NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f98_0_loop_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>-3 && arg1<1 && arg1<0 && 2+arg1==arg1P_2 ], cost: 1 2: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>0 && arg1<3 && -2+arg1==arg1P_3 ], cost: 1 3: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>2 && -arg1<-1 && 2-arg1==arg1P_4 ], cost: 1 4: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<-1 && arg1<0 && arg1<-2 && 3<=-arg1 && arg1<1 && -2-arg1==arg1P_5 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f98_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=2+arg1, arg2'=arg2P_2, [ arg1>-3 && arg1<0 ], cost: 1 2: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=-2+arg1, arg2'=arg2P_3, [ arg1>0 && arg1<3 ], cost: 1 3: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=2-arg1, arg2'=arg2P_4, [ arg1>2 ], cost: 1 4: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=-2-arg1, arg2'=arg2P_5, [ arg1<-2 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=2+arg1, arg2'=arg2P_2, [ arg1>-3 && arg1<0 ], cost: 1 2: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=-2+arg1, arg2'=arg2P_3, [ arg1>0 && arg1<3 ], cost: 1 3: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=2-arg1, arg2'=arg2P_4, [ arg1>2 ], cost: 1 4: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=-2-arg1, arg2'=arg2P_5, [ arg1<-2 ], cost: 1 Failed to prove monotonicity of the guard of rule 1. Failed to prove monotonicity of the guard of rule 2. Failed to prove monotonicity of the guard of rule 3. Failed to prove monotonicity of the guard of rule 4. [accelerate] Nesting with 4 inner and 4 outer candidates Nested simple loops 2 (outer loop) and 1 (inner loop) with Rule(1 | 1+arg1==0, | NONTERM || 3 | ), resulting in the new rules: 6, 7. Nested simple loops 1 (outer loop) and 2 (inner loop) with Rule(1 | 1-arg1==0, | NONTERM || 3 | ), resulting in the new rules: 8, 9. Nested simple loops 4 (outer loop) and 3 (inner loop) with Rule(1 | k>=1, -2+4*k-arg1<-2, | 2*k || 1 | 0=-4*k+arg1, 1=arg2P_5, ), resulting in the new rules: 10, 11. Nested simple loops 3 (outer loop) and 4 (inner loop) with Rule(1 | k_1>=1, 2-arg1-4*k_1>2, | 2*k_1 || 1 | 0=arg1+4*k_1, 1=arg2P_4, ), resulting in the new rules: 12, 13. Removing the simple loops: 1 2 3 4. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f98_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 6: f98_0_loop_EQ -> [3] : [ 1+arg1==0 ], cost: NONTERM 7: f98_0_loop_EQ -> [3] : [ -1+arg1==0 ], cost: NONTERM 8: f98_0_loop_EQ -> [3] : [ 1-arg1==0 ], cost: NONTERM 9: f98_0_loop_EQ -> [3] : [ -1-arg1==0 ], cost: NONTERM 10: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=-4*k+arg1, arg2'=arg2P_5, [ k>=1 && -2+4*k-arg1<-2 ], cost: 2*k 11: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=-2-4*k-arg1, arg2'=arg2P_5, [ arg1<-2 && k>=1 && 4*k+arg1<-2 ], cost: 1+2*k 12: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=arg1+4*k_1, arg2'=arg2P_4, [ k_1>=1 && 2-arg1-4*k_1>2 ], cost: 2*k_1 13: f98_0_loop_EQ -> f98_0_loop_EQ : arg1'=2-arg1+4*k_1, arg2'=arg2P_4, [ arg1>2 && k_1>=1 && arg1-4*k_1>2 ], cost: 1+2*k_1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f98_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 14: f1_0_main_Load -> [3] : [ arg1>0 && -1+arg2==0 ], cost: NONTERM 15: f1_0_main_Load -> [3] : [ arg1>0 && 1-arg2==0 ], cost: NONTERM 16: f1_0_main_Load -> f98_0_loop_EQ : arg1'=arg2-4*k, arg2'=arg2P_5, [ arg1>0 && arg2>-1 && k>=1 && -2-arg2+4*k<-2 ], cost: 1+2*k 17: f1_0_main_Load -> f98_0_loop_EQ : arg1'=2-arg2+4*k_1, arg2'=arg2P_4, [ arg1>0 && arg2>2 && k_1>=1 && arg2-4*k_1>2 ], cost: 2+2*k_1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 14: f1_0_main_Load -> [3] : [ arg1>0 && -1+arg2==0 ], cost: NONTERM 15: f1_0_main_Load -> [3] : [ arg1>0 && 1-arg2==0 ], cost: NONTERM 16: f1_0_main_Load -> f98_0_loop_EQ : arg1'=arg2-4*k, arg2'=arg2P_5, [ arg1>0 && arg2>-1 && k>=1 && -2-arg2+4*k<-2 ], cost: 1+2*k 17: f1_0_main_Load -> f98_0_loop_EQ : arg1'=2-arg2+4*k_1, arg2'=arg2P_4, [ arg1>0 && arg2>2 && k_1>=1 && arg2-4*k_1>2 ], cost: 2+2*k_1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 18: __init -> [3] : [ arg1P_6>0 && -1+arg2P_6==0 ], cost: NONTERM 19: __init -> [3] : [ arg1P_6>0 && 1-arg2P_6==0 ], cost: NONTERM 20: __init -> f98_0_loop_EQ : arg1'=arg2P_6-4*k, arg2'=arg2P_5, [ arg1P_6>0 && arg2P_6>-1 && k>=1 && -2-arg2P_6+4*k<-2 ], cost: 2+2*k 21: __init -> f98_0_loop_EQ : arg1'=2-arg2P_6+4*k_1, arg2'=arg2P_4, [ arg1P_6>0 && arg2P_6>2 && k_1>=1 && arg2P_6-4*k_1>2 ], cost: 3+2*k_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 18: __init -> [3] : [ arg1P_6>0 && -1+arg2P_6==0 ], cost: NONTERM 19: __init -> [3] : [ arg1P_6>0 && 1-arg2P_6==0 ], cost: NONTERM 20: __init -> f98_0_loop_EQ : arg1'=arg2P_6-4*k, arg2'=arg2P_5, [ arg1P_6>0 && arg2P_6>-1 && k>=1 && -2-arg2P_6+4*k<-2 ], cost: 2+2*k 21: __init -> f98_0_loop_EQ : arg1'=2-arg2P_6+4*k_1, arg2'=arg2P_4, [ arg1P_6>0 && arg2P_6>2 && k_1>=1 && arg2P_6-4*k_1>2 ], cost: 3+2*k_1 Computing asymptotic complexity for rule 18 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: [ arg1P_6>0 && -1+arg2P_6==0 ] NO