NO ### 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, arg6'=arg6P_1, arg7'=arg7P_1, [ 0==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 && arg5==arg5P_1 && arg6==arg6P_1 && arg7==arg7P_1 ], cost: 1 24: f2 -> f3 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, arg5'=arg5P_25, arg6'=arg6P_25, arg7'=arg7P_25, [ arg1<100 && arg1==arg1P_25 && arg2==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 && arg5==arg5P_25 && arg6==arg6P_25 && arg7==arg7P_25 ], cost: 1 26: f2 -> f23 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, arg5'=arg5P_27, arg6'=arg6P_27, arg7'=arg7P_27, [ arg1>=100 && arg1==arg1P_27 && arg2==arg2P_27 && arg3==arg3P_27 && arg4==arg4P_27 && arg5==arg5P_27 && arg6==arg6P_27 && arg7==arg7P_27 ], cost: 1 1: f3 -> f4 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, arg6'=arg6P_2, arg7'=arg7P_2, [ arg6P_2==2+arg1 && arg1==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg5==arg5P_2 && arg7==arg7P_2 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, arg7'=arg7P_3, [ arg1==arg1P_3 && 0==arg2P_3 && arg3==arg3P_3 && arg4==arg4P_3 && arg5==arg5P_3 && arg6==arg6P_3 && arg7==arg7P_3 ], cost: 1 20: f5 -> f6 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, arg5'=arg5P_21, arg6'=arg6P_21, arg7'=arg7P_21, [ arg2 f21 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, arg5'=arg5P_23, arg6'=arg6P_23, arg7'=arg7P_23, [ arg2>=arg6 && arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 && arg5==arg5P_23 && arg6==arg6P_23 && arg7==arg7P_23 ], cost: 1 3: f6 -> f7 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, [ arg3P_4==3+arg2+arg1 && arg1==arg1P_4 && arg2==arg2P_4 && arg4==arg4P_4 && arg5==arg5P_4 && arg6==arg6P_4 && arg7==arg7P_4 ], cost: 1 16: f7 -> f8 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, arg5'=arg5P_17, arg6'=arg6P_17, arg7'=arg7P_17, [ arg3>=0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 && arg5==arg5P_17 && arg6==arg6P_17 && arg7==arg7P_17 ], cost: 1 18: f7 -> f19 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, arg5'=arg5P_19, arg6'=arg6P_19, arg7'=arg7P_19, [ arg3<0 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 && arg5==arg5P_19 && arg6==arg6P_19 && arg7==arg7P_19 ], cost: 1 4: f8 -> f9 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, [ arg7P_5==4+arg2+arg3+arg1 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 && arg5==arg5P_5 && arg6==arg6P_5 ], cost: 1 5: f9 -> f10 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, arg6'=arg6P_6, arg7'=arg7P_6, [ arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && 0==arg4P_6 && arg5==arg5P_6 && arg6==arg6P_6 && arg7==arg7P_6 ], cost: 1 12: f10 -> f11 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, arg6'=arg6P_13, arg7'=arg7P_13, [ arg4 f17 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, arg6'=arg6P_15, arg7'=arg7P_15, [ arg4>=arg7 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 && arg5==arg5P_15 && arg6==arg6P_15 && arg7==arg7P_15 ], cost: 1 6: f11 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, arg6'=arg6P_7, arg7'=arg7P_7, [ arg5P_7==1000+arg2+arg3+arg4+arg1 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 && arg6==arg6P_7 && arg7==arg7P_7 ], cost: 1 8: f12 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, arg7'=arg7P_9, [ arg5>=0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 && arg5==arg5P_9 && arg6==arg6P_9 && arg7==arg7P_9 ], cost: 1 10: f12 -> f15 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, arg6'=arg6P_11, arg7'=arg7P_11, [ arg5<0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 && arg6==arg6P_11 && arg7==arg7P_11 ], cost: 1 7: f13 -> f14 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, arg6'=arg6P_8, arg7'=arg7P_8, [ arg5P_8==arg5 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 && arg6==arg6P_8 && arg7==arg7P_8 ], cost: 1 9: f14 -> f12 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, arg6'=arg6P_10, arg7'=arg7P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 && arg5==arg5P_10 && arg6==arg6P_10 && arg7==arg7P_10 ], cost: 1 11: f15 -> f16 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, arg6'=arg6P_12, arg7'=arg7P_12, [ arg4P_12==1+arg4 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg5==arg5P_12 && arg6==arg6P_12 && arg7==arg7P_12 ], cost: 1 13: f16 -> f10 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, arg6'=arg6P_14, arg7'=arg7P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 && arg6==arg6P_14 && arg7==arg7P_14 ], cost: 1 15: f17 -> f18 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, arg5'=arg5P_16, arg6'=arg6P_16, arg7'=arg7P_16, [ arg3P_16==-1+arg3 && arg1==arg1P_16 && arg2==arg2P_16 && arg4==arg4P_16 && arg5==arg5P_16 && arg6==arg6P_16 && arg7==arg7P_16 ], cost: 1 17: f18 -> f7 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, arg5'=arg5P_18, arg6'=arg6P_18, arg7'=arg7P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 && arg5==arg5P_18 && arg6==arg6P_18 && arg7==arg7P_18 ], cost: 1 19: f19 -> f20 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, arg5'=arg5P_20, arg6'=arg6P_20, arg7'=arg7P_20, [ arg2P_20==1+arg2 && arg1==arg1P_20 && arg3==arg3P_20 && arg4==arg4P_20 && arg5==arg5P_20 && arg6==arg6P_20 && arg7==arg7P_20 ], cost: 1 21: f20 -> f5 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, arg5'=arg5P_22, arg6'=arg6P_22, arg7'=arg7P_22, [ arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 && arg5==arg5P_22 && arg6==arg6P_22 && arg7==arg7P_22 ], cost: 1 23: f21 -> f22 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, arg6'=arg6P_24, arg7'=arg7P_24, [ arg1P_24==1+arg1 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 && arg5==arg5P_24 && arg6==arg6P_24 && arg7==arg7P_24 ], cost: 1 25: f22 -> f2 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, arg5'=arg5P_26, arg6'=arg6P_26, arg7'=arg7P_26, [ arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 && arg5==arg5P_26 && arg6==arg6P_26 && arg7==arg7P_26 ], cost: 1 27: __init -> f1 : arg1'=arg1P_28, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 27: __init -> f1 : arg1'=arg1P_28, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], 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, arg6'=arg6P_1, arg7'=arg7P_1, [ 0==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 && arg5==arg5P_1 && arg6==arg6P_1 && arg7==arg7P_1 ], cost: 1 24: f2 -> f3 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, arg5'=arg5P_25, arg6'=arg6P_25, arg7'=arg7P_25, [ arg1<100 && arg1==arg1P_25 && arg2==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 && arg5==arg5P_25 && arg6==arg6P_25 && arg7==arg7P_25 ], cost: 1 1: f3 -> f4 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, arg6'=arg6P_2, arg7'=arg7P_2, [ arg6P_2==2+arg1 && arg1==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg5==arg5P_2 && arg7==arg7P_2 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, arg7'=arg7P_3, [ arg1==arg1P_3 && 0==arg2P_3 && arg3==arg3P_3 && arg4==arg4P_3 && arg5==arg5P_3 && arg6==arg6P_3 && arg7==arg7P_3 ], cost: 1 20: f5 -> f6 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, arg5'=arg5P_21, arg6'=arg6P_21, arg7'=arg7P_21, [ arg2 f21 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, arg5'=arg5P_23, arg6'=arg6P_23, arg7'=arg7P_23, [ arg2>=arg6 && arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 && arg5==arg5P_23 && arg6==arg6P_23 && arg7==arg7P_23 ], cost: 1 3: f6 -> f7 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, [ arg3P_4==3+arg2+arg1 && arg1==arg1P_4 && arg2==arg2P_4 && arg4==arg4P_4 && arg5==arg5P_4 && arg6==arg6P_4 && arg7==arg7P_4 ], cost: 1 16: f7 -> f8 