NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 18: f2 -> f3 : arg1'=arg1P_19, [ arg1<0 && arg1==arg1P_19 ], cost: 1 19: f2 -> f3 : arg1'=arg1P_20, [ arg1>0 && arg1==arg1P_20 ], cost: 1 21: f2 -> f17 : arg1'=arg1P_22, [ arg1==0 && arg1==arg1P_22 ], cost: 1 1: f7 -> f10 : arg1'=arg1P_2, [ arg1P_2==-5 ], cost: 1 10: f10 -> f9 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1 2: f11 -> f14 : arg1'=arg1P_3, [ 35==arg1P_3 ], cost: 1 6: f14 -> f13 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1 3: f12 -> f15 : arg1'=arg1P_4, [ arg1P_4==-1+arg1 ], cost: 1 7: f15 -> f13 : arg1'=arg1P_8, [ arg1==arg1P_8 ], cost: 1 4: f8 -> f11 : arg1'=arg1P_5, [ arg1>30 && arg1==arg1P_5 ], cost: 1 5: f8 -> f12 : arg1'=arg1P_6, [ arg1<=30 && arg1==arg1P_6 ], cost: 1 11: f13 -> f9 : arg1'=arg1P_12, [ arg1==arg1P_12 ], cost: 1 8: f4 -> f7 : arg1'=arg1P_9, [ arg1<0 && arg1==arg1P_9 ], cost: 1 9: f4 -> f8 : arg1'=arg1P_10, [ arg1>=0 && arg1==arg1P_10 ], cost: 1 16: f9 -> f6 : arg1'=arg1P_17, [ arg1==arg1P_17 ], cost: 1 12: f5 -> f16 : arg1'=arg1P_13, [ 0==arg1P_13 ], cost: 1 17: f16 -> f6 : arg1'=arg1P_18, [ arg1==arg1P_18 ], cost: 1 13: f3 -> f4 : arg1'=arg1P_14, [ -5<=arg1 && arg1<=35 && arg1==arg1P_14 ], cost: 1 14: f3 -> f5 : arg1'=arg1P_15, [ -5>arg1 && arg1==arg1P_15 ], cost: 1 15: f3 -> f5 : arg1'=arg1P_16, [ arg1>35 && arg1==arg1P_16 ], cost: 1 20: f6 -> f2 : arg1'=arg1P_21, [ arg1==arg1P_21 ], cost: 1 22: __init -> f1 : arg1'=arg1P_23, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 22: __init -> f1 : arg1'=arg1P_23, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 18: f2 -> f3 : arg1'=arg1P_19, [ arg1<0 && arg1==arg1P_19 ], cost: 1 19: f2 -> f3 : arg1'=arg1P_20, [ arg1>0 && arg1==arg1P_20 ], cost: 1 1: f7 -> f10 : arg1'=arg1P_2, [ arg1P_2==-5 ], cost: 1 10: f10 -> f9 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1 2: f11 -> f14 : arg1'=arg1P_3, [ 35==arg1P_3 ], cost: 1 6: f14 -> f13 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1 3: f12 -> f15 : arg1'=arg1P_4, [ arg1P_4==-1+arg1 ], cost: 1 7: f15 -> f13 : arg1'=arg1P_8, [ arg1==arg1P_8 ], cost: 1 4: f8 -> f11 : arg1'=arg1P_5, [ arg1>30 && arg1==arg1P_5 ], cost: 1 5: f8 -> f12 : arg1'=arg1P_6, [ arg1<=30 && arg1==arg1P_6 ], cost: 1 11: f13 -> f9 : arg1'=arg1P_12, [ arg1==arg1P_12 ], cost: 1 8: f4 -> f7 : arg1'=arg1P_9, [ arg1<0 && arg1==arg1P_9 ], cost: 1 9: f4 -> f8 : arg1'=arg1P_10, [ arg1>=0 && arg1==arg1P_10 ], cost: 1 16: f9 -> f6 : arg1'=arg1P_17, [ arg1==arg1P_17 ], cost: 1 12: f5 -> f16 : arg1'=arg1P_13, [ 0==arg1P_13 ], cost: 1 17: f16 -> f6 : arg1'=arg1P_18, [ arg1==arg1P_18 ], cost: 1 13: f3 -> f4 : arg1'=arg1P_14, [ -5<=arg1 && arg1<=35 && arg1==arg1P_14 ], cost: 1 14: f3 -> f5 : arg1'=arg1P_15, [ -5>arg1 && arg1==arg1P_15 ], cost: 1 15: f3 -> f5 : arg1'=arg1P_16, [ arg1>35 && arg1==arg1P_16 ], cost: 1 20: f6 -> f2 : arg1'=arg1P_21, [ arg1==arg1P_21 ], cost: 1 22: __init -> f1 : arg1'=arg1P_23, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 18: f2 -> f3 : [ arg1<0 ], cost: 1 19: f2 -> f3 : [ arg1>0 ], cost: 1 1: f7 -> f10 : arg1'=-5, [], cost: 1 10: f10 -> f9 : [], cost: 1 2: f11 -> f14 : arg1'=35, [], cost: 1 6: f14 -> f13 : [], cost: 1 3: f12 -> f15 : arg1'=-1+arg1, [], cost: 1 7: f15 -> f13 : [], cost: 1 4: f8 -> f11 : [ arg1>30 ], cost: 1 5: f8 -> f12 : [ arg1<=30 ], cost: 1 11: f13 -> f9 : [], cost: 1 8: f4 -> f7 : [ arg1<0 ], cost: 1 9: f4 -> f8 : [ arg1>=0 ], cost: 1 16: f9 -> f6 : [], cost: 1 12: f5 -> f16 : arg1'=0, [], cost: 1 17: f16 -> f6 : [], cost: 1 13: f3 -> f4 : [ -5<=arg1 && arg1<=35 ], cost: 1 14: f3 -> f5 : [ -5>arg1 ], cost: 1 15: f3 -> f5 : [ arg1>35 ], cost: 1 20: f6 -> f2 : [], cost: 1 22: __init -> f1 : arg1'=arg1P_23, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 18: f2 -> f3 : [ arg1<0 ], cost: 1 19: f2 -> f3 : [ arg1>0 ], cost: 1 28: f8 -> f13 : arg1'=35, [ arg1>30 ], cost: 3 29: f8 -> f13 : arg1'=-1+arg1, [ arg1<=30 ], cost: 3 11: f13 -> f9 : [], cost: 1 9: f4 -> f8 : [ arg1>=0 ], cost: 1 25: f4 -> f9 : arg1'=-5, [ arg1<0 ], cost: 3 16: f9 -> f6 : [], cost: 1 30: f5 -> f6 : arg1'=0, [], cost: 2 13: f3 -> f4 : [ -5<=arg1 && arg1<=35 ], cost: 1 14: f3 -> f5 : [ -5>arg1 ], cost: 1 15: f3 -> f5 : [ arg1>35 ], cost: 1 20: f6 -> f2 : [], cost: 1 23: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 31: f2 -> f4 : [ arg1<0 && -5<=arg1 ], cost: 2 32: f2 -> f5 : [ -5>arg1 ], cost: 2 33: f2 -> f4 : [ arg1>0 && arg1<=35 ], cost: 2 34: f2 -> f5 : [ arg1>35 ], cost: 2 11: f13 -> f9 : [], cost: 1 25: f4 -> f9 : arg1'=-5, [ arg1<0 ], cost: 3 35: f4 -> f13 : arg1'=35, [ arg1>30 ], cost: 4 36: f4 -> f13 : arg1'=-1+arg1, [ arg1>=0 && arg1<=30 ], cost: 4 16: f9 -> f6 : [], cost: 1 30: f5 -> f6 : arg1'=0, [], cost: 2 20: f6 -> f2 : [], cost: 1 23: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 37: f2 -> f9 : arg1'=-5, [ arg1<0 && -5<=arg1 ], cost: 5 38: f2 -> f13 : arg1'=35, [ arg1<=35 && arg1>30 ], cost: 6 39: f2 -> f13 : arg1'=-1+arg1, [ arg1>0 && arg1<=30 ], cost: 6 40: f2 -> f6 : arg1'=0, [ -5>arg1 ], cost: 4 41: f2 -> f6 : arg1'=0, [ arg1>35 ], cost: 4 11: f13 -> f9 : [], cost: 1 16: f9 -> f6 : [], cost: 1 20: f6 -> f2 : [], cost: 1 23: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 47: f2 -> f2 : arg1'=0, [ -5>arg1 ], cost: 5 48: f2 -> f2 : arg1'=0, [ arg1>35 ], cost: 5 49: f2 -> f2 : arg1'=-5, [ arg1<0 && -5<=arg1 ], cost: 7 50: f2 -> f2 : arg1'=35, [ arg1<=35 && arg1>30 ], cost: 9 51: f2 -> f2 : arg1'=-1+arg1, [ arg1>0 && arg1<=30 ], cost: 9 23: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 47: f2 -> f2 : arg1'=0, [ -5>arg1 ], cost: 5 48: f2 -> f2 : arg1'=0, [ arg1>35 ], cost: 5 49: f2 -> f2 : arg1'=-5, [ arg1<0 && -5<=arg1 ], cost: 7 50: f2 -> f2 : arg1'=35, [ arg1<=35 && arg1>30 ], cost: 9 51: f2 -> f2 : arg1'=-1+arg1, [ arg1>0 && arg1<=30 ], cost: 9 Failed to prove monotonicity of the guard of rule 47. Failed to prove monotonicity of the guard of rule 48. Accelerated rule 49 with non-termination, yielding the new rule 52. Accelerated rule 50 with non-termination, yielding the new rule 53. Accelerated rule 51 with backward acceleration, yielding the new rule 54. [accelerate] Nesting with 3 inner and 3 outer candidates Removing the simple loops: 49 50 51. Accelerated all simple loops using metering functions (where possible): Start location: __init 47: f2 -> f2 : arg1'=0, [ -5>arg1 ], cost: 5 48: f2 -> f2 : arg1'=0, [ arg1>35 ], cost: 5 52: f2 -> [18] : [ arg1<0 && -5<=arg1 ], cost: NONTERM 53: f2 -> [18] : [ arg1<=35 && arg1>30 ], cost: NONTERM 54: f2 -> f2 : arg1'=0, [ arg1<=30 && arg1>=0 ], cost: 9*arg1 23: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 23: __init -> f2 : arg1'=arg1P_1, [], cost: 2 55: __init -> f2 : arg1'=0, [], cost: 7 56: __init -> f2 : arg1'=0, [], cost: 7 57: __init -> [18] : [], cost: NONTERM 58: __init -> [18] : [], cost: NONTERM 59: __init -> f2 : arg1'=0, [ arg1P_1<=30 && arg1P_1>=0 ], cost: 2+9*arg1P_1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 57: __init -> [18] : [], cost: NONTERM 58: __init -> [18] : [], cost: NONTERM 59: __init -> f2 : arg1'=0, [ arg1P_1<=30 && arg1P_1>=0 ], cost: 2+9*arg1P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 58: __init -> [18] : [], cost: NONTERM 59: __init -> f2 : arg1'=0, [ arg1P_1<=30 && arg1P_1>=0 ], cost: 2+9*arg1P_1 Computing asymptotic complexity for rule 58 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