NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l4 0: l0 -> l1 : Result_4^0'=Result_4^post_1, cnt_15^0'=cnt_15^post_1, cnt_20^0'=cnt_20^post_1, lt_7^0'=lt_7^post_1, lt_8^0'=lt_8^post_1, lt_9^0'=lt_9^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ y_6^post_1==y_6^post_1 && x_5^post_1==x_5^post_1 && Result_4^0==Result_4^post_1 && cnt_15^0==cnt_15^post_1 && cnt_20^0==cnt_20^post_1 && lt_7^0==lt_7^post_1 && lt_8^0==lt_8^post_1 && lt_9^0==lt_9^post_1 ], cost: 1 1: l1 -> l2 : Result_4^0'=Result_4^post_2, cnt_15^0'=cnt_15^post_2, cnt_20^0'=cnt_20^post_2, lt_7^0'=lt_7^post_2, lt_8^0'=lt_8^post_2, lt_9^0'=lt_9^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ lt_8^1_1==cnt_15^0 && lt_9^1_1==cnt_20^0 && -lt_8^1_1+lt_9^1_1<=0 && lt_8^post_2==lt_8^post_2 && lt_9^post_2==lt_9^post_2 && Result_4^post_2==Result_4^post_2 && cnt_15^0==cnt_15^post_2 && cnt_20^0==cnt_20^post_2 && lt_7^0==lt_7^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post_3, cnt_15^0'=cnt_15^post_3, cnt_20^0'=cnt_20^post_3, lt_7^0'=lt_7^post_3, lt_8^0'=lt_8^post_3, lt_9^0'=lt_9^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ lt_8^1_2_1==cnt_15^0 && lt_9^1_2_1==cnt_20^0 && 0<=-1-lt_8^1_2_1+lt_9^1_2_1 && lt_8^post_3==lt_8^post_3 && lt_9^post_3==lt_9^post_3 && lt_7^1_1==cnt_15^0 && lt_7^post_3==lt_7^post_3 && Result_4^0==Result_4^post_3 && cnt_15^0==cnt_15^post_3 && cnt_20^0==cnt_20^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1 3: l3 -> l1 : Result_4^0'=Result_4^post_4, cnt_15^0'=cnt_15^post_4, cnt_20^0'=cnt_20^post_4, lt_7^0'=lt_7^post_4, lt_8^0'=lt_8^post_4, lt_9^0'=lt_9^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ Result_4^0==Result_4^post_4 && cnt_15^0==cnt_15^post_4 && cnt_20^0==cnt_20^post_4 && lt_7^0==lt_7^post_4 && lt_8^0==lt_8^post_4 && lt_9^0==lt_9^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 ], cost: 1 4: l4 -> l0 : Result_4^0'=Result_4^post_5, cnt_15^0'=cnt_15^post_5, cnt_20^0'=cnt_20^post_5, lt_7^0'=lt_7^post_5, lt_8^0'=lt_8^post_5, lt_9^0'=lt_9^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ Result_4^0==Result_4^post_5 && cnt_15^0==cnt_15^post_5 && cnt_20^0==cnt_20^post_5 && lt_7^0==lt_7^post_5 && lt_8^0==lt_8^post_5 && lt_9^0==lt_9^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: l4 -> l0 : Result_4^0'=Result_4^post_5, cnt_15^0'=cnt_15^post_5, cnt_20^0'=cnt_20^post_5, lt_7^0'=lt_7^post_5, lt_8^0'=lt_8^post_5, lt_9^0'=lt_9^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ Result_4^0==Result_4^post_5 && cnt_15^0==cnt_15^post_5 && cnt_20^0==cnt_20^post_5 && lt_7^0==lt_7^post_5 && lt_8^0==lt_8^post_5 && lt_9^0==lt_9^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1 Removed unreachable and leaf rules: Start location: l4 0: l0 -> l1 : Result_4^0'=Result_4^post_1, cnt_15^0'=cnt_15^post_1, cnt_20^0'=cnt_20^post_1, lt_7^0'=lt_7^post_1, lt_8^0'=lt_8^post_1, lt_9^0'=lt_9^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ y_6^post_1==y_6^post_1 && x_5^post_1==x_5^post_1 && Result_4^0==Result_4^post_1 && cnt_15^0==cnt_15^post_1 && cnt_20^0==cnt_20^post_1 && lt_7^0==lt_7^post_1 && lt_8^0==lt_8^post_1 && lt_9^0==lt_9^post_1 ], cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post_3, cnt_15^0'=cnt_15^post_3, cnt_20^0'=cnt_20^post_3, lt_7^0'=lt_7^post_3, lt_8^0'=lt_8^post_3, lt_9^0'=lt_9^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ lt_8^1_2_1==cnt_15^0 && lt_9^1_2_1==cnt_20^0 && 0<=-1-lt_8^1_2_1+lt_9^1_2_1 && lt_8^post_3==lt_8^post_3 && lt_9^post_3==lt_9^post_3 && lt_7^1_1==cnt_15^0 && lt_7^post_3==lt_7^post_3 && Result_4^0==Result_4^post_3 && cnt_15^0==cnt_15^post_3 && cnt_20^0==cnt_20^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1 3: l3 -> l1 : Result_4^0'=Result_4^post_4, cnt_15^0'=cnt_15^post_4, cnt_20^0'=cnt_20^post_4, lt_7^0'=lt_7^post_4, lt_8^0'=lt_8^post_4, lt_9^0'=lt_9^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ Result_4^0==Result_4^post_4 && cnt_15^0==cnt_15^post_4 && cnt_20^0==cnt_20^post_4 && lt_7^0==lt_7^post_4 && lt_8^0==lt_8^post_4 && lt_9^0==lt_9^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 ], cost: 1 4: l4 -> l0 : Result_4^0'=Result_4^post_5, cnt_15^0'=cnt_15^post_5, cnt_20^0'=cnt_20^post_5, lt_7^0'=lt_7^post_5, lt_8^0'=lt_8^post_5, lt_9^0'=lt_9^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ Result_4^0==Result_4^post_5 && cnt_15^0==cnt_15^post_5 && cnt_20^0==cnt_20^post_5 && lt_7^0==lt_7^post_5 && lt_8^0==lt_8^post_5 && lt_9^0==lt_9^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1 Simplified all rules, resulting in: Start location: l4 0: l0 -> l1 : x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [], cost: 1 2: l1 -> l3 : lt_7^0'=lt_7^post_3, lt_8^0'=lt_8^post_3, lt_9^0'=lt_9^post_3, [ 0<=-1-cnt_15^0+cnt_20^0 ], cost: 1 3: l3 -> l1 : [], cost: 1 4: l4 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l4 6: l1 -> l1 : lt_7^0'=lt_7^post_3, lt_8^0'=lt_8^post_3, lt_9^0'=lt_9^post_3, [ 0<=-1-cnt_15^0+cnt_20^0 ], cost: 2 5: l4 -> l1 : x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 6: l1 -> l1 : lt_7^0'=lt_7^post_3, lt_8^0'=lt_8^post_3, lt_9^0'=lt_9^post_3, [ 0<=-1-cnt_15^0+cnt_20^0 ], 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: l1 -> [5] : [ 0<=-1-cnt_15^0+cnt_20^0 ], cost: NONTERM 5: l4 -> l1 : x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l4 5: l4 -> l1 : x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [], cost: 2 8: l4 -> [5] : [ 0<=-1-cnt_15^0+cnt_20^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l4 8: l4 -> [5] : [ 0<=-1-cnt_15^0+cnt_20^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l4 8: l4 -> [5] : [ 0<=-1-cnt_15^0+cnt_20^0 ], 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_15^0+cnt_20^0 ] NO