NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1 3: f3 -> f4 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && arg2>0 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1 5: f3 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1<=0 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1 6: f3 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2<=0 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==10*arg2-2*arg1 && arg2==arg2P_3 ], cost: 1 4: f5 -> f3 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1 7: __init -> f1 : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: __init -> f1 : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1 3: f3 -> f4 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && arg2>0 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==10*arg2-2*arg1 && arg2==arg2P_3 ], cost: 1 4: f5 -> f3 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1 7: __init -> f1 : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1 3: f3 -> f4 : [ arg1>0 && arg2>0 ], cost: 1 2: f4 -> f5 : arg1'=10*arg2-2*arg1, [], cost: 1 4: f5 -> f3 : [], cost: 1 7: __init -> f1 : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 11: f3 -> f3 : arg1'=10*arg2-2*arg1, [ arg1>0 && arg2>0 ], cost: 3 9: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3 Accelerating simple loops of location 2. Accelerating the following rules: 11: f3 -> f3 : arg1'=10*arg2-2*arg1, [ arg1>0 && arg2>0 ], cost: 3 Accelerated rule 11 with non-termination, yielding the new rule 12. Accelerated rule 11 with backward acceleration, yielding the new rule 13. [accelerate] Nesting with 1 inner and 0 outer candidates Removing the simple loops: 11. Accelerated all simple loops using metering functions (where possible): Start location: __init 12: f3 -> [7] : [ 10*arg2-2*arg1>0 && arg2==3 && arg1==10 ], cost: NONTERM 13: f3 -> f3 : arg1'=4^k*arg1+10/3*arg2-10/3*4^k*arg2, [ arg2>0 && k>=0 && 4^(-1+k)*arg1+10/3*arg2-10/3*arg2*4^(-1+k)>0 && -2*4^(-1+k)*arg1+10/3*arg2+20/3*arg2*4^(-1+k)>0 ], cost: 6*k 9: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3 Chained accelerated rules (with incoming rules): Start location: __init 9: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3 14: __init -> [7] : [], cost: NONTERM 15: __init -> f3 : arg1'=10/3*arg2P_2+4^k*arg1P_1-10/3*4^k*arg2P_2, arg2'=arg2P_2, [ arg2P_2>0 && k>=0 && 10/3*arg2P_2-10/3*arg2P_2*4^(-1+k)+arg1P_1*4^(-1+k)>0 && 10/3*arg2P_2+20/3*arg2P_2*4^(-1+k)-2*arg1P_1*4^(-1+k)>0 ], cost: 3+6*k Removed unreachable locations (and leaf rules with constant cost): Start location: __init 14: __init -> [7] : [], cost: NONTERM 15: __init -> f3 : arg1'=10/3*arg2P_2+4^k*arg1P_1-10/3*4^k*arg2P_2, arg2'=arg2P_2, [ arg2P_2>0 && k>=0 && 10/3*arg2P_2-10/3*arg2P_2*4^(-1+k)+arg1P_1*4^(-1+k)>0 && 10/3*arg2P_2+20/3*arg2P_2*4^(-1+k)-2*arg1P_1*4^(-1+k)>0 ], cost: 3+6*k ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 14: __init -> [7] : [], cost: NONTERM 15: __init -> f3 : arg1'=10/3*arg2P_2+4^k*arg1P_1-10/3*4^k*arg2P_2, arg2'=arg2P_2, [ arg2P_2>0 && k>=0 && 10/3*arg2P_2-10/3*arg2P_2*4^(-1+k)+arg1P_1*4^(-1+k)>0 && 10/3*arg2P_2+20/3*arg2P_2*4^(-1+k)-2*arg1P_1*4^(-1+k)>0 ], cost: 3+6*k Computing asymptotic complexity for rule 14 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