NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f74_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 && 0==arg2P_1 && arg2==arg3P_1 && arg2==arg4P_1 ], cost: 1 1: f74_0_loop_LE -> f74_0_loop_LE\' : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg4>-1 && arg3>0 && x7_1<=arg1 && arg1>0 && x7_1>0 && arg1==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1 2: f74_0_loop_LE\' -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg4>-1 && arg3>0 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 && -arg2-2*x13_1+arg4<2 && -arg2-2*x13_1+arg4>=0 && arg2+x13_1==arg2P_3 && -arg2-x13_1+arg4==arg3P_3 && arg4==arg4P_3 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f74_0_loop_LE : arg1'=arg1P_1, arg2'=0, arg3'=arg2, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 1: f74_0_loop_LE -> f74_0_loop_LE\' : [ arg4>-1 && arg3>0 && arg1>0 ], cost: 1 2: f74_0_loop_LE\' -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=arg2+x13_1, arg3'=-arg2-x13_1+arg4, [ arg4>-1 && arg3>0 && arg1P_3<=arg1 && arg1>0 && arg1P_3>0 && -arg2-2*x13_1+arg4<2 && -arg2-2*x13_1+arg4>=0 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 5: f74_0_loop_LE -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=arg2+x13_1, arg3'=-arg2-x13_1+arg4, [ arg4>-1 && arg3>0 && arg1>0 && arg1P_3<=arg1 && arg1P_3>0 && -arg2-2*x13_1+arg4<2 && -arg2-2*x13_1+arg4>=0 ], cost: 2 4: __init -> f74_0_loop_LE : arg1'=arg1P_1, arg2'=0, arg3'=arg2P_4, arg4'=arg2P_4, [ arg1P_1<=arg1P_4 && arg2P_4>-1 && arg1P_4>0 && arg1P_1>0 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 5: f74_0_loop_LE -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=arg2+x13_1, arg3'=-arg2-x13_1+arg4, [ arg4>-1 && arg3>0 && arg1>0 && arg1P_3<=arg1 && arg1P_3>0 && -arg2-2*x13_1+arg4<2 && -arg2-2*x13_1+arg4>=0 ], cost: 2 [test] deduced invariant arg2+arg3-arg4<=0 [test] deduced pseudo-invariant 1-x13_1<=0, also trying -1+x13_1<=-1 Accelerated rule 5 with non-termination, yielding the new rule 6. Accelerated rule 5 with backward acceleration, yielding the new rule 7. Accelerated rule 5 with non-termination, yielding the new rule 8. Accelerated rule 5 with backward acceleration, yielding the new rule 9. [accelerate] Nesting with 1 inner and 1 outer candidates Also removing duplicate rules: 8. Accelerated all simple loops using metering functions (where possible): Start location: __init 5: f74_0_loop_LE -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=arg2+x13_1, arg3'=-arg2-x13_1+arg4, [ arg4>-1 && arg3>0 && arg1>0 && arg1P_3<=arg1 && arg1P_3>0 && -arg2-2*x13_1+arg4<2 && -arg2-2*x13_1+arg4>=0 ], cost: 2 6: f74_0_loop_LE -> [4] : [ arg1P_3<=arg1 && -arg2-2*x13_1+arg4<2 && -arg2-2*x13_1+arg4>=0 && arg1P_3==1 && arg2==-1 && arg3==1 && x13_1==0 && arg4==0 && arg1==1 ], cost: NONTERM 7: f74_0_loop_LE -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=arg2+x13_1*k, arg3'=-arg2-(-1+k)*x13_1-x13_1+arg4, [ arg4>-1 && arg3>0 && arg1>0 && arg1P_3<=arg1 && arg1P_3>0 && -arg2-2*x13_1+arg4<2 && arg2+arg3-arg4<=0 && 1-x13_1<=0 && k>=1 && -arg2-(-1+k)*x13_1-2*x13_1+arg4>=0 ], cost: 2*k 9: f74_0_loop_LE -> [4] : [ arg4>-1 && arg3>0 && arg1>0 && arg1P_3<=arg1 && arg1P_3>0 && -arg2-2*x13_1+arg4<2 && -arg2-2*x13_1+arg4>=0 && arg2+arg3-arg4<=0 && -1+x13_1<=-1 ], cost: NONTERM 4: __init -> f74_0_loop_LE : arg1'=arg1P_1, arg2'=0, arg3'=arg2P_4, arg4'=arg2P_4, [ arg1P_1<=arg1P_4 && arg2P_4>-1 && arg1P_4>0 && arg1P_1>0 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 4: __init -> f74_0_loop_LE : arg1'=arg1P_1, arg2'=0, arg3'=arg2P_4, arg4'=arg2P_4, [ arg1P_1<=arg1P_4 && arg2P_4>-1 && arg1P_4>0 && arg1P_1>0 ], cost: 2 10: __init -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=x13_1, arg3'=-x13_1+arg2P_4, arg4'=arg2P_4, [ arg2P_4>0 && arg1P_3>0 && -2*x13_1+arg2P_4<2 && -2*x13_1+arg2P_4>=0 ], cost: 4 11: __init -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=x13_1*k, arg3'=-(-1+k)*x13_1-x13_1+arg2P_4, arg4'=arg2P_4, [ arg2P_4>0 && arg1P_3>0 && -2*x13_1+arg2P_4<2 && 1-x13_1<=0 && k>=1 && -(-1+k)*x13_1-2*x13_1+arg2P_4>=0 ], cost: 2+2*k 12: __init -> [4] : [ -1+x13_1<=-1 && 1<=1+2*x13_1 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: __init 11: __init -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=x13_1*k, arg3'=-(-1+k)*x13_1-x13_1+arg2P_4, arg4'=arg2P_4, [ arg2P_4>0 && arg1P_3>0 && -2*x13_1+arg2P_4<2 && 1-x13_1<=0 && k>=1 && -(-1+k)*x13_1-2*x13_1+arg2P_4>=0 ], cost: 2+2*k 12: __init -> [4] : [ -1+x13_1<=-1 && 1<=1+2*x13_1 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> f74_0_loop_LE : arg1'=arg1P_3, arg2'=x13_1*k, arg3'=-(-1+k)*x13_1-x13_1+arg2P_4, arg4'=arg2P_4, [ arg2P_4>0 && arg1P_3>0 && -2*x13_1+arg2P_4<2 && 1-x13_1<=0 && k>=1 && -(-1+k)*x13_1-2*x13_1+arg2P_4>=0 ], cost: 2+2*k 12: __init -> [4] : [ -1+x13_1<=-1 && 1<=1+2*x13_1 ], cost: NONTERM Computing asymptotic complexity for rule 12 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+x13_1<=-1 && 1<=1+2*x13_1 ] NO