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, arg5'=arg5P_17, arg6'=arg6P_17, arg7'=arg7P_17, [ arg3>=0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 && arg5==arg5P_17 && arg6==arg6P_17 && arg7==arg7P_17 ], cost: 1 18: f7 -> f19 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, arg5'=arg5P_19, arg6'=arg6P_19, arg7'=arg7P_19, [ arg3<0 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 && arg5==arg5P_19 && arg6==arg6P_19 && arg7==arg7P_19 ], cost: 1 4: f8 -> f9 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, [ arg7P_5==4+arg2+arg3+arg1 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 && arg5==arg5P_5 && arg6==arg6P_5 ], cost: 1 5: f9 -> f10 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, arg6'=arg6P_6, arg7'=arg7P_6, [ arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && 0==arg4P_6 && arg5==arg5P_6 && arg6==arg6P_6 && arg7==arg7P_6 ], cost: 1 12: f10 -> f11 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, arg6'=arg6P_13, arg7'=arg7P_13, [ arg4 f17 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, arg6'=arg6P_15, arg7'=arg7P_15, [ arg4>=arg7 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 && arg5==arg5P_15 && arg6==arg6P_15 && arg7==arg7P_15 ], cost: 1 6: f11 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, arg6'=arg6P_7, arg7'=arg7P_7, [ arg5P_7==1000+arg2+arg3+arg4+arg1 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 && arg6==arg6P_7 && arg7==arg7P_7 ], cost: 1 8: f12 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, arg7'=arg7P_9, [ arg5>=0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 && arg5==arg5P_9 && arg6==arg6P_9 && arg7==arg7P_9 ], cost: 1 10: f12 -> f15 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, arg6'=arg6P_11, arg7'=arg7P_11, [ arg5<0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 && arg6==arg6P_11 && arg7==arg7P_11 ], cost: 1 7: f13 -> f14 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, arg6'=arg6P_8, arg7'=arg7P_8, [ arg5P_8==arg5 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 && arg6==arg6P_8 && arg7==arg7P_8 ], cost: 1 9: f14 -> f12 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, arg6'=arg6P_10, arg7'=arg7P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 && arg5==arg5P_10 && arg6==arg6P_10 && arg7==arg7P_10 ], cost: 1 11: f15 -> f16 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, arg6'=arg6P_12, arg7'=arg7P_12, [ arg4P_12==1+arg4 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg5==arg5P_12 && arg6==arg6P_12 && arg7==arg7P_12 ], cost: 1 13: f16 -> f10 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, arg6'=arg6P_14, arg7'=arg7P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 && arg6==arg6P_14 && arg7==arg7P_14 ], cost: 1 15: f17 -> f18 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, arg5'=arg5P_16, arg6'=arg6P_16, arg7'=arg7P_16, [ arg3P_16==-1+arg3 && arg1==arg1P_16 && arg2==arg2P_16 && arg4==arg4P_16 && arg5==arg5P_16 && arg6==arg6P_16 && arg7==arg7P_16 ], cost: 1 17: f18 -> f7 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, arg5'=arg5P_18, arg6'=arg6P_18, arg7'=arg7P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 && arg5==arg5P_18 && arg6==arg6P_18 && arg7==arg7P_18 ], cost: 1 19: f19 -> f20 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, arg5'=arg5P_20, arg6'=arg6P_20, arg7'=arg7P_20, [ arg2P_20==1+arg2 && arg1==arg1P_20 && arg3==arg3P_20 && arg4==arg4P_20 && arg5==arg5P_20 && arg6==arg6P_20 && arg7==arg7P_20 ], cost: 1 21: f20 -> f5 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, arg5'=arg5P_22, arg6'=arg6P_22, arg7'=arg7P_22, [ arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 && arg5==arg5P_22 && arg6==arg6P_22 && arg7==arg7P_22 ], cost: 1 23: f21 -> f22 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, arg6'=arg6P_24, arg7'=arg7P_24, [ arg1P_24==1+arg1 