NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l5 0: l0 -> l1 : Result_4^0'=Result_4^post_1, __const_19^0'=__const_19^post_1, __const_29^0'=__const_29^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 1+__const_19^0-x_5^0<=0 && Result_4^post_1==Result_4^post_1 && __const_19^0==__const_19^post_1 && __const_29^0==__const_29^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1 1: l0 -> l2 : Result_4^0'=Result_4^post_2, __const_19^0'=__const_19^post_2, __const_29^0'=__const_29^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ 0<=__const_19^0-x_5^0 && Result_4^0==Result_4^post_2 && __const_19^0==__const_19^post_2 && __const_29^0==__const_29^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1 3: l2 -> l0 : Result_4^0'=Result_4^post_4, __const_19^0'=__const_19^post_4, __const_29^0'=__const_29^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ 1-y_6^0+__const_29^0<=0 && x_5^post_4==-1+x_5^0 && Result_4^0==Result_4^post_4 && __const_19^0==__const_19^post_4 && __const_29^0==__const_29^post_4 && y_6^0==y_6^post_4 ], cost: 1 4: l2 -> l4 : Result_4^0'=Result_4^post_5, __const_19^0'=__const_19^post_5, __const_29^0'=__const_29^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ 0<=-y_6^0+__const_29^0 && x_5^post_5==-1+x_5^0 && Result_4^0==Result_4^post_5 && __const_19^0==__const_19^post_5 && __const_29^0==__const_29^post_5 && y_6^0==y_6^post_5 ], cost: 1 2: l3 -> l0 : Result_4^0'=Result_4^post_3, __const_19^0'=__const_19^post_3, __const_29^0'=__const_29^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && __const_19^0==__const_19^post_3 && __const_29^0==__const_29^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1 5: l4 -> l2 : Result_4^0'=Result_4^post_6, __const_19^0'=__const_19^post_6, __const_29^0'=__const_29^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ Result_4^0==Result_4^post_6 && __const_19^0==__const_19^post_6 && __const_29^0==__const_29^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1 6: l5 -> l3 : Result_4^0'=Result_4^post_7, __const_19^0'=__const_19^post_7, __const_29^0'=__const_29^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && __const_19^0==__const_19^post_7 && __const_29^0==__const_29^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: l5 -> l3 : Result_4^0'=Result_4^post_7, __const_19^0'=__const_19^post_7, __const_29^0'=__const_29^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && __const_19^0==__const_19^post_7 && __const_29^0==__const_29^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1 Removed unreachable and leaf rules: Start location: l5 1: l0 -> l2 : Result_4^0'=Result_4^post_2, __const_19^0'=__const_19^post_2, __const_29^0'=__const_29^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ 0<=__const_19^0-x_5^0 && Result_4^0==Result_4^post_2 && __const_19^0==__const_19^post_2 && __const_29^0==__const_29^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1 3: l2 -> l0 : Result_4^0'=Result_4^post_4, __const_19^0'=__const_19^post_4, __const_29^0'=__const_29^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ 1-y_6^0+__const_29^0<=0 && x_5^post_4==-1+x_5^0 && Result_4^0==Result_4^post_4 && __const_19^0==__const_19^post_4 && __const_29^0==__const_29^post_4 && y_6^0==y_6^post_4 ], cost: 1 4: l2 -> l4 : Result_4^0'=Result_4^post_5, __const_19^0'=__const_19^post_5, __const_29^0'=__const_29^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ 0<=-y_6^0+__const_29^0 && x_5^post_5==-1+x_5^0 && Result_4^0==Result_4^post_5 && __const_19^0==__const_19^post_5 && __const_29^0==__const_29^post_5 && y_6^0==y_6^post_5 ], cost: 1 2: l3 -> l0 : Result_4^0'=Result_4^post_3, __const_19^0'=__const_19^post_3, __const_29^0'=__const_29^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && __const_19^0==__const_19^post_3 && __const_29^0==__const_29^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1 5: l4 -> l2 : Result_4^0'=Result_4^post_6, __const_19^0'=__const_19^post_6, __const_29^0'=__const_29^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ Result_4^0==Result_4^post_6 && __const_19^0==__const_19^post_6 && __const_29^0==__const_29^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1 6: l5 -> l3 : Result_4^0'=Result_4^post_7, __const_19^0'=__const_19^post_7, __const_29^0'=__const_29^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && __const_19^0==__const_19^post_7 && __const_29^0==__const_29^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1 Simplified all rules, resulting in: Start location: l5 1: l0 -> l2 : [ 0<=__const_19^0-x_5^0 ], cost: 1 3: l2 -> l0 : x_5^0'=-1+x_5^0, [ 1-y_6^0+__const_29^0<=0 ], cost: 1 4: l2 -> l4 : x_5^0'=-1+x_5^0, [ 0<=-y_6^0+__const_29^0 ], cost: 1 2: l3 -> l0 : [], cost: 1 5: l4 -> l2 : [], cost: 1 6: l5 -> l3 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l5 1: l0 -> l2 : [ 0<=__const_19^0-x_5^0 ], cost: 1 3: l2 -> l0 : x_5^0'=-1+x_5^0, [ 1-y_6^0+__const_29^0<=0 ], cost: 1 8: l2 -> l2 : x_5^0'=-1+x_5^0, [ 0<=-y_6^0+__const_29^0 ], cost: 2 7: l5 -> l0 : [], cost: 2 Accelerating simple loops of location 2. Accelerating the following rules: 8: l2 -> l2 : x_5^0'=-1+x_5^0, [ 0<=-y_6^0+__const_29^0 ], cost: 2 Accelerated rule 8 with non-termination, yielding the new rule 9. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 8. Accelerated all simple loops using metering functions (where possible): Start location: l5 1: l0 -> l2 : [ 0<=__const_19^0-x_5^0 ], cost: 1 3: l2 -> l0 : x_5^0'=-1+x_5^0, [ 1-y_6^0+__const_29^0<=0 ], cost: 1 9: l2 -> [6] : [ 0<=-y_6^0+__const_29^0 ], cost: NONTERM 7: l5 -> l0 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l5 1: l0 -> l2 : [ 0<=__const_19^0-x_5^0 ], cost: 1 10: l0 -> [6] : [ 0<=__const_19^0-x_5^0 && 0<=-y_6^0+__const_29^0 ], cost: NONTERM 3: l2 -> l0 : x_5^0'=-1+x_5^0, [ 1-y_6^0+__const_29^0<=0 ], cost: 1 7: l5 -> l0 : [], cost: 2 Eliminated locations (on linear paths): Start location: l5 10: l0 -> [6] : [ 0<=__const_19^0-x_5^0 && 0<=-y_6^0+__const_29^0 ], cost: NONTERM 11: l0 -> l0 : x_5^0'=-1+x_5^0, [ 0<=__const_19^0-x_5^0 && 1-y_6^0+__const_29^0<=0 ], cost: 2 7: l5 -> l0 : [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 11: l0 -> l0 : x_5^0'=-1+x_5^0, [ 0<=__const_19^0-x_5^0 && 1-y_6^0+__const_29^0<=0 ], cost: 2 Accelerated rule 11 with non-termination, yielding the new rule 12. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 11. Accelerated all simple loops using metering functions (where possible): Start location: l5 10: l0 -> [6] : [ 0<=__const_19^0-x_5^0 && 0<=-y_6^0+__const_29^0 ], cost: NONTERM 12: l0 -> [7] : [ 0<=__const_19^0-x_5^0 && 1-y_6^0+__const_29^0<=0 ], cost: NONTERM 7: l5 -> l0 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l5 10: l0 -> [6] : [ 0<=__const_19^0-x_5^0 && 0<=-y_6^0+__const_29^0 ], cost: NONTERM 7: l5 -> l0 : [], cost: 2 13: l5 -> [7] : [ 0<=__const_19^0-x_5^0 && 1-y_6^0+__const_29^0<=0 ], cost: NONTERM Eliminated locations (on linear paths): Start location: l5 13: l5 -> [7] : [ 0<=__const_19^0-x_5^0 && 1-y_6^0+__const_29^0<=0 ], cost: NONTERM 14: l5 -> [6] : [ 0<=__const_19^0-x_5^0 && 0<=-y_6^0+__const_29^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l5 13: l5 -> [7] : [ 0<=__const_19^0-x_5^0 && 1-y_6^0+__const_29^0<=0 ], cost: NONTERM 14: l5 -> [6] : [ 0<=__const_19^0-x_5^0 && 0<=-y_6^0+__const_29^0 ], cost: NONTERM Computing asymptotic complexity for rule 13 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<=__const_19^0-x_5^0 && 1-y_6^0+__const_29^0<=0 ] NO