NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: [0] 0: [0] -> [1] : z'=2, [ x>=y ], cost: 1 1: [1] -> [2] : x'=5, y'=6, [], cost: 1 2: [2] -> [3] : [ z>=0 ], cost: 1 3: [2] -> [4] : [ z<0 ], cost: 1 4: [3] -> [5] : [ x<=-1+y ], cost: 1 7: [3] -> [7] : [ x>-1+y ], cost: 1 5: [5] -> [6] : x'=y, y'=1+y, [], cost: 1 6: [6] -> [3] : [ 0<=0 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: [0] -> [1] : z'=2, [ x>=y ], cost: 1 Removed unreachable and leaf rules: Start location: [0] 0: [0] -> [1] : z'=2, [ x>=y ], cost: 1 1: [1] -> [2] : x'=5, y'=6, [], cost: 1 2: [2] -> [3] : [ z>=0 ], cost: 1 4: [3] -> [5] : [ x<=-1+y ], cost: 1 5: [5] -> [6] : x'=y, y'=1+y, [], cost: 1 6: [6] -> [3] : [ 0<=0 ], cost: 1 Simplified all rules, resulting in: Start location: [0] 0: [0] -> [1] : z'=2, [ x>=y ], cost: 1 1: [1] -> [2] : x'=5, y'=6, [], cost: 1 2: [2] -> [3] : [ z>=0 ], cost: 1 4: [3] -> [5] : [ x<=-1+y ], cost: 1 5: [5] -> [6] : x'=y, y'=1+y, [], cost: 1 6: [6] -> [3] : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: [0] 9: [0] -> [3] : z'=2, x'=5, y'=6, [ x>=y ], cost: 3 11: [3] -> [3] : x'=y, y'=1+y, [ x<=-1+y ], cost: 3 Accelerating simple loops of location 3. Accelerating the following rules: 11: [3] -> [3] : x'=y, y'=1+y, [ x<=-1+y ], cost: 3 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: [0] 9: [0] -> [3] : z'=2, x'=5, y'=6, [ x>=y ], cost: 3 12: [3] -> [8] : [ x<=-1+y ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: [0] 9: [0] -> [3] : z'=2, x'=5, y'=6, [ x>=y ], cost: 3 13: [0] -> [8] : [ x>=y ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: [0] 13: [0] -> [8] : [ x>=y ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: [0] 13: [0] -> [8] : [ x>=y ], 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: [ x>=y ] NO