NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l6 0: l0 -> l2 : Result_4^0'=Result_4^post_1, __disjvr_0^0'=__disjvr_0^post_1, b_7^0'=b_7^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 0<=-1+y_6^0-x_5^0 && Result_4^0==Result_4^post_1 && __disjvr_0^0==__disjvr_0^post_1 && b_7^0==b_7^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1 3: l0 -> l4 : Result_4^0'=Result_4^post_4, __disjvr_0^0'=__disjvr_0^post_4, b_7^0'=b_7^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ y_6^0-x_5^0<=0 && Result_4^post_4==Result_4^post_4 && __disjvr_0^0==__disjvr_0^post_4 && b_7^0==b_7^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 ], cost: 1 1: l2 -> l3 : Result_4^0'=Result_4^post_2, __disjvr_0^0'=__disjvr_0^post_2, b_7^0'=b_7^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ __disjvr_0^post_2==__disjvr_0^0 && Result_4^0==Result_4^post_2 && __disjvr_0^0==__disjvr_0^post_2 && b_7^0==b_7^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1 2: l3 -> l1 : Result_4^0'=Result_4^post_3, __disjvr_0^0'=__disjvr_0^post_3, b_7^0'=b_7^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ b_7^post_3==0 && y_6^post_3==1+y_6^0 && Result_4^0==Result_4^post_3 && __disjvr_0^0==__disjvr_0^post_3 && x_5^0==x_5^post_3 ], cost: 1 5: l1 -> l0 : Result_4^0'=Result_4^post_6, __disjvr_0^0'=__disjvr_0^post_6, b_7^0'=b_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ 0<=-1+y_6^0-x_5^0 && b_7^0<=0 && 0<=b_7^0 && b_7^post_6==1 && x_5^post_6==1+x_5^0 && Result_4^0==Result_4^post_6 && __disjvr_0^0==__disjvr_0^post_6 && y_6^0==y_6^post_6 ], cost: 1 6: l1 -> l4 : Result_4^0'=Result_4^post_7, __disjvr_0^0'=__disjvr_0^post_7, b_7^0'=b_7^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ y_6^0-x_5^0<=0 && Result_4^post_7==Result_4^post_7 && __disjvr_0^0==__disjvr_0^post_7 && b_7^0==b_7^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1 4: l5 -> l1 : Result_4^0'=Result_4^post_5, __disjvr_0^0'=__disjvr_0^post_5, b_7^0'=b_7^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ b_7^post_5==0 && Result_4^0==Result_4^post_5 && __disjvr_0^0==__disjvr_0^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1 7: l6 -> l5 : Result_4^0'=Result_4^post_8, __disjvr_0^0'=__disjvr_0^post_8, b_7^0'=b_7^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ Result_4^0==Result_4^post_8 && __disjvr_0^0==__disjvr_0^post_8 && b_7^0==b_7^post_8 && x_5^0==x_5^post_8 && y_6^0==y_6^post_8 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: l6 -> l5 : Result_4^0'=Result_4^post_8, __disjvr_0^0'=__disjvr_0^post_8, b_7^0'=b_7^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ Result_4^0==Result_4^post_8 && __disjvr_0^0==__disjvr_0^post_8 && b_7^0==b_7^post_8 && x_5^0==x_5^post_8 && y_6^0==y_6^post_8 ], cost: 1 Removed unreachable and leaf rules: Start location: l6 0: l0 -> l2 : Result_4^0'=Result_4^post_1, __disjvr_0^0'=__disjvr_0^post_1, b_7^0'=b_7^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 0<=-1+y_6^0-x_5^0 && Result_4^0==Result_4^post_1 && __disjvr_0^0==__disjvr_0^post_1 && b_7^0==b_7^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1 1: l2 -> l3 : Result_4^0'=Result_4^post_2, __disjvr_0^0'=__disjvr_0^post_2, b_7^0'=b_7^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ __disjvr_0^post_2==__disjvr_0^0 && Result_4^0==Result_4^post_2 && __disjvr_0^0==__disjvr_0^post_2 && b_7^0==b_7^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1 2: l3 -> l1 : Result_4^0'=Result_4^post_3, __disjvr_0^0'=__disjvr_0^post_3, b_7^0'=b_7^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ b_7^post_3==0 && y_6^post_3==1+y_6^0 && Result_4^0==Result_4^post_3 && __disjvr_0^0==__disjvr_0^post_3 && x_5^0==x_5^post_3 ], cost: 1 5: l1 -> l0 : Result_4^0'=Result_4^post_6, __disjvr_0^0'=__disjvr_0^post_6, b_7^0'=b_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ 0<=-1+y_6^0-x_5^0 && b_7^0<=0 && 0<=b_7^0 && b_7^post_6==1 && x_5^post_6==1+x_5^0 && Result_4^0==Result_4^post_6 && __disjvr_0^0==__disjvr_0^post_6 && y_6^0==y_6^post_6 ], cost: 1 4: l5 -> l1 : Result_4^0'=Result_4^post_5, __disjvr_0^0'=__disjvr_0^post_5, b_7^0'=b_7^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ b_7^post_5==0 && Result_4^0==Result_4^post_5 && __disjvr_0^0==__disjvr_0^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1 7: l6 -> l5 : Result_4^0'=Result_4^post_8, __disjvr_0^0'=__disjvr_0^post_8, b_7^0'=b_7^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ Result_4^0==Result_4^post_8 && __disjvr_0^0==__disjvr_0^post_8 && b_7^0==b_7^post_8 && x_5^0==x_5^post_8 && y_6^0==y_6^post_8 ], cost: 1 Simplified all rules, resulting in: Start location: l6 0: l0 -> l2 : [ 0<=-1+y_6^0-x_5^0 ], cost: 1 1: l2 -> l3 : [], cost: 1 2: l3 -> l1 : b_7^0'=0, y_6^0'=1+y_6^0, [], cost: 1 5: l1 -> l0 : b_7^0'=1, x_5^0'=1+x_5^0, [ 0<=-1+y_6^0-x_5^0 && b_7^0==0 ], cost: 1 4: l5 -> l1 : b_7^0'=0, [], cost: 1 7: l6 -> l5 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l6 11: l1 -> l1 : b_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+y_6^0, [ b_7^0==0 && 0<=-2+y_6^0-x_5^0 ], cost: 4 8: l6 -> l1 : b_7^0'=0, [], cost: 2 Accelerating simple loops of location 3. Accelerating the following rules: 11: l1 -> l1 : b_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+y_6^0, [ b_7^0==0 && 0<=-2+y_6^0-x_5^0 ], cost: 4 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: l6 12: l1 -> [7] : [ b_7^0==0 && 0<=-2+y_6^0-x_5^0 ], cost: NONTERM 8: l6 -> l1 : b_7^0'=0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l6 8: l6 -> l1 : b_7^0'=0, [], cost: 2 13: l6 -> [7] : [ 0<=-2+y_6^0-x_5^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l6 13: l6 -> [7] : [ 0<=-2+y_6^0-x_5^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l6 13: l6 -> [7] : [ 0<=-2+y_6^0-x_5^0 ], 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<=-2+y_6^0-x_5^0 ] NO