NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l3 0: l0 -> l1 : elem_13^0'=elem_13^post_1, l_11^0'=l_11^post_1, len_98^0'=len_98^post_1, x_12^0'=x_12^post_1, [ 1<=1+len_98^0 && 1<=len_98^0 && len_98^1_1==len_98^1_1 && elem_13^post_1==l_11^0 && 1<=1+len_98^1_1 && 1<=len_98^1_1 && len_98^post_1==len_98^post_1 && 0<=-elem_13^post_1 && -elem_13^post_1<=0 && l_11^post_1==x_12^0 && x_12^0==x_12^post_1 ], cost: 1 1: l1 -> l0 : elem_13^0'=elem_13^post_2, l_11^0'=l_11^post_2, len_98^0'=len_98^post_2, x_12^0'=x_12^post_2, [ elem_13^0==elem_13^post_2 && l_11^0==l_11^post_2 && len_98^0==len_98^post_2 && x_12^0==x_12^post_2 ], cost: 1 2: l2 -> l0 : elem_13^0'=elem_13^post_3, l_11^0'=l_11^post_3, len_98^0'=len_98^post_3, x_12^0'=x_12^post_3, [ elem_13^0==elem_13^post_3 && l_11^0==l_11^post_3 && len_98^0==len_98^post_3 && x_12^0==x_12^post_3 ], cost: 1 3: l3 -> l2 : elem_13^0'=elem_13^post_4, l_11^0'=l_11^post_4, len_98^0'=len_98^post_4, x_12^0'=x_12^post_4, [ elem_13^0==elem_13^post_4 && l_11^0==l_11^post_4 && len_98^0==len_98^post_4 && x_12^0==x_12^post_4 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: l3 -> l2 : elem_13^0'=elem_13^post_4, l_11^0'=l_11^post_4, len_98^0'=len_98^post_4, x_12^0'=x_12^post_4, [ elem_13^0==elem_13^post_4 && l_11^0==l_11^post_4 && len_98^0==len_98^post_4 && x_12^0==x_12^post_4 ], cost: 1 Simplified all rules, resulting in: Start location: l3 0: l0 -> l1 : elem_13^0'=l_11^0, l_11^0'=x_12^0, len_98^0'=len_98^post_1, [ 1<=len_98^0 && l_11^0==0 ], cost: 1 1: l1 -> l0 : [], cost: 1 2: l2 -> l0 : [], cost: 1 3: l3 -> l2 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l3 5: l0 -> l0 : elem_13^0'=l_11^0, l_11^0'=x_12^0, len_98^0'=len_98^post_1, [ 1<=len_98^0 && l_11^0==0 ], cost: 2 4: l3 -> l0 : [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 5: l0 -> l0 : elem_13^0'=l_11^0, l_11^0'=x_12^0, len_98^0'=len_98^post_1, [ 1<=len_98^0 && l_11^0==0 ], cost: 2 Accelerated rule 5 with non-termination, yielding the new rule 6. [accelerate] Nesting with 0 inner and 1 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: l3 5: l0 -> l0 : elem_13^0'=l_11^0, l_11^0'=x_12^0, len_98^0'=len_98^post_1, [ 1<=len_98^0 && l_11^0==0 ], cost: 2 6: l0 -> [4] : [ 1<=len_98^0 && l_11^0==0 && 1<=len_98^post_1 && x_12^0==0 ], cost: NONTERM 4: l3 -> l0 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l3 4: l3 -> l0 : [], cost: 2 7: l3 -> l0 : elem_13^0'=l_11^0, l_11^0'=x_12^0, len_98^0'=len_98^post_1, [ 1<=len_98^0 && l_11^0==0 ], cost: 4 8: l3 -> [4] : [ 1<=len_98^0 && l_11^0==0 && x_12^0==0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l3 8: l3 -> [4] : [ 1<=len_98^0 && l_11^0==0 && x_12^0==0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l3 8: l3 -> [4] : [ 1<=len_98^0 && l_11^0==0 && x_12^0==0 ], cost: NONTERM Computing asymptotic complexity for rule 8 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<=len_98^0 && l_11^0==0 && x_12^0==0 ] NO