NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l6 0: l0 -> l1 : __const_10^0'=__const_10^post_1, i^0'=i^post_1, j^0'=j^post_1, temp^0'=temp^post_1, [ __const_10^0==__const_10^post_1 && i^0==i^post_1 && j^0==j^post_1 && temp^0==temp^post_1 ], cost: 1 4: l1 -> l4 : __const_10^0'=__const_10^post_5, i^0'=i^post_5, j^0'=j^post_5, temp^0'=temp^post_5, [ 1+__const_10^0<=i^0 && __const_10^0==__const_10^post_5 && i^0==i^post_5 && j^0==j^post_5 && temp^0==temp^post_5 ], cost: 1 5: l1 -> l2 : __const_10^0'=__const_10^post_6, i^0'=i^post_6, j^0'=j^post_6, temp^0'=temp^post_6, [ i^0<=__const_10^0 && j^post_6==i^0 && __const_10^0==__const_10^post_6 && i^0==i^post_6 && temp^0==temp^post_6 ], cost: 1 1: l2 -> l3 : __const_10^0'=__const_10^post_2, i^0'=i^post_2, j^0'=j^post_2, temp^0'=temp^post_2, [ __const_10^0==__const_10^post_2 && i^0==i^post_2 && j^0==j^post_2 && temp^0==temp^post_2 ], cost: 1 2: l3 -> l2 : __const_10^0'=__const_10^post_3, i^0'=i^post_3, j^0'=j^post_3, temp^0'=temp^post_3, [ temp^post_3==temp^post_3 && j^post_3==-1+j^0 && __const_10^0==__const_10^post_3 && i^0==i^post_3 ], cost: 1 3: l3 -> l0 : __const_10^0'=__const_10^post_4, i^0'=i^post_4, j^0'=j^post_4, temp^0'=temp^post_4, [ i^post_4==1+i^0 && __const_10^0==__const_10^post_4 && j^0==j^post_4 && temp^0==temp^post_4 ], cost: 1 6: l5 -> l0 : __const_10^0'=__const_10^post_7, i^0'=i^post_7, j^0'=j^post_7, temp^0'=temp^post_7, [ i^post_7==2 && __const_10^0==__const_10^post_7 && j^0==j^post_7 && temp^0==temp^post_7 ], cost: 1 7: l6 -> l5 : __const_10^0'=__const_10^post_8, i^0'=i^post_8, j^0'=j^post_8, temp^0'=temp^post_8, [ __const_10^0==__const_10^post_8 && i^0==i^post_8 && j^0==j^post_8 && temp^0==temp^post_8 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: l6 -> l5 : __const_10^0'=__const_10^post_8, i^0'=i^post_8, j^0'=j^post_8, temp^0'=temp^post_8, [ __const_10^0==__const_10^post_8 && i^0==i^post_8 && j^0==j^post_8 && temp^0==temp^post_8 ], cost: 1 Removed unreachable and leaf rules: Start location: l6 0: l0 -> l1 : __const_10^0'=__const_10^post_1, i^0'=i^post_1, j^0'=j^post_1, temp^0'=temp^post_1, [ __const_10^0==__const_10^post_1 && i^0==i^post_1 && j^0==j^post_1 && temp^0==temp^post_1 ], cost: 1 5: l1 -> l2 : __const_10^0'=__const_10^post_6, i^0'=i^post_6, j^0'=j^post_6, temp^0'=temp^post_6, [ i^0<=__const_10^0 && j^post_6==i^0 && __const_10^0==__const_10^post_6 && i^0==i^post_6 && temp^0==temp^post_6 ], cost: 1 1: l2 -> l3 : __const_10^0'=__const_10^post_2, i^0'=i^post_2, j^0'=j^post_2, temp^0'=temp^post_2, [ __const_10^0==__const_10^post_2 && i^0==i^post_2 && j^0==j^post_2 && temp^0==temp^post_2 ], cost: 1 2: l3 -> l2 : __const_10^0'=__const_10^post_3, i^0'=i^post_3, j^0'=j^post_3, temp^0'=temp^post_3, [ temp^post_3==temp^post_3 && j^post_3==-1+j^0 && __const_10^0==__const_10^post_3 && i^0==i^post_3 ], cost: 1 3: l3 -> l0 : __const_10^0'=__const_10^post_4, i^0'=i^post_4, j^0'=j^post_4, temp^0'=temp^post_4, [ i^post_4==1+i^0 && __const_10^0==__const_10^post_4 && j^0==j^post_4 && temp^0==temp^post_4 ], cost: 1 6: l5 -> l0 : __const_10^0'=__const_10^post_7, i^0'=i^post_7, j^0'=j^post_7, temp^0'=temp^post_7, [ i^post_7==2 && __const_10^0==__const_10^post_7 && j^0==j^post_7 && temp^0==temp^post_7 ], cost: 1 7: l6 -> l5 : __const_10^0'=__const_10^post_8, i^0'=i^post_8, j^0'=j^post_8, temp^0'=temp^post_8, [ __const_10^0==__const_10^post_8 && i^0==i^post_8 && j^0==j^post_8 && temp^0==temp^post_8 ], cost: 1 Simplified all rules, resulting in: Start location: l6 0: l0 -> l1 : [], cost: 1 5: l1 -> l2 : j^0'=i^0, [ i^0<=__const_10^0 ], cost: 1 1: l2 -> l3 : [], cost: 1 2: l3 -> l2 : j^0'=-1+j^0, temp^0'=temp^post_3, [], cost: 1 3: l3 -> l0 : i^0'=1+i^0, [], cost: 1 6: l5 -> l0 : i^0'=2, [], cost: 1 7: l6 -> l5 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l6 9: l0 -> l2 : j^0'=i^0, [ i^0<=__const_10^0 ], cost: 2 1: l2 -> l3 : [], cost: 1 2: l3 -> l2 : j^0'=-1+j^0, temp^0'=temp^post_3, [], cost: 1 3: l3 -> l0 : i^0'=1+i^0, [], cost: 1 8: l6 -> l0 : i^0'=2, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l6 9: l0 -> l2 : j^0'=i^0, [ i^0<=__const_10^0 ], cost: 2 10: l2 -> l2 : j^0'=-1+j^0, temp^0'=temp^post_3, [], cost: 2 11: l2 -> l0 : i^0'=1+i^0, [], cost: 2 8: l6 -> l0 : i^0'=2, [], cost: 2 Accelerating simple loops of location 2. Accelerating the following rules: 10: l2 -> l2 : j^0'=-1+j^0, temp^0'=temp^post_3, [], cost: 2 Accelerated rule 10 with non-termination, yielding the new rule 12. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 10. Accelerated all simple loops using metering functions (where possible): Start location: l6 9: l0 -> l2 : j^0'=i^0, [ i^0<=__const_10^0 ], cost: 2 11: l2 -> l0 : i^0'=1+i^0, [], cost: 2 12: l2 -> [7] : [], cost: NONTERM 8: l6 -> l0 : i^0'=2, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l6 9: l0 -> l2 : j^0'=i^0, [ i^0<=__const_10^0 ], cost: 2 13: l0 -> [7] : [ i^0<=__const_10^0 ], cost: NONTERM 11: l2 -> l0 : i^0'=1+i^0, [], cost: 2 8: l6 -> l0 : i^0'=2, [], cost: 2 Eliminated locations (on linear paths): Start location: l6 13: l0 -> [7] : [ i^0<=__const_10^0 ], cost: NONTERM 14: l0 -> l0 : i^0'=1+i^0, j^0'=i^0, [ i^0<=__const_10^0 ], cost: 4 8: l6 -> l0 : i^0'=2, [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 14: l0 -> l0 : i^0'=1+i^0, j^0'=i^0, [ i^0<=__const_10^0 ], cost: 4 Accelerated rule 14 with backward acceleration, yielding the new rule 15. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 14. Accelerated all simple loops using metering functions (where possible): Start location: l6 13: l0 -> [7] : [ i^0<=__const_10^0 ], cost: NONTERM 15: l0 -> l0 : i^0'=1+__const_10^0, j^0'=__const_10^0, [ 1-i^0+__const_10^0>=1 ], cost: 4-4*i^0+4*__const_10^0 8: l6 -> l0 : i^0'=2, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l6 13: l0 -> [7] : [ i^0<=__const_10^0 ], cost: NONTERM 8: l6 -> l0 : i^0'=2, [], cost: 2 16: l6 -> l0 : i^0'=1+__const_10^0, j^0'=__const_10^0, [ -1+__const_10^0>=1 ], cost: -2+4*__const_10^0 Eliminated locations (on tree-shaped paths): Start location: l6 17: l6 -> [7] : [ 2<=__const_10^0 ], cost: NONTERM 18: l6 -> [9] : [ -1+__const_10^0>=1 ], cost: -2+4*__const_10^0 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l6 17: l6 -> [7] : [ 2<=__const_10^0 ], cost: NONTERM 18: l6 -> [9] : [ -1+__const_10^0>=1 ], cost: -2+4*__const_10^0 Computing asymptotic complexity for rule 17 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: [ 2<=__const_10^0 ] NO