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 && arg5==arg5P_24 && arg6==arg6P_24 && arg7==arg7P_24 ], cost: 1 25: f22 -> f2 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, arg5'=arg5P_26, arg6'=arg6P_26, arg7'=arg7P_26, [ arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 && arg5==arg5P_26 && arg6==arg6P_26 && arg7==arg7P_26 ], cost: 1 27: __init -> f1 : arg1'=arg1P_28, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=0, [], cost: 1 24: f2 -> f3 : [ arg1<100 ], cost: 1 1: f3 -> f4 : arg6'=2+arg1, [], cost: 1 2: f4 -> f5 : arg2'=0, [], cost: 1 20: f5 -> f6 : [ arg2 f21 : [ arg2>=arg6 ], cost: 1 3: f6 -> f7 : arg3'=3+arg2+arg1, [], cost: 1 16: f7 -> f8 : [ arg3>=0 ], cost: 1 18: f7 -> f19 : [ arg3<0 ], cost: 1 4: f8 -> f9 : arg7'=4+arg2+arg3+arg1, [], cost: 1 5: f9 -> f10 : arg4'=0, [], cost: 1 12: f10 -> f11 : [ arg4 f17 : [ arg4>=arg7 ], cost: 1 6: f11 -> f12 : arg5'=1000+arg2+arg3+arg4+arg1, [], cost: 1 8: f12 -> f13 : [ arg5>=0 ], cost: 1 10: f12 -> f15 : [ arg5<0 ], cost: 1 7: f13 -> f14 : [], cost: 1 9: f14 -> f12 : [], cost: 1 11: f15 -> f16 : arg4'=1+arg4, [], cost: 1 13: f16 -> f10 : [], cost: 1 15: f17 -> f18 : arg3'=-1+arg3, [], cost: 1 17: f18 -> f7 : [], cost: 1 19: f19 -> f20 : arg2'=1+arg2, [], cost: 1 21: f20 -> f5 : [], cost: 1 23: f21 -> f22 : arg1'=1+arg1, [], cost: 1 25: f22 -> f2 : [], cost: 1 27: __init -> f1 : arg1'=arg1P_28, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 36: f7 -> f10 : arg4'=0, arg7'=4+arg2+arg3+arg1, [ arg3>=0 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 38: f10 -> f12 : arg5'=1000+arg2+arg3+arg4+arg1, [ arg4 f7 : arg3'=-1+arg3, [ arg4>=arg7 ], cost: 3 43: f12 -> f12 : [ arg5>=0 ], cost: 3 44: f12 -> f10 : arg4'=1+arg4, [ arg5<0 ], cost: 3 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Accelerating simple loops of location 11. Accelerating the following rules: 43: f12 -> f12 : [ arg5>=0 ], cost: 3 Accelerated rule 43 with non-termination, yielding the new rule 45. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 43. Accelerated all simple loops using metering functions (where possible): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 36: f7 -> f10 : arg4'=0, arg7'=4+arg2+arg3+arg1, [ arg3>=0 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 38: f10 -> f12 : arg5'=1000+arg2+arg3+arg4+arg1, [ arg4 f7 : arg3'=-1+arg3, [ arg4>=arg7 ], cost: 3 44: f12 -> f10 : arg4'=1+arg4, [ arg5<0 ], cost: 3 45: f12 -> [24] : [ arg5>=0 ], cost: NONTERM 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 36: f7 -> f10 : arg4'=0, arg7'=4+arg2+arg3+arg1, [ arg3>=0 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 38: f10 -> f12 : arg5'=1000+arg2+arg3+arg4+arg1, [ arg4 f7 : arg3'=-1+arg3, [ arg4>=arg7 ], cost: 3 46: f10 -> [24] : [ arg4=0 ], cost: NONTERM 44: f12 -> f10 : arg4'=1+arg4, [ arg5<0 ], cost: 3 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Eliminated locations (on linear paths): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 36: f7 -> f10 : arg4'=0, arg7'=4+arg2+arg3+arg1, [ arg3>=0 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 40: f10 -> f7 : arg3'=-1+arg3, [ arg4>=arg7 ], cost: 3 46: f10 -> [24] : [ arg4=0 ], cost: NONTERM 47: f10 -> f10 : arg4'=1+arg4, arg5'=1000+arg2+arg3+arg4+arg1, [ arg4 f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Accelerating simple loops of location 9. Accelerating the following rules: 47: f10 -> f10 : arg4'=1+arg4, arg5'=1000+arg2+arg3+arg4+arg1, [ arg4 f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 36: f7 -> f10 : arg4'=0, arg7'=4+arg2+arg3+arg1, [ arg3>=0 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 40: f10 -> f7 : arg3'=-1+arg3, [ arg4>=arg7 ], cost: 3 46: f10 -> [24] : [ arg4=0 ], cost: NONTERM 48: f10 -> f10 : arg4'=arg7, arg5'=999+arg2+arg3+arg7+arg1, [ arg7-arg4>=1 && 