37 && arg5==arg5P_37 ], cost: 1 38: __init -> f1 : arg1'=arg1P_39, arg2'=arg2P_39, arg3'=arg3P_39, arg4'=arg4P_39, arg5'=arg5P_39, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=10, [], cost: 1 1: f2 -> f3 : arg2'=0, [], cost: 1 2: f3 -> f4 : arg3'=0, [], cost: 1 3: f4 -> f5 : arg4'=0, [], cost: 1 35: f5 -> f6 : [ arg4 f7 : arg4'=1+arg4, [], cost: 1 5: f7 -> f8 : arg5'=arg5P_6, [], cost: 1 30: f8 -> f9 : [ arg5>=0 && arg5<=3 ], cost: 1 31: f8 -> f10 : [ arg5<0 ], cost: 1 32: f8 -> f10 : [ arg5>3 ], cost: 1 6: f12 -> f15 : arg2'=1+arg2, [], cost: 1 28: f15 -> f14 : [], cost: 1 7: f16 -> f19 : arg2'=-1+arg2, [], cost: 1 23: f19 -> f18 : [], cost: 1 8: f20 -> f23 : arg3'=1+arg3, [], cost: 1 18: f23 -> f22 : [], cost: 1 9: f24 -> f27 : arg3'=-1+arg3, [], cost: 1 13: f27 -> f26 : [], cost: 1 10: f21 -> f24 : [ arg5==3 ], cost: 1 11: f21 -> f25 : [ arg5<3 ], cost: 1 12: f21 -> f25 : [ arg5>3 ], cost: 1 14: f25 -> f26 : [], cost: 1 19: f26 -> f22 : [], cost: 1 15: f17 -> f20 : [ arg5==2 ], cost: 1 16: f17 -> f21 : [ arg5<2 ], cost: 1 17: f17 -> f21 : [ arg5>2 ], cost: 1 24: f22 -> f18 : [], cost: 1 20: f13 -> f16 : [ arg5==1 ], cost: 1 21: f13 -> f17 : [ arg5<1 ], cost: 1 22: f13 -> f17 : [ arg5>1 ], cost: 1 29: f18 -> f14 : [], cost: 1 25: f9 -> f12 : [ arg5==0 ], cost: 1 26: f9 -> f13 : [ arg5<0 ], cost: 1 27: f9 -> f13 : [ arg5>0 ], cost: 1 33: f14 -> f11 : [], cost: 1 34: f10 -> f11 : [], cost: 1 36: f11 -> f5 : [], cost: 1 38: __init -> f1 : arg1'=arg1P_39, arg2'=arg2P_39, arg3'=arg3P_39, arg4'=arg4P_39, arg5'=arg5P_39, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 44: f5 -> f8 : arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f9 : [ arg5>=0 && arg5<=3 ], cost: 1 31: f8 -> f10 : [ arg5<0 ], cost: 1 32: f8 -> f10 : [ arg5>3 ], cost: 1 11: f21 -> f25 : [ arg5<3 ], cost: 1 12: f21 -> f25 : [ arg5>3 ], cost: 1 52: f21 -> f26 : arg3'=-1+arg3, [ arg5==3 ], cost: 3 14: f25 -> f26 : [], cost: 1 19: f26 -> f22 : [], cost: 1 16: f17 -> f21 : [ arg5<2 ], cost: 1 17: f17 -> f21 : [ arg5>2 ], cost: 1 50: f17 -> f22 : arg3'=1+arg3, [ arg5==2 ], cost: 3 24: f22 -> f18 : [], cost: 1 21: f13 -> f17 : [ arg5<1 ], cost: 1 22: f13 -> f17 : [ arg5>1 ], cost: 1 48: f13 -> f18 : arg2'=-1+arg2, [ arg5==1 ], cost: 3 29: f18 -> f14 : [], cost: 1 26: f9 -> f13 : [ arg5<0 ], cost: 1 27: f9 -> f13 : [ arg5>0 ], cost: 1 46: f9 -> f14 : arg2'=1+arg2, [ arg5==0 ], cost: 3 33: f14 -> f11 : [], cost: 1 34: f10 -> f11 : [], cost: 1 36: f11 -> f5 : [], cost: 1 42: __init -> f5 : arg1'=10, arg2'=0, arg3'=0, arg4'=0, arg5'=arg5P_39, [], cost: 5 Eliminated locations (on tree-shaped paths): Start location: __init 53: f5 -> f9 : arg4'=1+arg4, arg5'=arg5P_6, [ arg4=0 && arg5P_6<=3 ], cost: 4 54: f5 -> f10 : arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f10 : arg4'=1+arg4, arg5'=arg5P_6, [ arg43 ], cost: 4 14: f25 -> f26 : [], cost: 1 19: f26 -> f22 : [], cost: 1 50: f17 -> f22 : arg3'=1+arg3, [ arg5==2 ], cost: 3 59: f17 -> f25 : [ arg5<2 ], cost: 2 60: f17 -> f25 : [ arg5>3 ], cost: 2 61: f17 -> f26 : arg3'=-1+arg3, [ arg5==3 ], cost: 4 24: f22 -> f18 : [], cost: 1 29: f18 -> f14 : [], cost: 1 46: f9 -> f14 : arg2'=1+arg2, [ arg5==0 ], cost: 3 56: f9 -> f17 : [ arg5<0 ], cost: 2 57: f9 -> f17 : [ arg5>1 ], cost: 2 58: f9 -> f18 : arg2'=-1+arg2, [ arg5==1 ], cost: 4 33: f14 -> f11 : [], cost: 1 34: f10 -> f11 : [], cost: 1 36: f11 -> f5 : [], cost: 1 42: __init -> f5 : arg1'=10, arg2'=0, arg3'=0, arg4'=0, arg5'=arg5P_39, [], cost: 5 Eliminated locations (on tree-shaped paths): Start location: __init 62: f5 -> f14 : arg2'=1+arg2, arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f17 : arg4'=1+arg4, arg5'=arg5P_6, [ arg41 ], cost: 6 64: f5 -> f18 : arg2'=-1+arg2, arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f11 : arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f11 : arg4'=1+arg4, arg5'=arg5P_6, [ arg43 ], cost: 5 72: f17 -> f18 : arg3'=1+arg3, [ arg5==2 ], cost: 4 73: f17 -> f18 : arg3'=-1+arg3, [ arg5==3 ], cost: 6 74: f17 -> f18 : [ arg5<2 ], cost: 5 75: f17 -> f18 : [ arg5>3 ], cost: 5 29: f18 -> f14 : [], cost: 1 33: f14 -> f11 : [], cost: 1 36: f11 -> f5 : [], cost: 1 42: __init -> f5 : arg1'=10, arg2'=0, arg3'=0, arg4'=0, arg5'=arg5P_39, [], cost: 5 Eliminated locations (on tree-shaped paths): Start location: __init 85: f5 -> f5 : arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f5 : arg4'=1+arg4, arg5'=arg5P_6, [ arg43 ], cost: 6 87: f5 -> f5 : arg2'=1+arg2, arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f5 : arg2'=-1+arg2, arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f5 : arg3'=1+arg3, arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f5 : arg3'=-1+arg3, arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f5 : arg1'=10, arg2'=0, arg3'=0, arg4'=0, arg5'=arg5P_39, [], cost: 5 Accelerating simple loops of location 4. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 85: f5 -> f5 : arg4'=1+arg4, arg5'=arg5P_6, [ arg4 f5 : arg4'=1+arg4, arg5'=arg5P_6, [ arg43 ], cost: 6 87: f5 -> f5 : arg2'=1+arg2, arg4'=1+arg4, arg5'=0, [ arg4 f5 : arg2'=-1+arg2, arg4'=1+arg4, arg5'=1, [ arg4 f5 : arg3'=1+arg3, arg4'=1+arg4, arg5'=2, [ arg4 f5 : arg3'=-1+arg3, arg4'=1+arg4, arg5'=3, [ arg4 f5 : arg4'=arg1, arg5'=arg5P_6, [ arg5P_6<0 && -arg4+arg1>=1 ], cost: -6*arg4+6*arg1 92: f5 -> f5 : arg4'=arg1, arg5'=arg5P_6, [ arg5P_6>3 && -arg4+arg1>=1 ], cost: -6*arg4+6*arg1 93: f5 -> f5 : arg2'=arg2-arg4+arg1, arg4'=arg1, arg5'=0, [ -arg4+arg1>=1 ], cost: -9*arg4+9*arg1 94: f5 -> f5 : arg2'=arg2+arg4-arg1, arg4'=arg1, arg5'=1, [ -arg4+arg1>=1 ], cost: -11*arg4+11*arg1 95: f5 -> f5 : arg3'=arg3-arg4+arg1, arg4'=arg1, arg5'=2, [ -arg4+arg1>=1 ], cost: -13*arg4+13*arg1 96: f5 -> f5 : arg3'=arg3+arg4-arg1, arg4'=arg1, arg5'=3, [ -arg4+arg1>=1 ], cost: -15*arg4+15*arg1 42: __init -> f5 : arg1'=10, arg2'=0, arg3'=0, arg4'=0, arg5'=arg5P_39, [], cost: 5 Chained accelerated rules (with incoming rules): Start location: __init 42: __init -> f5 : arg1'=10, arg2'=0, arg3'=0, arg4'=0, arg5'=arg5P_39, [], cost: 5 97: __init -> f5 : arg1'=10, arg2'=0, arg3'=0, arg4'=10, arg5'=arg5P_6, [ arg5P_6<0 ], cost: 65 98: __init -> f5 : arg1'=10, arg2'=0, arg3'=0, arg4'=10, arg5'=arg5P_6, [ arg5P_6>3 ], cost: 65 99: __init -> f5 : arg1'=10, arg2'=10, arg3'=0, arg4'=10, arg5'=0, [], cost: 95 100: __init -> f5 : arg1'=10, arg2'=-10, arg3'=0, arg4'=10, arg5'=1, [], cost: 115 101: __init -> f5 : arg1'=10, arg2'=0, arg3'=10, arg4'=10, arg5'=2, [], cost: 135 102: __init -> f5 : arg1'=10, arg2'=0, arg3'=-10, arg4'=10, arg5'=3, [], cost: 155 Removed unreachable locations (and leaf rules with constant cost): Start location: __init ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 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),?)