NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l6 0: l0 -> l1 : Result_4^0'=Result_4^post_1, ___cil_tmp2_10^0'=___cil_tmp2_10^post_1, ___cil_tmp4_8^0'=___cil_tmp4_8^post_1, ___retres1_9^0'=___retres1_9^post_1, ___retres3_7^0'=___retres3_7^post_1, d_6^0'=d_6^post_1, i_5^0'=i_5^post_1, [ Result_4^0==Result_4^post_1 && ___cil_tmp2_10^0==___cil_tmp2_10^post_1 && ___cil_tmp4_8^0==___cil_tmp4_8^post_1 && ___retres1_9^0==___retres1_9^post_1 && ___retres3_7^0==___retres3_7^post_1 && d_6^0==d_6^post_1 && i_5^0==i_5^post_1 ], cost: 1 4: l1 -> l3 : Result_4^0'=Result_4^post_5, ___cil_tmp2_10^0'=___cil_tmp2_10^post_5, ___cil_tmp4_8^0'=___cil_tmp4_8^post_5, ___retres1_9^0'=___retres1_9^post_5, ___retres3_7^0'=___retres3_7^post_5, d_6^0'=d_6^post_5, i_5^0'=i_5^post_5, [ -d_6^0<=0 && ___retres3_7^post_5==0 && ___cil_tmp4_8^post_5==___retres3_7^post_5 && Result_4^post_5==___cil_tmp4_8^post_5 && ___cil_tmp2_10^0==___cil_tmp2_10^post_5 && ___retres1_9^0==___retres1_9^post_5 && d_6^0==d_6^post_5 && i_5^0==i_5^post_5 ], cost: 1 5: l1 -> l2 : Result_4^0'=Result_4^post_6, ___cil_tmp2_10^0'=___cil_tmp2_10^post_6, ___cil_tmp4_8^0'=___cil_tmp4_8^post_6, ___retres1_9^0'=___retres1_9^post_6, ___retres3_7^0'=___retres3_7^post_6, d_6^0'=d_6^post_6, i_5^0'=i_5^post_6, [ 0<=-1-d_6^0 && Result_4^0==Result_4^post_6 && ___cil_tmp2_10^0==___cil_tmp2_10^post_6 && ___cil_tmp4_8^0==___cil_tmp4_8^post_6 && ___retres1_9^0==___retres1_9^post_6 && ___retres3_7^0==___retres3_7^post_6 && d_6^0==d_6^post_6 && i_5^0==i_5^post_6 ], cost: 1 1: l2 -> l3 : Result_4^0'=Result_4^post_2, ___cil_tmp2_10^0'=___cil_tmp2_10^post_2, ___cil_tmp4_8^0'=___cil_tmp4_8^post_2, ___retres1_9^0'=___retres1_9^post_2, ___retres3_7^0'=___retres3_7^post_2, d_6^0'=d_6^post_2, i_5^0'=i_5^post_2, [ 1+i_5^0<=0 && ___retres3_7^post_2==0 && ___cil_tmp4_8^post_2==___retres3_7^post_2 && Result_4^post_2==___cil_tmp4_8^post_2 && ___cil_tmp2_10^0==___cil_tmp2_10^post_2 && ___retres1_9^0==___retres1_9^post_2 && d_6^0==d_6^post_2 && i_5^0==i_5^post_2 ], cost: 1 2: l2 -> l4 : Result_4^0'=Result_4^post_3, ___cil_tmp2_10^0'=___cil_tmp2_10^post_3, ___cil_tmp4_8^0'=___cil_tmp4_8^post_3, ___retres1_9^0'=___retres1_9^post_3, ___retres3_7^0'=___retres3_7^post_3, d_6^0'=d_6^post_3, i_5^0'=i_5^post_3, [ 0<=i_5^0 && i_5^post_3==-d_6^0+i_5^0 && Result_4^0==Result_4^post_3 && ___cil_tmp2_10^0==___cil_tmp2_10^post_3 && ___cil_tmp4_8^0==___cil_tmp4_8^post_3 && ___retres1_9^0==___retres1_9^post_3 && ___retres3_7^0==___retres3_7^post_3 && d_6^0==d_6^post_3 ], cost: 1 6: l3 -> l5 : Result_4^0'=Result_4^post_7, ___cil_tmp2_10^0'=___cil_tmp2_10^post_7, ___cil_tmp4_8^0'=___cil_tmp4_8^post_7, ___retres1_9^0'=___retres1_9^post_7, ___retres3_7^0'=___retres3_7^post_7, d_6^0'=d_6^post_7, i_5^0'=i_5^post_7, [ ___retres1_9^post_7==0 && ___cil_tmp2_10^post_7==___retres1_9^post_7 && Result_4^post_7==___cil_tmp2_10^post_7 && ___cil_tmp4_8^0==___cil_tmp4_8^post_7 && ___retres3_7^0==___retres3_7^post_7 && d_6^0==d_6^post_7 && i_5^0==i_5^post_7 ], cost: 1 3: l4 -> l2 : Result_4^0'=Result_4^post_4, ___cil_tmp2_10^0'=___cil_tmp2_10^post_4, ___cil_tmp4_8^0'=___cil_tmp4_8^post_4, ___retres1_9^0'=___retres1_9^post_4, ___retres3_7^0'=___retres3_7^post_4, d_6^0'=d_6^post_4, i_5^0'=i_5^post_4, [ Result_4^0==Result_4^post_4 && ___cil_tmp2_10^0==___cil_tmp2_10^post_4 && ___cil_tmp4_8^0==___cil_tmp4_8^post_4 && ___retres1_9^0==___retres1_9^post_4 && ___retres3_7^0==___retres3_7^post_4 && d_6^0==d_6^post_4 && i_5^0==i_5^post_4 ], cost: 1 7: l6 -> l0 : Result_4^0'=Result_4^post_8, ___cil_tmp2_10^0'=___cil_tmp2_10^post_8, ___cil_tmp4_8^0'=___cil_tmp4_8^post_8, ___retres1_9^0'=___retres1_9^post_8, ___retres3_7^0'=___retres3_7^post_8, d_6^0'=d_6^post_8, i_5^0'=i_5^post_8, [ Result_4^0==Result_4^post_8 && ___cil_tmp2_10^0==___cil_tmp2_10^post_8 && ___cil_tmp4_8^0==___cil_tmp4_8^post_8 && ___retres1_9^0==___retres1_9^post_8 && ___retres3_7^0==___retres3_7^post_8 && d_6^0==d_6^post_8 && i_5^0==i_5^post_8 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: l6 -> l0 : Result_4^0'=Result_4^post_8, ___cil_tmp2_10^0'=___cil_tmp2_10^post_8, ___cil_tmp4_8^0'=___cil_tmp4_8^post_8, ___retres1_9^0'=___retres1_9^post_8, ___retres3_7^0'=___retres3_7^post_8, d_6^0'=d_6^post_8, i_5^0'=i_5^post_8, [ Result_4^0==Result_4^post_8 && ___cil_tmp2_10^0==___cil_tmp2_10^post_8 && ___cil_tmp4_8^0==___cil_tmp4_8^post_8 && ___retres1_9^0==___retres1_9^post_8 && ___retres3_7^0==___retres3_7^post_8 && d_6^0==d_6^post_8 && i_5^0==i_5^post_8 ], cost: 1 Removed unreachable and leaf rules: Start location: l6 0: l0 -> l1 : Result_4^0'=Result_4^post_1, ___cil_tmp2_10^0'=___cil_tmp2_10^post_1, ___cil_tmp4_8^0'=___cil_tmp4_8^post_1, ___retres1_9^0'=___retres1_9^post_1, ___retres3_7^0'=___retres3_7^post_1, d_6^0'=d_6^post_1, i_5^0'=i_5^post_1, [ Result_4^0==Result_4^post_1 && ___cil_tmp2_10^0==___cil_tmp2_10^post_1 && ___cil_tmp4_8^0==___cil_tmp4_8^post_1 && ___retres1_9^0==___retres1_9^post_1 && ___retres3_7^0==___retres3_7^post_1 && d_6^0==d_6^post_1 && i_5^0==i_5^post_1 ], cost: 1 5: l1 -> l2 : Result_4^0'=Result_4^post_6, ___cil_tmp2_10^0'=___cil_tmp2_10^post_6, ___cil_tmp4_8^0'=___cil_tmp4_8^post_6, ___retres1_9^0'=___retres1_9^post_6, ___retres3_7^0'=___retres3_7^post_6, d_6^0'=d_6^post_6, i_5^0'=i_5^post_6, [ 0<=-1-d_6^0 && Result_4^0==Result_4^post_6 && ___cil_tmp2_10^0==___cil_tmp2_10^post_6 && ___cil_tmp4_8^0==___cil_tmp4_8^post_6 && ___retres1_9^0==___retres1_9^post_6 && ___retres3_7^0==___retres3_7^post_6 && d_6^0==d_6^post_6 && i_5^0==i_5^post_6 ], cost: 1 2: l2 -> l4 : Result_4^0'=Result_4^post_3, ___cil_tmp2_10^0'=___cil_tmp2_10^post_3, ___cil_tmp4_8^0'=___cil_tmp4_8^post_3, ___retres1_9^0'=___retres1_9^post_3, ___retres3_7^0'=___retres3_7^post_3, d_6^0'=d_6^post_3, i_5^0'=i_5^post_3, [ 0<=i_5^0 && i_5^post_3==-d_6^0+i_5^0 && Result_4^0==Result_4^post_3 && ___cil_tmp2_10^0==___cil_tmp2_10^post_3 && ___cil_tmp4_8^0==___cil_tmp4_8^post_3 && ___retres1_9^0==___retres1_9^post_3 && ___retres3_7^0==___retres3_7^post_3 && d_6^0==d_6^post_3 ], cost: 1 3: l4 -> l2 : Result_4^0'=Result_4^post_4, ___cil_tmp2_10^0'=___cil_tmp2_10^post_4, ___cil_tmp4_8^0'=___cil_tmp4_8^post_4, ___retres1_9^0'=___retres1_9^post_4, ___retres3_7^0'=___retres3_7^post_4, d_6^0'=d_6^post_4, i_5^0'=i_5^post_4, [ Result_4^0==Result_4^post_4 && ___cil_tmp2_10^0==___cil_tmp2_10^post_4 && ___cil_tmp4_8^0==___cil_tmp4_8^post_4 && ___retres1_9^0==___retres1_9^post_4 && ___retres3_7^0==___retres3_7^post_4 && d_6^0==d_6^post_4 && i_5^0==i_5^post_4 ], cost: 1 7: l6 -> l0 : Result_4^0'=Result_4^post_8, ___cil_tmp2_10^0'=___cil_tmp2_10^post_8, ___cil_tmp4_8^0'=___cil_tmp4_8^post_8, ___retres1_9^0'=___retres1_9^post_8, ___retres3_7^0'=___retres3_7^post_8, d_6^0'=d_6^post_8, i_5^0'=i_5^post_8, [ Result_4^0==Result_4^post_8 && ___cil_tmp2_10^0==___cil_tmp2_10^post_8 && ___cil_tmp4_8^0==___cil_tmp4_8^post_8 && ___retres1_9^0==___retres1_9^post_8 && ___retres3_7^0==___retres3_7^post_8 && d_6^0==d_6^post_8 && i_5^0==i_5^post_8 ], cost: 1 Simplified all rules, resulting in: Start location: l6 0: l0 -> l1 : [], cost: 1 5: l1 -> l2 : [ 0<=-1-d_6^0 ], cost: 1 2: l2 -> l4 : i_5^0'=-d_6^0+i_5^0, [ 0<=i_5^0 ], cost: 1 3: l4 -> l2 : [], cost: 1 7: l6 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l6 10: l2 -> l2 : i_5^0'=-d_6^0+i_5^0, [ 0<=i_5^0 ], cost: 2 9: l6 -> l2 : [ 0<=-1-d_6^0 ], cost: 3 Accelerating simple loops of location 2. Accelerating the following rules: 10: l2 -> l2 : i_5^0'=-d_6^0+i_5^0, [ 0<=i_5^0 ], cost: 2 [test] deduced invariant d_6^0<=0 Accelerated rule 10 with non-termination, yielding the new rule 11. Accelerated rule 10 with non-termination, yielding the new rule 12. Accelerated rule 10 with backward acceleration, yielding the new rule 13. [accelerate] Nesting with 0 inner and 1 outer candidates Also removing duplicate rules: 12. Accelerated all simple loops using metering functions (where possible): Start location: l6 10: l2 -> l2 : i_5^0'=-d_6^0+i_5^0, [ 0<=i_5^0 ], cost: 2 11: l2 -> [7] : [ d_6^0==0 && i_5^0==0 ], cost: NONTERM 13: l2 -> [7] : [ 0<=i_5^0 && d_6^0<=0 ], cost: NONTERM 9: l6 -> l2 : [ 0<=-1-d_6^0 ], cost: 3 Chained accelerated rules (with incoming rules): Start location: l6 9: l6 -> l2 : [ 0<=-1-d_6^0 ], cost: 3 14: l6 -> l2 : i_5^0'=-d_6^0+i_5^0, [ 0<=-1-d_6^0 && 0<=i_5^0 ], cost: 5 15: l6 -> [7] : [ 0<=-1-d_6^0 && 0<=i_5^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l6 15: l6 -> [7] : [ 0<=-1-d_6^0 && 0<=i_5^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l6 15: l6 -> [7] : [ 0<=-1-d_6^0 && 0<=i_5^0 ], cost: NONTERM Computing asymptotic complexity for rule 15 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: [ 0<=-1-d_6^0 && 0<=i_5^0 ] NO