999+arg2+arg3+arg7+arg1<0 ], cost: 5*arg7-5*arg4 49: f10 -> f10 : arg4'=-1000-arg2-arg3-arg1, arg5'=-1, [ -1000-arg2-arg3-arg4-arg1>=1 && -1001-arg2-arg3-arg1 f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 36: f7 -> f10 : arg4'=0, arg7'=4+arg2+arg3+arg1, [ arg3>=0 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 40: f10 -> f7 : arg3'=-1+arg3, [ arg4>=arg7 ], cost: 3 46: f10 -> [24] : [ arg4=0 ], cost: NONTERM 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 50: f7 -> f7 : arg3'=-1+arg3, arg4'=0, arg7'=4+arg2+arg3+arg1, [ arg3>=0 && 0>=4+arg2+arg3+arg1 ], cost: 6 51: f7 -> [24] : [ arg3>=0 && 0<4+arg2+arg3+arg1 ], cost: NONTERM 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Accelerating simple loops of location 6. Accelerating the following rules: 50: f7 -> f7 : arg3'=-1+arg3, arg4'=0, arg7'=4+arg2+arg3+arg1, [ arg3>=0 && 0>=4+arg2+arg3+arg1 ], cost: 6 Accelerated rule 50 with backward acceleration, yielding the new rule 52. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 50. Accelerated all simple loops using metering functions (where possible): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 51: f7 -> [24] : [ arg3>=0 && 0<4+arg2+arg3+arg1 ], cost: NONTERM 52: f7 -> f7 : arg3'=-1, arg4'=0, arg7'=4+arg2+arg1, [ 0>=4+arg2+arg3+arg1 && 1+arg3>=1 ], cost: 6+6*arg3 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 31: f5 -> f7 : arg3'=3+arg2+arg1, [ arg2 f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 37: f7 -> f5 : arg2'=1+arg2, [ arg3<0 ], cost: 3 51: f7 -> [24] : [ arg3>=0 && 0<4+arg2+arg3+arg1 ], cost: NONTERM 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 33: f5 -> f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 53: f5 -> f5 : arg2'=1+arg2, arg3'=3+arg2+arg1, [ arg2 [24] : [ arg2=0 && 0<7+2*arg2+2*arg1 ], cost: NONTERM 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Accelerating simple loops of location 4. Accelerating the following rules: 53: f5 -> f5 : arg2'=1+arg2, arg3'=3+arg2+arg1, [ arg2 f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 33: f5 -> f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 54: f5 -> [24] : [ arg2=0 && 0<7+2*arg2+2*arg1 ], cost: NONTERM 55: f5 -> f5 : arg2'=arg6, arg3'=2+arg6+arg1, [ -arg2+arg6>=1 && 2+arg6+arg1<0 ], cost: -5*arg2+5*arg6 56: f5 -> f5 : arg2'=-3-arg1, arg3'=-1, [ -3-arg2-arg1>=1 && -4-arg1 f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 30: f2 -> f5 : arg2'=0, arg6'=2+arg1, [ arg1<100 ], cost: 3 33: f5 -> f2 : arg1'=1+arg1, [ arg2>=arg6 ], cost: 3 54: f5 -> [24] : [ arg2=0 && 0<7+2*arg2+2*arg1 ], cost: NONTERM 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 57: f2 -> f2 : arg1'=1+arg1, arg2'=0, arg6'=2+arg1, [ 0>=2+arg1 ], cost: 6 58: f2 -> [24] : [ arg1<100 && 0<2+arg1 && 0<7+2*arg1 ], cost: NONTERM 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 57: f2 -> f2 : arg1'=1+arg1, arg2'=0, arg6'=2+arg1, [ 0>=2+arg1 ], cost: 6 Accelerated rule 57 with backward acceleration, yielding the new rule 59. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 57. Accelerated all simple loops using metering functions (where possible): Start location: __init 58: f2 -> [24] : [ arg1<100 && 0<2+arg1 && 0<7+2*arg1 ], cost: NONTERM 59: f2 -> f2 : arg1'=-1, arg2'=0, arg6'=0, [ -1-arg1>=1 ], cost: -6-6*arg1 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 58: f2 -> [24] : [ arg1<100 && 0<2+arg1 && 0<7+2*arg1 ], cost: NONTERM 28: __init -> f2 : arg1'=0, arg2'=arg2P_28, arg3'=arg3P_28, arg4'=arg4P_28, arg5'=arg5P_28, arg6'=arg6P_28, arg7'=arg7P_28, [], cost: 2 Eliminated locations (on linear paths): Start location: __init 60: __init -> [24] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 60: __init -> [24] : [], cost: NONTERM Computing asymptotic complexity for rule 60 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [] NO