NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 16: f2 -> f3 : arg1'=arg1P_17, [ arg1<0 && arg1==arg1P_17 ], cost: 1 17: f2 -> f3 : arg1'=arg1P_18, [ arg1>0 && arg1==arg1P_18 ], cost: 1 19: f2 -> f15 : arg1'=arg1P_20, [ arg1==0 && arg1==arg1P_20 ], cost: 1 1: f7 -> f10 : arg1'=arg1P_2, [ arg1P_2==1+arg1 ], cost: 1 4: f10 -> f9 : arg1'=arg1P_5, [ arg1==arg1P_5 ], cost: 1 2: f4 -> f7 : arg1'=arg1P_3, [ arg1<0 && arg1==arg1P_3 ], cost: 1 3: f4 -> f8 : arg1'=arg1P_4, [ arg1>=0 && arg1==arg1P_4 ], cost: 1 5: f8 -> f9 : arg1'=arg1P_6, [ arg1==arg1P_6 ], cost: 1 7: f9 -> f11 : arg1'=arg1P_8, [ arg1>0 && arg1==arg1P_8 ], cost: 1 8: f9 -> f12 : arg1'=arg1P_9, [ arg1<=0 && arg1==arg1P_9 ], cost: 1 6: f11 -> f14 : arg1'=arg1P_7, [ arg1P_7==-1+arg1 ], cost: 1 9: f14 -> f13 : arg1'=arg1P_10, [ arg1==arg1P_10 ], cost: 1 10: f12 -> f13 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1 14: f13 -> f6 : arg1'=arg1P_15, [ arg1==arg1P_15 ], cost: 1 11: f3 -> f4 : arg1'=arg1P_12, [ arg1>-5 && arg1<5 && arg1==arg1P_12 ], cost: 1 12: f3 -> f5 : arg1'=arg1P_13, [ arg1<=-5 && arg1==arg1P_13 ], cost: 1 13: f3 -> f5 : arg1'=arg1P_14, [ arg1>=5 && arg1==arg1P_14 ], cost: 1 15: f5 -> f6 : arg1'=arg1P_16, [ arg1==arg1P_16 ], cost: 1 18: f6 -> f2 : arg1'=arg1P_19, [ arg1==arg1P_19 ], cost: 1 20: __init -> f1 : arg1'=arg1P_21, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 20: __init -> f1 : arg1'=arg1P_21, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 16: f2 -> f3 : arg1'=arg1P_17, [ arg1<0 && arg1==arg1P_17 ], cost: 1 17: f2 -> f3 : arg1'=arg1P_18, [ arg1>0 && arg1==arg1P_18 ], cost: 1 1: f7 -> f10 : arg1'=arg1P_2, [ arg1P_2==1+arg1 ], cost: 1 4: f10 -> f9 : arg1'=arg1P_5, [ arg1==arg1P_5 ], cost: 1 2: f4 -> f7 : arg1'=arg1P_3, [ arg1<0 && arg1==arg1P_3 ], cost: 1 3: f4 -> f8 : arg1'=arg1P_4, [ arg1>=0 && arg1==arg1P_4 ], cost: 1 5: f8 -> f9 : arg1'=arg1P_6, [ arg1==arg1P_6 ], cost: 1 7: f9 -> f11 : arg1'=arg1P_8, [ arg1>0 && arg1==arg1P_8 ], cost: 1 8: f9 -> f12 : arg1'=arg1P_9, [ arg1<=0 && arg1==arg1P_9 ], cost: 1 6: f11 -> f14 : arg1'=arg1P_7, [ arg1P_7==-1+arg1 ], cost: 1 9: f14 -> f13 : arg1'=arg1P_10, [ arg1==arg1P_10 ], cost: 1 10: f12 -> f13 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1 14: f13 -> f6 : arg1'=arg1P_15, [ arg1==arg1P_15 ], cost: 1 11: f3 -> f4 : arg1'=arg1P_12, [ arg1>-5 && arg1<5 && arg1==arg1P_12 ], cost: 1 12: f3 -> f5 : arg1'=arg1P_13, [ arg1<=-5 && arg1==arg1P_13 ], cost: 1 13: f3 -> f5 : arg1'=arg1P_14, [ arg1>=5 && arg1==arg1P_14 ], cost: 1 15: f5 -> f6 : arg1'=arg1P_16, [ arg1==arg1P_16 ], cost: 1 18: f6 -> f2 : arg1'=arg1P_19, [ arg1==arg1P_19 ], cost: 1 20: __init -> f1 : arg1'=arg1P_21, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 16: f2 -> f3 : [ arg1<0 ], cost: 1 17: f2 -> f3 : [ arg1>0 ], cost: 1 1: f7 -> f10 : arg1'=1+arg1, [], cost: 1 4: f10 -> f9 : [], cost: 1 2: f4 -> f7 : [ arg1<0 ], cost: 1 3: f4 -> f8 : [ arg1>=0 ], cost: 1 5: f8 -> f9 : [], cost: 1 7: f9 -> f11 : [ arg1>0 ], cost: 1 8: f9 -> f12 : [ arg1<=0 ], cost: 1 6: f11 -> f14 : arg1'=-1+arg1, [], cost: 1 9: f14 -> f13 : [], cost: 1 10: f12 -> f13 : [], cost: 1 14: f13 -> f6 : [], cost: 1 11: f3 -> f4 : [ arg1>-5 && arg1<5 ], cost: 1 12: f3 -> f5 : [ arg1<=-5 ], cost: 1 13: f3 -> f5 : [ arg1>=5 ], cost: 1 15: f5 -> f6 : [], cost: 1 18: f6 -> f2 : [], cost: 1 20: __init -> f1 : arg1'=arg1P_21, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 16: f2 -> f3 : [ arg1<0 ], cost: 1 17: f2 -> f3 : [ arg1>0 ], cost: 1 23: f4 -> f9 : [ arg1>=0 ], cost: 2 24: f4 -> f9 : arg1'=1+arg1, [ arg1<0 ], cost: 3 26: f9 -> f13 : [ arg1<=0 ], cost: 2 27: f9 -> f13 : arg1'=-1+arg1, [ arg1>0 ], cost: 3 14: f13 -> f6 : [], cost: 1 11: f3 -> f4 : [ arg1>-5 && arg1<5 ], cost: 1 12: f3 -> f5 : [ arg1<=-5 ], cost: 1 13: f3 -> f5 : [ arg1>=5 ], cost: 1 15: f5 -> f6 : [], cost: 1 18: f6 -> f2 : [], cost: 1 21: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 28: f2 -> f4 : [ arg1<0 && arg1>-5 ], cost: 2 29: f2 -> f5 : [ arg1<=-5 ], cost: 2 30: f2 -> f4 : [ arg1>0 && arg1<5 ], cost: 2 31: f2 -> f5 : [ arg1>=5 ], cost: 2 32: f4 -> f13 : [ arg1>=0 && arg1<=0 ], cost: 4 33: f4 -> f13 : arg1'=-1+arg1, [ arg1>0 ], cost: 5 34: f4 -> f13 : arg1'=1+arg1, [ arg1<0 ], cost: 5 14: f13 -> f6 : [], cost: 1 15: f5 -> f6 : [], cost: 1 18: f6 -> f2 : [], cost: 1 21: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 35: f2 -> f13 : arg1'=1+arg1, [ arg1<0 && arg1>-5 ], cost: 7 36: f2 -> f13 : arg1'=-1+arg1, [ arg1>0 && arg1<5 ], cost: 7 37: f2 -> f6 : [ arg1<=-5 ], cost: 3 38: f2 -> f6 : [ arg1>=5 ], cost: 3 14: f13 -> f6 : [], cost: 1 18: f6 -> f2 : [], cost: 1 21: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 41: f2 -> f2 : [ arg1<=-5 ], cost: 4 42: f2 -> f2 : [ arg1>=5 ], cost: 4 43: f2 -> f2 : arg1'=1+arg1, [ arg1<0 && arg1>-5 ], cost: 9 44: f2 -> f2 : arg1'=-1+arg1, [ arg1>0 && arg1<5 ], cost: 9 21: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 41: f2 -> f2 : [ arg1<=-5 ], cost: 4 42: f2 -> f2 : [ arg1>=5 ], cost: 4 43: f2 -> f2 : arg1'=1+arg1, [ arg1<0 && arg1>-5 ], cost: 9 44: f2 -> f2 : arg1'=-1+arg1, [ arg1>0 && arg1<5 ], cost: 9 Accelerated rule 41 with non-termination, yielding the new rule 45. Accelerated rule 42 with non-termination, yielding the new rule 46. Accelerated rule 43 with backward acceleration, yielding the new rule 47. Accelerated rule 44 with backward acceleration, yielding the new rule 48. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 41 42 43 44. Accelerated all simple loops using metering functions (where possible): Start location: __init 45: f2 -> [16] : [ arg1<=-5 ], cost: NONTERM 46: f2 -> [16] : [ arg1>=5 ], cost: NONTERM 47: f2 -> f2 : arg1'=0, [ arg1>-5 && -arg1>=0 ], cost: -9*arg1 48: f2 -> f2 : arg1'=0, [ arg1<5 && arg1>=0 ], cost: 9*arg1 21: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 21: __init -> f2 : arg1'=arg1P_1, [], cost: 2 49: __init -> [16] : [], cost: NONTERM 50: __init -> [16] : [], cost: NONTERM 51: __init -> f2 : arg1'=0, [ arg1P_1>-5 && -arg1P_1>=0 ], cost: 2-9*arg1P_1 52: __init -> f2 : arg1'=0, [ arg1P_1<5 && arg1P_1>=0 ], cost: 2+9*arg1P_1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 49: __init -> [16] : [], cost: NONTERM 50: __init -> [16] : [], cost: NONTERM 51: __init -> f2 : arg1'=0, [ arg1P_1>-5 && -arg1P_1>=0 ], cost: 2-9*arg1P_1 52: __init -> f2 : arg1'=0, [ arg1P_1<5 && arg1P_1>=0 ], cost: 2+9*arg1P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 50: __init -> [16] : [], cost: NONTERM 51: __init -> f2 : arg1'=0, [ arg1P_1>-5 && -arg1P_1>=0 ], cost: 2-9*arg1P_1 52: __init -> f2 : arg1'=0, [ arg1P_1<5 && arg1P_1>=0 ], cost: 2+9*arg1P_1 Computing asymptotic complexity for rule 50 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