NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l5 0: l0 -> l1 : a_19^0'=a_19^post_1, i_13^0'=i_13^post_1, i_20^0'=i_20^post_1, rt_11^0'=rt_11^post_1, st_14^0'=st_14^post_1, [ i_13^post_1==0 && 0<=i_13^post_1 && i_13^post_1<=0 && a_19^0==a_19^post_1 && i_20^0==i_20^post_1 && rt_11^0==rt_11^post_1 && st_14^0==st_14^post_1 ], cost: 1 2: l1 -> l3 : a_19^0'=a_19^post_3, i_13^0'=i_13^post_3, i_20^0'=i_20^post_3, rt_11^0'=rt_11^post_3, st_14^0'=st_14^post_3, [ 10<=i_13^0 && rt_11^post_3==st_14^0 && a_19^0==a_19^post_3 && i_13^0==i_13^post_3 && i_20^0==i_20^post_3 && st_14^0==st_14^post_3 ], cost: 1 3: l1 -> l4 : a_19^0'=a_19^post_4, i_13^0'=i_13^post_4, i_20^0'=i_20^post_4, rt_11^0'=rt_11^post_4, st_14^0'=st_14^post_4, [ i_20^post_4==i_20^post_4 && 1+i_13^0<=10 && i_13^post_4==-1+i_13^0 && i_13^post_4<=-1+i_20^post_4 && -1+i_20^post_4<=i_13^post_4 && 1+i_20^post_4<=10 && a_19^0==a_19^post_4 && rt_11^0==rt_11^post_4 && st_14^0==st_14^post_4 ], cost: 1 1: l2 -> l1 : a_19^0'=a_19^post_2, i_13^0'=i_13^post_2, i_20^0'=i_20^post_2, rt_11^0'=rt_11^post_2, st_14^0'=st_14^post_2, [ 1+i_13^0<=10 && i_13^1_1==-1+i_13^0 && i_13^post_2==i_13^post_2 && -1<=i_13^post_2 && i_13^post_2<=-1 && a_19^post_2==a_19^post_2 && a_19^post_2<=i_13^post_2 && i_13^post_2<=a_19^post_2 && i_20^0==i_20^post_2 && rt_11^0==rt_11^post_2 && st_14^0==st_14^post_2 ], cost: 1 4: l4 -> l1 : a_19^0'=a_19^post_5, i_13^0'=i_13^post_5, i_20^0'=i_20^post_5, rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, [ a_19^0==a_19^post_5 && i_13^0==i_13^post_5 && i_20^0==i_20^post_5 && rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 ], cost: 1 5: l5 -> l0 : a_19^0'=a_19^post_6, i_13^0'=i_13^post_6, i_20^0'=i_20^post_6, rt_11^0'=rt_11^post_6, st_14^0'=st_14^post_6, [ a_19^0==a_19^post_6 && i_13^0==i_13^post_6 && i_20^0==i_20^post_6 && rt_11^0==rt_11^post_6 && st_14^0==st_14^post_6 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 5: l5 -> l0 : a_19^0'=a_19^post_6, i_13^0'=i_13^post_6, i_20^0'=i_20^post_6, rt_11^0'=rt_11^post_6, st_14^0'=st_14^post_6, [ a_19^0==a_19^post_6 && i_13^0==i_13^post_6 && i_20^0==i_20^post_6 && rt_11^0==rt_11^post_6 && st_14^0==st_14^post_6 ], cost: 1 Removed unreachable and leaf rules: Start location: l5 0: l0 -> l1 : a_19^0'=a_19^post_1, i_13^0'=i_13^post_1, i_20^0'=i_20^post_1, rt_11^0'=rt_11^post_1, st_14^0'=st_14^post_1, [ i_13^post_1==0 && 0<=i_13^post_1 && i_13^post_1<=0 && a_19^0==a_19^post_1 && i_20^0==i_20^post_1 && rt_11^0==rt_11^post_1 && st_14^0==st_14^post_1 ], cost: 1 3: l1 -> l4 : a_19^0'=a_19^post_4, i_13^0'=i_13^post_4, i_20^0'=i_20^post_4, rt_11^0'=rt_11^post_4, st_14^0'=st_14^post_4, [ i_20^post_4==i_20^post_4 && 1+i_13^0<=10 && i_13^post_4==-1+i_13^0 && i_13^post_4<=-1+i_20^post_4 && -1+i_20^post_4<=i_13^post_4 && 1+i_20^post_4<=10 && a_19^0==a_19^post_4 && rt_11^0==rt_11^post_4 && st_14^0==st_14^post_4 ], cost: 1 4: l4 -> l1 : a_19^0'=a_19^post_5, i_13^0'=i_13^post_5, i_20^0'=i_20^post_5, rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, [ a_19^0==a_19^post_5 && i_13^0==i_13^post_5 && i_20^0==i_20^post_5 && rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 ], cost: 1 5: l5 -> l0 : a_19^0'=a_19^post_6, i_13^0'=i_13^post_6, i_20^0'=i_20^post_6, rt_11^0'=rt_11^post_6, st_14^0'=st_14^post_6, [ a_19^0==a_19^post_6 && i_13^0==i_13^post_6 && i_20^0==i_20^post_6 && rt_11^0==rt_11^post_6 && st_14^0==st_14^post_6 ], cost: 1 Simplified all rules, resulting in: Start location: l5 0: l0 -> l1 : i_13^0'=0, [], cost: 1 3: l1 -> l4 : i_13^0'=-1+i_13^0, i_20^0'=i_13^0, [ 1+i_13^0<=10 ], cost: 1 4: l4 -> l1 : [], cost: 1 5: l5 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l5 7: l1 -> l1 : i_13^0'=-1+i_13^0, i_20^0'=i_13^0, [ 1+i_13^0<=10 ], cost: 2 6: l5 -> l1 : i_13^0'=0, [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 7: l1 -> l1 : i_13^0'=-1+i_13^0, i_20^0'=i_13^0, [ 1+i_13^0<=10 ], cost: 2 Accelerated rule 7 with non-termination, yielding the new rule 8. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 7. Accelerated all simple loops using metering functions (where possible): Start location: l5 8: l1 -> [6] : [ 1+i_13^0<=10 ], cost: NONTERM 6: l5 -> l1 : i_13^0'=0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l5 6: l5 -> l1 : i_13^0'=0, [], cost: 2 9: l5 -> [6] : [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l5 9: l5 -> [6] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l5 9: l5 -> [6] : [], cost: NONTERM Computing asymptotic complexity for rule 9 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