NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l4 0: l0 -> l1 : Result_4^0'=Result_4^post_1, cnt_29^0'=cnt_29^post_1, lt_10^0'=lt_10^post_1, lt_11^0'=lt_11^post_1, lt_12^0'=lt_12^post_1, px_8^0'=px_8^post_1, py_6^0'=py_6^post_1, q_9^0'=q_9^post_1, x_7^0'=x_7^post_1, y_5^0'=y_5^post_1, [ lt_11^1_1==x_7^0 && lt_12^1_1==cnt_29^0 && 0<=-1+lt_12^1_1 && lt_11^post_1==lt_11^post_1 && lt_12^post_1==lt_12^post_1 && lt_10^1_1==cnt_29^0 && lt_10^post_1==lt_10^post_1 && Result_4^0==Result_4^post_1 && cnt_29^0==cnt_29^post_1 && px_8^0==px_8^post_1 && py_6^0==py_6^post_1 && q_9^0==q_9^post_1 && x_7^0==x_7^post_1 && y_5^0==y_5^post_1 ], cost: 1 2: l0 -> l2 : Result_4^0'=Result_4^post_3, cnt_29^0'=cnt_29^post_3, lt_10^0'=lt_10^post_3, lt_11^0'=lt_11^post_3, lt_12^0'=lt_12^post_3, px_8^0'=px_8^post_3, py_6^0'=py_6^post_3, q_9^0'=q_9^post_3, x_7^0'=x_7^post_3, y_5^0'=y_5^post_3, [ lt_11^1_2==x_7^0 && lt_12^1_2_1==cnt_29^0 && lt_12^1_2_1<=0 && lt_11^post_3==lt_11^post_3 && lt_12^post_3==lt_12^post_3 && Result_4^post_3==Result_4^post_3 && cnt_29^0==cnt_29^post_3 && lt_10^0==lt_10^post_3 && px_8^0==px_8^post_3 && py_6^0==py_6^post_3 && q_9^0==q_9^post_3 && x_7^0==x_7^post_3 && y_5^0==y_5^post_3 ], cost: 1 1: l1 -> l0 : Result_4^0'=Result_4^post_2, cnt_29^0'=cnt_29^post_2, lt_10^0'=lt_10^post_2, lt_11^0'=lt_11^post_2, lt_12^0'=lt_12^post_2, px_8^0'=px_8^post_2, py_6^0'=py_6^post_2, q_9^0'=q_9^post_2, x_7^0'=x_7^post_2, y_5^0'=y_5^post_2, [ Result_4^0==Result_4^post_2 && cnt_29^0==cnt_29^post_2 && lt_10^0==lt_10^post_2 && lt_11^0==lt_11^post_2 && lt_12^0==lt_12^post_2 && px_8^0==px_8^post_2 && py_6^0==py_6^post_2 && q_9^0==q_9^post_2 && x_7^0==x_7^post_2 && y_5^0==y_5^post_2 ], cost: 1 3: l3 -> l0 : Result_4^0'=Result_4^post_4, cnt_29^0'=cnt_29^post_4, lt_10^0'=lt_10^post_4, lt_11^0'=lt_11^post_4, lt_12^0'=lt_12^post_4, px_8^0'=px_8^post_4, py_6^0'=py_6^post_4, q_9^0'=q_9^post_4, x_7^0'=x_7^post_4, y_5^0'=y_5^post_4, [ px_8^post_4==px_8^post_4 && x_7^post_4==x_7^post_4 && y_5^post_4==y_5^post_4 && py_6^post_4==y_5^post_4 && q_9^post_4==px_8^post_4 && Result_4^0==Result_4^post_4 && cnt_29^0==cnt_29^post_4 && lt_10^0==lt_10^post_4 && lt_11^0==lt_11^post_4 && lt_12^0==lt_12^post_4 ], cost: 1 4: l4 -> l3 : Result_4^0'=Result_4^post_5, cnt_29^0'=cnt_29^post_5, lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_12^0'=lt_12^post_5, px_8^0'=px_8^post_5, py_6^0'=py_6^post_5, q_9^0'=q_9^post_5, x_7^0'=x_7^post_5, y_5^0'=y_5^post_5, [ Result_4^0==Result_4^post_5 && cnt_29^0==cnt_29^post_5 && lt_10^0==lt_10^post_5 && lt_11^0==lt_11^post_5 && lt_12^0==lt_12^post_5 && px_8^0==px_8^post_5 && py_6^0==py_6^post_5 && q_9^0==q_9^post_5 && x_7^0==x_7^post_5 && y_5^0==y_5^post_5 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: l4 -> l3 : Result_4^0'=Result_4^post_5, cnt_29^0'=cnt_29^post_5, lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_12^0'=lt_12^post_5, px_8^0'=px_8^post_5, py_6^0'=py_6^post_5, q_9^0'=q_9^post_5, x_7^0'=x_7^post_5, y_5^0'=y_5^post_5, [ Result_4^0==Result_4^post_5 && cnt_29^0==cnt_29^post_5 && lt_10^0==lt_10^post_5 && lt_11^0==lt_11^post_5 && lt_12^0==lt_12^post_5 && px_8^0==px_8^post_5 && py_6^0==py_6^post_5 && q_9^0==q_9^post_5 && x_7^0==x_7^post_5 && y_5^0==y_5^post_5 ], cost: 1 Removed unreachable and leaf rules: Start location: l4 0: l0 -> l1 : Result_4^0'=Result_4^post_1, cnt_29^0'=cnt_29^post_1, lt_10^0'=lt_10^post_1, lt_11^0'=lt_11^post_1, lt_12^0'=lt_12^post_1, px_8^0'=px_8^post_1, py_6^0'=py_6^post_1, q_9^0'=q_9^post_1, x_7^0'=x_7^post_1, y_5^0'=y_5^post_1, [ lt_11^1_1==x_7^0 && lt_12^1_1==cnt_29^0 && 0<=-1+lt_12^1_1 && lt_11^post_1==lt_11^post_1 && lt_12^post_1==lt_12^post_1 && lt_10^1_1==cnt_29^0 && lt_10^post_1==lt_10^post_1 && Result_4^0==Result_4^post_1 && cnt_29^0==cnt_29^post_1 && px_8^0==px_8^post_1 && py_6^0==py_6^post_1 && q_9^0==q_9^post_1 && x_7^0==x_7^post_1 && y_5^0==y_5^post_1 ], cost: 1 1: l1 -> l0 : Result_4^0'=Result_4^post_2, cnt_29^0'=cnt_29^post_2, lt_10^0'=lt_10^post_2, lt_11^0'=lt_11^post_2, lt_12^0'=lt_12^post_2, px_8^0'=px_8^post_2, py_6^0'=py_6^post_2, q_9^0'=q_9^post_2, x_7^0'=x_7^post_2, y_5^0'=y_5^post_2, [ Result_4^0==Result_4^post_2 && cnt_29^0==cnt_29^post_2 && lt_10^0==lt_10^post_2 && lt_11^0==lt_11^post_2 && lt_12^0==lt_12^post_2 && px_8^0==px_8^post_2 && py_6^0==py_6^post_2 && q_9^0==q_9^post_2 && x_7^0==x_7^post_2 && y_5^0==y_5^post_2 ], cost: 1 3: l3 -> l0 : Result_4^0'=Result_4^post_4, cnt_29^0'=cnt_29^post_4, lt_10^0'=lt_10^post_4, lt_11^0'=lt_11^post_4, lt_12^0'=lt_12^post_4, px_8^0'=px_8^post_4, py_6^0'=py_6^post_4, q_9^0'=q_9^post_4, x_7^0'=x_7^post_4, y_5^0'=y_5^post_4, [ px_8^post_4==px_8^post_4 && x_7^post_4==x_7^post_4 && y_5^post_4==y_5^post_4 && py_6^post_4==y_5^post_4 && q_9^post_4==px_8^post_4 && Result_4^0==Result_4^post_4 && cnt_29^0==cnt_29^post_4 && lt_10^0==lt_10^post_4 && lt_11^0==lt_11^post_4 && lt_12^0==lt_12^post_4 ], cost: 1 4: l4 -> l3 : Result_4^0'=Result_4^post_5, cnt_29^0'=cnt_29^post_5, lt_10^0'=lt_10^post_5, lt_11^0'=lt_11^post_5, lt_12^0'=lt_12^post_5, px_8^0'=px_8^post_5, py_6^0'=py_6^post_5, q_9^0'=q_9^post_5, x_7^0'=x_7^post_5, y_5^0'=y_5^post_5, [ Result_4^0==Result_4^post_5 && cnt_29^0==cnt_29^post_5 && lt_10^0==lt_10^post_5 && lt_11^0==lt_11^post_5 && lt_12^0==lt_12^post_5 && px_8^0==px_8^post_5 && py_6^0==py_6^post_5 && q_9^0==q_9^post_5 && x_7^0==x_7^post_5 && y_5^0==y_5^post_5 ], cost: 1 Simplified all rules, resulting in: Start location: l4 0: l0 -> l1 : lt_10^0'=lt_10^post_1, lt_11^0'=lt_11^post_1, lt_12^0'=lt_12^post_1, [ 0<=-1+cnt_29^0 ], cost: 1 1: l1 -> l0 : [], cost: 1 3: l3 -> l0 : px_8^0'=px_8^post_4, py_6^0'=py_6^post_4, q_9^0'=px_8^post_4, x_7^0'=x_7^post_4, y_5^0'=py_6^post_4, [], cost: 1 4: l4 -> l3 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l4 6: l0 -> l0 : lt_10^0'=lt_10^post_1, lt_11^0'=lt_11^post_1, lt_12^0'=lt_12^post_1, [ 0<=-1+cnt_29^0 ], cost: 2 5: l4 -> l0 : px_8^0'=px_8^post_4, py_6^0'=py_6^post_4, q_9^0'=px_8^post_4, x_7^0'=x_7^post_4, y_5^0'=py_6^post_4, [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 6: l0 -> l0 : lt_10^0'=lt_10^post_1, lt_11^0'=lt_11^post_1, lt_12^0'=lt_12^post_1, [ 0<=-1+cnt_29^0 ], cost: 2 Accelerated rule 6 with non-termination, yielding the new rule 7. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 6. Accelerated all simple loops using metering functions (where possible): Start location: l4 7: l0 -> [5] : [ 0<=-1+cnt_29^0 ], cost: NONTERM 5: l4 -> l0 : px_8^0'=px_8^post_4, py_6^0'=py_6^post_4, q_9^0'=px_8^post_4, x_7^0'=x_7^post_4, y_5^0'=py_6^post_4, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l4 5: l4 -> l0 : px_8^0'=px_8^post_4, py_6^0'=py_6^post_4, q_9^0'=px_8^post_4, x_7^0'=x_7^post_4, y_5^0'=py_6^post_4, [], cost: 2 8: l4 -> [5] : [ 0<=-1+cnt_29^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l4 8: l4 -> [5] : [ 0<=-1+cnt_29^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l4 8: l4 -> [5] : [ 0<=-1+cnt_29^0 ], 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: [ 0<=-1+cnt_29^0 ] NO