NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 11: f2 -> f3 : arg1'=arg1P_12, [ arg1>=-5 && arg1<=5 && arg1==arg1P_12 ], cost: 1 13: f2 -> f12 : arg1'=arg1P_14, [ arg1<-5 && arg1==arg1P_14 ], cost: 1 14: f2 -> f12 : arg1'=arg1P_15, [ arg1>5 && arg1==arg1P_15 ], cost: 1 1: f4 -> f7 : arg1'=arg1P_2, [ arg1P_2==-1+arg1 ], cost: 1 4: f7 -> f6 : arg1'=arg1P_5, [ arg1==arg1P_5 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, [ arg1>0 && arg1==arg1P_3 ], cost: 1 3: f3 -> f5 : arg1'=arg1P_4, [ arg1<=0 && arg1==arg1P_4 ], cost: 1 5: f5 -> f6 : arg1'=arg1P_6, [ arg1==arg1P_6 ], cost: 1 7: f6 -> f8 : arg1'=arg1P_8, [ arg1<0 && arg1==arg1P_8 ], cost: 1 8: f6 -> f9 : arg1'=arg1P_9, [ arg1>=0 && arg1==arg1P_9 ], cost: 1 6: f8 -> f11 : arg1'=arg1P_7, [ arg1P_7==1+arg1 ], cost: 1 9: f11 -> f10 : arg1'=arg1P_10, [ arg1==arg1P_10 ], cost: 1 10: f9 -> f10 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1 12: f10 -> f2 : arg1'=arg1P_13, [ arg1==arg1P_13 ], cost: 1 15: __init -> f1 : arg1'=arg1P_16, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 15: __init -> f1 : arg1'=arg1P_16, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 11: f2 -> f3 : arg1'=arg1P_12, [ arg1>=-5 && arg1<=5 && arg1==arg1P_12 ], cost: 1 1: f4 -> f7 : arg1'=arg1P_2, [ arg1P_2==-1+arg1 ], cost: 1 4: f7 -> f6 : arg1'=arg1P_5, [ arg1==arg1P_5 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, [ arg1>0 && arg1==arg1P_3 ], cost: 1 3: f3 -> f5 : arg1'=arg1P_4, [ arg1<=0 && arg1==arg1P_4 ], cost: 1 5: f5 -> f6 : arg1'=arg1P_6, [ arg1==arg1P_6 ], cost: 1 7: f6 -> f8 : arg1'=arg1P_8, [ arg1<0 && arg1==arg1P_8 ], cost: 1 8: f6 -> f9 : arg1'=arg1P_9, [ arg1>=0 && arg1==arg1P_9 ], cost: 1 6: f8 -> f11 : arg1'=arg1P_7, [ arg1P_7==1+arg1 ], cost: 1 9: f11 -> f10 : arg1'=arg1P_10, [ arg1==arg1P_10 ], cost: 1 10: f9 -> f10 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1 12: f10 -> f2 : arg1'=arg1P_13, [ arg1==arg1P_13 ], cost: 1 15: __init -> f1 : arg1'=arg1P_16, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 11: f2 -> f3 : [ arg1>=-5 && arg1<=5 ], cost: 1 1: f4 -> f7 : arg1'=-1+arg1, [], cost: 1 4: f7 -> f6 : [], cost: 1 2: f3 -> f4 : [ arg1>0 ], cost: 1 3: f3 -> f5 : [ arg1<=0 ], cost: 1 5: f5 -> f6 : [], cost: 1 7: f6 -> f8 : [ arg1<0 ], cost: 1 8: f6 -> f9 : [ arg1>=0 ], cost: 1 6: f8 -> f11 : arg1'=1+arg1, [], cost: 1 9: f11 -> f10 : [], cost: 1 10: f9 -> f10 : [], cost: 1 12: f10 -> f2 : [], cost: 1 15: __init -> f1 : arg1'=arg1P_16, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 11: f2 -> f3 : [ arg1>=-5 && arg1<=5 ], cost: 1 18: f3 -> f6 : [ arg1<=0 ], cost: 2 19: f3 -> f6 : arg1'=-1+arg1, [ arg1>0 ], cost: 3 21: f6 -> f10 : [ arg1>=0 ], cost: 2 22: f6 -> f10 : arg1'=1+arg1, [ arg1<0 ], cost: 3 12: f10 -> f2 : [], cost: 1 16: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 23: f2 -> f6 : [ arg1>=-5 && arg1<=0 ], cost: 3 24: f2 -> f6 : arg1'=-1+arg1, [ arg1<=5 && arg1>0 ], cost: 4 25: f6 -> f2 : [ arg1>=0 ], cost: 3 26: f6 -> f2 : arg1'=1+arg1, [ arg1<0 ], cost: 4 16: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 27: f2 -> f2 : [ arg1<=0 && arg1>=0 ], cost: 6 28: f2 -> f2 : arg1'=1+arg1, [ arg1>=-5 && arg1<0 ], cost: 7 29: f2 -> f2 : arg1'=-1+arg1, [ arg1<=5 && arg1>0 ], cost: 7 16: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Accelerating simple loops of location 1. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 27: f2 -> f2 : [ arg1==0 ], cost: 6 28: f2 -> f2 : arg1'=1+arg1, [ arg1>=-5 && arg1<0 ], cost: 7 29: f2 -> f2 : arg1'=-1+arg1, [ arg1<=5 && arg1>0 ], cost: 7 Accelerated rule 27 with non-termination, yielding the new rule 30. Accelerated rule 28 with backward acceleration, yielding the new rule 31. Accelerated rule 29 with backward acceleration, yielding the new rule 32. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 27 28 29. Accelerated all simple loops using metering functions (where possible): Start location: __init 30: f2 -> [13] : [ arg1==0 ], cost: NONTERM 31: f2 -> f2 : arg1'=0, [ arg1>=-5 && -arg1>=0 ], cost: -7*arg1 32: f2 -> f2 : arg1'=0, [ arg1<=5 && arg1>=0 ], cost: 7*arg1 16: __init -> f2 : arg1'=arg1P_1, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 16: __init -> f2 : arg1'=arg1P_1, [], cost: 2 33: __init -> [13] : [], cost: NONTERM 34: __init -> f2 : arg1'=0, [ arg1P_1>=-5 && -arg1P_1>=0 ], cost: 2-7*arg1P_1 35: __init -> f2 : arg1'=0, [ arg1P_1<=5 && arg1P_1>=0 ], cost: 2+7*arg1P_1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 33: __init -> [13] : [], cost: NONTERM 34: __init -> f2 : arg1'=0, [ arg1P_1>=-5 && -arg1P_1>=0 ], cost: 2-7*arg1P_1 35: __init -> f2 : arg1'=0, [ arg1P_1<=5 && arg1P_1>=0 ], cost: 2+7*arg1P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 33: __init -> [13] : [], cost: NONTERM 34: __init -> f2 : arg1'=0, [ arg1P_1>=-5 && -arg1P_1>=0 ], cost: 2-7*arg1P_1 35: __init -> f2 : arg1'=0, [ arg1P_1<=5 && arg1P_1>=0 ], cost: 2+7*arg1P_1 Computing asymptotic complexity for rule 33 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