NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_ConstantStackPush -> f79_0_loop_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 2==arg1P_1 && 2==arg2P_1 && 2==arg3P_1 && 0==arg4P_1 ], cost: 1 1: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg4>arg2 && arg2>0 && arg2==arg3 && arg1==arg1P_2 && 4+arg2==arg2P_2 && arg4==arg3P_2 ], cost: 1 2: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg4<=arg2 && arg2>0 && arg4>-1 && arg2==arg3 && arg1==arg1P_3 && 2+arg2==arg2P_3 && 1+arg4==arg3P_3 ], cost: 1 3: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg3>0 && arg1>1 && arg2>1 && arg2==arg1P_4 && arg2==arg2P_4 && arg2==arg3P_4 && arg3==arg4P_4 ], cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_ConstantStackPush -> f79_0_loop_GE : arg1'=2, arg2'=2, arg3'=2, arg4'=0, [], cost: 1 1: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=4+arg2, arg3'=arg4, arg4'=arg4P_2, [ arg4>arg2 && arg2>0 && arg2==arg3 ], cost: 1 2: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=2+arg2, arg3'=1+arg4, arg4'=arg4P_3, [ arg4<=arg2 && arg2>0 && arg4>-1 && arg2==arg3 ], cost: 1 3: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg1'=arg2, arg3'=arg2, arg4'=arg3, [ arg3>0 && arg1>1 && arg2>1 ], cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 1: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=4+arg2, arg3'=arg4, arg4'=arg4P_2, [ arg4>arg2 && arg2>0 && arg2==arg3 ], cost: 1 2: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=2+arg2, arg3'=1+arg4, arg4'=arg4P_3, [ arg4<=arg2 && arg2>0 && arg4>-1 && arg2==arg3 ], cost: 1 3: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg1'=arg2, arg3'=arg2, arg4'=arg3, [ arg3>0 && arg1>1 && arg2>1 ], cost: 1 5: __init -> f79_0_loop_GE : arg1'=2, arg2'=2, arg3'=2, arg4'=0, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 6: f79_0_loop_GE -> f79_0_loop_GE : arg1'=4+arg2, arg2'=4+arg2, arg3'=4+arg2, arg4'=arg4, [ arg4>arg2 && arg2>0 && arg2==arg3 && arg4>0 && arg1>1 ], cost: 2 7: f79_0_loop_GE -> f79_0_loop_GE : arg1'=2+arg2, arg2'=2+arg2, arg3'=2+arg2, arg4'=1+arg4, [ arg4<=arg2 && arg2>0 && arg4>-1 && arg2==arg3 && arg1>1 ], cost: 2 5: __init -> f79_0_loop_GE : arg1'=2, arg2'=2, arg3'=2, arg4'=0, [], cost: 2 Accelerating simple loops of location 1. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 6: f79_0_loop_GE -> f79_0_loop_GE : arg1'=4+arg2, arg2'=4+arg2, arg3'=4+arg2, [ arg4>arg2 && arg2>0 && arg2==arg3 && arg4>0 && arg1>1 ], cost: 2 7: f79_0_loop_GE -> f79_0_loop_GE : arg1'=2+arg2, arg2'=2+arg2, arg3'=2+arg2, arg4'=1+arg4, [ arg4<=arg2 && arg2>0 && arg4>-1 && arg2==arg3 && arg1>1 ], cost: 2 Accelerated rule 6 with backward acceleration, yielding the new rule 8. Accelerated rule 7 with non-termination, yielding the new rule 9. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 6 7. Accelerated all simple loops using metering functions (where possible): Start location: __init 8: f79_0_loop_GE -> f79_0_loop_GE : arg1'=arg2+4*k, arg2'=arg2+4*k, arg3'=arg2+4*k, [ arg2>0 && arg2==arg3 && arg4>0 && arg1>1 && k>=1 && arg4>-4+arg2+4*k ], cost: 2*k 9: f79_0_loop_GE -> [4] : [ arg4<=arg2 && arg2>0 && arg4>-1 && arg2==arg3 && arg1>1 ], cost: NONTERM 5: __init -> f79_0_loop_GE : arg1'=2, arg2'=2, arg3'=2, arg4'=0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 5: __init -> f79_0_loop_GE : arg1'=2, arg2'=2, arg3'=2, arg4'=0, [], cost: 2 10: __init -> [4] : [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: __init 10: __init -> [4] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 10: __init -> [4] : [], cost: NONTERM Computing asymptotic complexity for rule 10 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