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