NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 && 0==arg2P_1 && arg2==arg3P_1 ], cost: 1 1: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ x7_1>-1 && arg3>arg2 && arg2>-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2+x7_1==arg2P_2 && arg3==arg3P_2 ], cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 1: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P_2, arg2'=arg2+x7_1, [ x7_1>-1 && arg3>arg2 && arg2>-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P_2, arg2'=arg2+x7_1, [ x7_1>-1 && arg3>arg2 && arg2>-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 Accelerated rule 1 with non-termination, yielding the new rule 3. Accelerated rule 1 with backward acceleration, yielding the new rule 4. [accelerate] Nesting with 1 inner and 0 outer candidates Removing the simple loops: 1. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 3: f61_0_main_GE -> [3] : [ arg3>arg2 && arg1P_2<=arg1 && arg2==0 && arg3==1 && x7_1==0 && arg1==1 && arg1P_2==1 ], cost: NONTERM 4: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P_2, arg2'=arg2+k*x7_1, [ x7_1>-1 && arg2>-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && k>=1 && arg3>arg2+(-1+k)*x7_1 ], cost: k 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 5: f1_0_main_ConstantStackPush -> [3] : [ 1<=arg1 && arg2==1 ], cost: NONTERM 6: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P_2, arg2'=k*x7_1, arg3'=arg2, [ arg2>-1 && arg1>0 && x7_1>-1 && arg1P_2>0 && k>=1 && arg2>(-1+k)*x7_1 && arg1P_2<=arg1 ], cost: 1+k 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 5: f1_0_main_ConstantStackPush -> [3] : [ 1<=arg1 && arg2==1 ], cost: NONTERM 6: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P_2, arg2'=k*x7_1, arg3'=arg2, [ arg2>-1 && arg1>0 && x7_1>-1 && arg1P_2>0 && k>=1 && arg2>(-1+k)*x7_1 && arg1P_2<=arg1 ], cost: 1+k 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 7: __init -> [3] : [ 1<=arg1P_3 && arg2P_3==1 ], cost: NONTERM 8: __init -> f61_0_main_GE : arg1'=arg1P_2, arg2'=k*x7_1, arg3'=arg2P_3, [ arg2P_3>-1 && arg1P_3>0 && x7_1>-1 && arg1P_2>0 && k>=1 && arg2P_3>(-1+k)*x7_1 && arg1P_2<=arg1P_3 ], cost: 2+k ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 7: __init -> [3] : [ 1<=arg1P_3 && arg2P_3==1 ], cost: NONTERM 8: __init -> f61_0_main_GE : arg1'=arg1P_2, arg2'=k*x7_1, arg3'=arg2P_3, [ arg2P_3>-1 && arg1P_3>0 && x7_1>-1 && arg1P_2>0 && k>=1 && arg2P_3>(-1+k)*x7_1 && arg1P_2<=arg1P_3 ], cost: 2+k Computing asymptotic complexity for rule 7 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: [ 1<=arg1P_3 && arg2P_3==1 ] NO