NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f6 -> f9 : arg1'=arg1P_1, [ arg1P_1==-5 ], cost: 1 9: f9 -> f8 : arg1'=arg1P_10, [ arg1==arg1P_10 ], cost: 1 1: f10 -> f13 : arg1'=arg1P_2, [ 35==arg1P_2 ], cost: 1 5: f13 -> f12 : arg1'=arg1P_6, [ arg1==arg1P_6 ], cost: 1 2: f11 -> f14 : arg1'=arg1P_3, [ arg1P_3==-1+arg1 ], cost: 1 6: f14 -> f12 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1 3: f7 -> f10 : arg1'=arg1P_4, [ arg1>30 && arg1==arg1P_4 ], cost: 1 4: f7 -> f11 : arg1'=arg1P_5, [ arg1<=30 && arg1==arg1P_5 ], cost: 1 10: f12 -> f8 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1 7: f3 -> f6 : arg1'=arg1P_8, [ arg1<0 && arg1==arg1P_8 ], cost: 1 8: f3 -> f7 : arg1'=arg1P_9, [ arg1>=0 && arg1==arg1P_9 ], cost: 1 15: f8 -> f5 : arg1'=arg1P_16, [ arg1==arg1P_16 ], cost: 1 11: f4 -> f15 : arg1'=arg1P_12, [ 0==arg1P_12 ], cost: 1 16: f15 -> f5 : arg1'=arg1P_17, [ arg1==arg1P_17 ], cost: 1 12: f2 -> f3 : arg1'=arg1P_13, [ -5<=arg1 && arg1<=35 && arg1==arg1P_13 ], cost: 1 13: f2 -> f4 : arg1'=arg1P_14, [ -5>arg1 && arg1==arg1P_14 ], cost: 1 14: f2 -> f4 : arg1'=arg1P_15, [ arg1>35 && arg1==arg1P_15 ], cost: 1 19: f5 -> f1 : arg1'=arg1P_20, [ arg1==arg1P_20 ], cost: 1 17: f1 -> f2 : arg1'=arg1P_18, [ arg1<0 && arg1==arg1P_18 ], cost: 1 18: f1 -> f2 : arg1'=arg1P_19, [ arg1>0 && arg1==arg1P_19 ], cost: 1 20: f1 -> f16 : arg1'=arg1P_21, [ arg1==0 && arg1==arg1P_21 ], cost: 1 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f6 -> f9 : arg1'=arg1P_1, [ arg1P_1==-5 ], cost: 1 9: f9 -> f8 : arg1'=arg1P_10, [ arg1==arg1P_10 ], cost: 1 1: f10 -> f13 : arg1'=arg1P_2, [ 35==arg1P_2 ], cost: 1 5: f13 -> f12 : arg1'=arg1P_6, [ arg1==arg1P_6 ], cost: 1 2: f11 -> f14 : arg1'=arg1P_3, [ arg1P_3==-1+arg1 ], cost: 1 6: f14 -> f12 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1 3: f7 -> f10 : arg1'=arg1P_4, [ arg1>30 && arg1==arg1P_4 ], cost: 1 4: f7 -> f11 : arg1'=arg1P_5, [ arg1<=30 && arg1==arg1P_5 ], cost: 1 10: f12 -> f8 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1 7: f3 -> f6 : arg1'=arg1P_8, [ arg1<0 && arg1==arg1P_8 ], cost: 1 8: f3 -> f7 : arg1'=arg1P_9, [ arg1>=0 && arg1==arg1P_9 ], cost: 1 15: f8 -> f5 : arg1'=arg1P_16, [ arg1==arg1P_16 ], cost: 1 11: f4 -> f15 : arg1'=arg1P_12, [ 0==arg1P_12 ], cost: 1 16: f15 -> f5 : arg1'=arg1P_17, [ arg1==arg1P_17 ], cost: 1 12: f2 -> f3 : arg1'=arg1P_13, [ -5<=arg1 && arg1<=35 && arg1==arg1P_13 ], cost: 1 13: f2 -> f4 : arg1'=arg1P_14, [ -5>arg1 && arg1==arg1P_14 ], cost: 1 14: f2 -> f4 : arg1'=arg1P_15, [ arg1>35 && arg1==arg1P_15 ], cost: 1 19: f5 -> f1 : arg1'=arg1P_20, [ arg1==arg1P_20 ], cost: 1 17: f1 -> f2 : arg1'=arg1P_18, [ arg1<0 && arg1==arg1P_18 ], cost: 1 18: f1 -> f2 : arg1'=arg1P_19, [ arg1>0 && arg1==arg1P_19 ], cost: 1 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f6 -> f9 : arg1'=-5, [], cost: 1 9: f9 -> f8 : [], cost: 1 1: f10 -> f13 : arg1'=35, [], cost: 1 5: f13 -> f12 : [], cost: 1 2: f11 -> f14 : arg1'=-1+arg1, [], cost: 1 6: f14 -> f12 : [], cost: 1 3: f7 -> f10 : [ arg1>30 ], cost: 1 4: f7 -> f11 : [ arg1<=30 ], cost: 1 10: f12 -> f8 : [], cost: 1 7: f3 -> f6 : [ arg1<0 ], cost: 1 8: f3 -> f7 : [ arg1>=0 ], cost: 1 15: f8 -> f5 : [], cost: 1 11: f4 -> f15 : arg1'=0, [], cost: 1 16: f15 -> f5 : [], cost: 1 12: f2 -> f3 : [ -5<=arg1 && arg1<=35 ], cost: 1 13: f2 -> f4 : [ -5>arg1 ], cost: 1 14: f2 -> f4 : [ arg1>35 ], cost: 1 19: f5 -> f1 : [], cost: 1 17: f1 -> f2 : [ arg1<0 ], cost: 1 18: f1 -> f2 : [ arg1>0 ], cost: 1 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 26: f7 -> f12 : arg1'=35, [ arg1>30 ], cost: 3 27: f7 -> f12 : arg1'=-1+arg1, [ arg1<=30 ], cost: 3 10: f12 -> f8 : [], cost: 1 8: f3 -> f7 : [ arg1>=0 ], cost: 1 23: f3 -> f8 : arg1'=-5, [ arg1<0 ], cost: 3 15: f8 -> f5 : [], cost: 1 28: f4 -> f5 : arg1'=0, [], cost: 2 12: f2 -> f3 : [ -5<=arg1 && arg1<=35 ], cost: 1 13: f2 -> f4 : [ -5>arg1 ], cost: 1 14: f2 -> f4 : [ arg1>35 ], cost: 1 19: f5 -> f1 : [], cost: 1 17: f1 -> f2 : [ arg1<0 ], cost: 1 18: f1 -> f2 : [ arg1>0 ], cost: 1 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 10: f12 -> f8 : [], cost: 1 23: f3 -> f8 : arg1'=-5, [ arg1<0 ], cost: 3 33: f3 -> f12 : arg1'=35, [ arg1>30 ], cost: 4 34: f3 -> f12 : arg1'=-1+arg1, [ arg1>=0 && arg1<=30 ], cost: 4 15: f8 -> f5 : [], cost: 1 28: f4 -> f5 : arg1'=0, [], cost: 2 19: f5 -> f1 : [], cost: 1 29: f1 -> f3 : [ arg1<0 && -5<=arg1 ], cost: 2 30: f1 -> f4 : [ -5>arg1 ], cost: 2 31: f1 -> f3 : [ arg1>0 && arg1<=35 ], cost: 2 32: f1 -> f4 : [ arg1>35 ], cost: 2 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 10: f12 -> f8 : [], cost: 1 15: f8 -> f5 : [], cost: 1 19: f5 -> f1 : [], cost: 1 35: f1 -> f8 : arg1'=-5, [ arg1<0 && -5<=arg1 ], cost: 5 36: f1 -> f12 : arg1'=35, [ arg1<=35 && arg1>30 ], cost: 6 37: f1 -> f12 : arg1'=-1+arg1, [ arg1>0 && arg1<=30 ], cost: 6 38: f1 -> f5 : arg1'=0, [ -5>arg1 ], cost: 4 39: f1 -> f5 : arg1'=0, [ arg1>35 ], cost: 4 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 45: f1 -> f1 : arg1'=0, [ -5>arg1 ], cost: 5 46: f1 -> f1 : arg1'=0, [ arg1>35 ], cost: 5 47: f1 -> f1 : arg1'=-5, [ arg1<0 && -5<=arg1 ], cost: 7 48: f1 -> f1 : arg1'=35, [ arg1<=35 && arg1>30 ], cost: 9 49: f1 -> f1 : arg1'=-1+arg1, [ arg1>0 && arg1<=30 ], cost: 9 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 Accelerating simple loops of location 14. Accelerating the following rules: 45: f1 -> f1 : arg1'=0, [ -5>arg1 ], cost: 5 46: f1 -> f1 : arg1'=0, [ arg1>35 ], cost: 5 47: f1 -> f1 : arg1'=-5, [ arg1<0 && -5<=arg1 ], cost: 7 48: f1 -> f1 : arg1'=35, [ arg1<=35 && arg1>30 ], cost: 9 49: f1 -> f1 : arg1'=-1+arg1, [ arg1>0 && arg1<=30 ], cost: 9 Failed to prove monotonicity of the guard of rule 45. Failed to prove monotonicity of the guard of rule 46. Accelerated rule 47 with non-termination, yielding the new rule 50. Accelerated rule 48 with non-termination, yielding the new rule 51. Accelerated rule 49 with backward acceleration, yielding the new rule 52. [accelerate] Nesting with 3 inner and 3 outer candidates Removing the simple loops: 47 48 49. Accelerated all simple loops using metering functions (where possible): Start location: __init 45: f1 -> f1 : arg1'=0, [ -5>arg1 ], cost: 5 46: f1 -> f1 : arg1'=0, [ arg1>35 ], cost: 5 50: f1 -> [17] : [ arg1<0 && -5<=arg1 ], cost: NONTERM 51: f1 -> [17] : [ arg1<=35 && arg1>30 ], cost: NONTERM 52: f1 -> f1 : arg1'=0, [ arg1<=30 && arg1>=0 ], cost: 9*arg1 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 21: __init -> f1 : arg1'=arg1P_22, [], cost: 1 53: __init -> f1 : arg1'=0, [], cost: 6 54: __init -> f1 : arg1'=0, [], cost: 6 55: __init -> [17] : [], cost: NONTERM 56: __init -> [17] : [], cost: NONTERM 57: __init -> f1 : arg1'=0, [ arg1P_22<=30 && arg1P_22>=0 ], cost: 1+9*arg1P_22 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 55: __init -> [17] : [], cost: NONTERM 56: __init -> [17] : [], cost: NONTERM 57: __init -> f1 : arg1'=0, [ arg1P_22<=30 && arg1P_22>=0 ], cost: 1+9*arg1P_22 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 56: __init -> [17] : [], cost: NONTERM 57: __init -> f1 : arg1'=0, [ arg1P_22<=30 && arg1P_22>=0 ], cost: 1+9*arg1P_22 Computing asymptotic complexity for rule 56 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