NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l9 0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, [ Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 ], cost: 1 1: l1 -> l3 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, [ x_5^post_2==-1+x_5^0 && Result_4^0==Result_4^post_2 ], cost: 1 6: l1 -> l6 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, [ x_5^post_7==-1+x_5^0 && Result_4^0==Result_4^post_7 ], cost: 1 10: l1 -> l8 : Result_4^0'=Result_4^post_11, x_5^0'=x_5^post_11, [ x_5^1_1==-1+x_5^0 && x_5^1_1<=13 && 13<=x_5^1_1 && x_5^post_11==x_5^post_11 && -x_5^post_11<=0 && Result_4^0==Result_4^post_11 ], cost: 1 12: l1 -> l5 : Result_4^0'=Result_4^post_13, x_5^0'=x_5^post_13, [ x_5^1_2==-1+x_5^0 && x_5^1_2<=13 && 13<=x_5^1_2 && x_5^post_13==x_5^post_13 && 0<=-1-x_5^post_13 && Result_4^post_13==Result_4^post_13 ], cost: 1 2: l3 -> l4 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ 1+x_5^0<=13 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 ], cost: 1 3: l3 -> l4 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ 14<=x_5^0 && Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 ], cost: 1 4: l4 -> l2 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ -x_5^0<=0 && Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1 5: l2 -> l1 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, [ Result_4^0==Result_4^post_6 && x_5^0==x_5^post_6 ], cost: 1 7: l6 -> l7 : Result_4^0'=Result_4^post_8, x_5^0'=x_5^post_8, [ 1+x_5^0<=13 && Result_4^0==Result_4^post_8 && x_5^0==x_5^post_8 ], cost: 1 8: l6 -> l7 : Result_4^0'=Result_4^post_9, x_5^0'=x_5^post_9, [ 14<=x_5^0 && Result_4^0==Result_4^post_9 && x_5^0==x_5^post_9 ], cost: 1 9: l7 -> l5 : Result_4^0'=Result_4^post_10, x_5^0'=x_5^post_10, [ 0<=-1-x_5^0 && Result_4^post_10==Result_4^post_10 && x_5^0==x_5^post_10 ], cost: 1 11: l8 -> l1 : Result_4^0'=Result_4^post_12, x_5^0'=x_5^post_12, [ Result_4^0==Result_4^post_12 && x_5^0==x_5^post_12 ], cost: 1 13: l9 -> l0 : Result_4^0'=Result_4^post_14, x_5^0'=x_5^post_14, [ Result_4^0==Result_4^post_14 && x_5^0==x_5^post_14 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 13: l9 -> l0 : Result_4^0'=Result_4^post_14, x_5^0'=x_5^post_14, [ Result_4^0==Result_4^post_14 && x_5^0==x_5^post_14 ], cost: 1 Removed unreachable and leaf rules: Start location: l9 0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, [ Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 ], cost: 1 1: l1 -> l3 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, [ x_5^post_2==-1+x_5^0 && Result_4^0==Result_4^post_2 ], cost: 1 10: l1 -> l8 : Result_4^0'=Result_4^post_11, x_5^0'=x_5^post_11, [ x_5^1_1==-1+x_5^0 && x_5^1_1<=13 && 13<=x_5^1_1 && x_5^post_11==x_5^post_11 && -x_5^post_11<=0 && Result_4^0==Result_4^post_11 ], cost: 1 2: l3 -> l4 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ 1+x_5^0<=13 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 ], cost: 1 3: l3 -> l4 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ 14<=x_5^0 && Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 ], cost: 1 4: l4 -> l2 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ -x_5^0<=0 && Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1 5: l2 -> l1 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, [ Result_4^0==Result_4^post_6 && x_5^0==x_5^post_6 ], cost: 1 11: l8 -> l1 : Result_4^0'=Result_4^post_12, x_5^0'=x_5^post_12, [ Result_4^0==Result_4^post_12 && x_5^0==x_5^post_12 ], cost: 1 13: l9 -> l0 : Result_4^0'=Result_4^post_14, x_5^0'=x_5^post_14, [ Result_4^0==Result_4^post_14 && x_5^0==x_5^post_14 ], cost: 1 Simplified all rules, resulting in: Start location: l9 0: l0 -> l1 : [], cost: 1 1: l1 -> l3 : x_5^0'=-1+x_5^0, [], cost: 1 10: l1 -> l8 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 1 2: l3 -> l4 : [ 1+x_5^0<=13 ], cost: 1 3: l3 -> l4 : [ 14<=x_5^0 ], cost: 1 4: l4 -> l2 : [ -x_5^0<=0 ], cost: 1 5: l2 -> l1 : [], cost: 1 11: l8 -> l1 : [], cost: 1 13: l9 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l9 1: l1 -> l3 : x_5^0'=-1+x_5^0, [], cost: 1 15: l1 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 2 2: l3 -> l4 : [ 1+x_5^0<=13 ], cost: 1 3: l3 -> l4 : [ 14<=x_5^0 ], cost: 1 16: l4 -> l1 : [ -x_5^0<=0 ], cost: 2 14: l9 -> l1 : [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 15: l1 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 2 Accelerated rule 15 with non-termination, yielding the new rule 17. [accelerate] Nesting with 0 inner and 1 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: l9 1: l1 -> l3 : x_5^0'=-1+x_5^0, [], cost: 1 15: l1 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 2 17: l1 -> [10] : [ -14+x_5^0==0 && -14+x_5^post_11==0 ], cost: NONTERM 2: l3 -> l4 : [ 1+x_5^0<=13 ], cost: 1 3: l3 -> l4 : [ 14<=x_5^0 ], cost: 1 16: l4 -> l1 : [ -x_5^0<=0 ], cost: 2 14: l9 -> l1 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l9 1: l1 -> l3 : x_5^0'=-1+x_5^0, [], cost: 1 2: l3 -> l4 : [ 1+x_5^0<=13 ], cost: 1 3: l3 -> l4 : [ 14<=x_5^0 ], cost: 1 16: l4 -> l1 : [ -x_5^0<=0 ], cost: 2 19: l4 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 4 21: l4 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM 14: l9 -> l1 : [], cost: 2 18: l9 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 4 20: l9 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l9 22: l1 -> l4 : x_5^0'=-1+x_5^0, [ x_5^0<=13 ], cost: 2 23: l1 -> l4 : x_5^0'=-1+x_5^0, [ 14<=-1+x_5^0 ], cost: 2 16: l4 -> l1 : [ -x_5^0<=0 ], cost: 2 19: l4 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 4 21: l4 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM 14: l9 -> l1 : [], cost: 2 18: l9 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 4 20: l9 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l9 24: l1 -> l1 : x_5^0'=-1+x_5^0, [ x_5^0<=13 && 1-x_5^0<=0 ], cost: 4 25: l1 -> l1 : x_5^0'=-1+x_5^0, [ 14<=-1+x_5^0 ], cost: 4 26: l1 -> l1 : x_5^0'=x_5^post_11, [ -15+x_5^0==0 && -x_5^post_11<=0 ], cost: 6 27: l1 -> [10] : [ -15+x_5^0==0 ], cost: NONTERM 14: l9 -> l1 : [], cost: 2 18: l9 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 4 20: l9 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM Accelerating simple loops of location 1. Accelerating the following rules: 24: l1 -> l1 : x_5^0'=-1+x_5^0, [ x_5^0<=13 && 1-x_5^0<=0 ], cost: 4 25: l1 -> l1 : x_5^0'=-1+x_5^0, [ 14<=-1+x_5^0 ], cost: 4 26: l1 -> l1 : x_5^0'=x_5^post_11, [ -15+x_5^0==0 && -x_5^post_11<=0 ], cost: 6 Accelerated rule 24 with backward acceleration, yielding the new rule 28. Accelerated rule 25 with backward acceleration, yielding the new rule 29. Accelerated rule 26 with non-termination, yielding the new rule 30. [accelerate] Nesting with 2 inner and 3 outer candidates Removing the simple loops: 24 25. Accelerated all simple loops using metering functions (where possible): Start location: l9 26: l1 -> l1 : x_5^0'=x_5^post_11, [ -15+x_5^0==0 && -x_5^post_11<=0 ], cost: 6 27: l1 -> [10] : [ -15+x_5^0==0 ], cost: NONTERM 28: l1 -> l1 : x_5^0'=0, [ x_5^0<=13 && x_5^0>=0 ], cost: 4*x_5^0 29: l1 -> l1 : x_5^0'=14, [ -14+x_5^0>=0 ], cost: -56+4*x_5^0 30: l1 -> [11] : [ -15+x_5^0==0 && -15+x_5^post_11==0 ], cost: NONTERM 14: l9 -> l1 : [], cost: 2 18: l9 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 4 20: l9 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: l9 27: l1 -> [10] : [ -15+x_5^0==0 ], cost: NONTERM 14: l9 -> l1 : [], cost: 2 18: l9 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 4 20: l9 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM 31: l9 -> l1 : x_5^0'=x_5^post_11, [ -15+x_5^0==0 && -x_5^post_11<=0 ], cost: 8 32: l9 -> l1 : x_5^0'=15, [ -14+x_5^0==0 ], cost: 10 33: l9 -> l1 : x_5^0'=0, [ x_5^0<=13 && x_5^0>=0 ], cost: 2+4*x_5^0 34: l9 -> l1 : x_5^0'=0, [ -14+x_5^0==0 && -x_5^post_11<=0 && x_5^post_11<=13 ], cost: 4+4*x_5^post_11 35: l9 -> l1 : x_5^0'=14, [ -14+x_5^0>=0 ], cost: -54+4*x_5^0 36: l9 -> l1 : x_5^0'=14, [ -14+x_5^0==0 && -14+x_5^post_11>=0 ], cost: -52+4*x_5^post_11 37: l9 -> [11] : [ -15+x_5^0==0 ], cost: NONTERM 38: l9 -> [11] : [ -14+x_5^0==0 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: l9 20: l9 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM 37: l9 -> [11] : [ -15+x_5^0==0 ], cost: NONTERM 38: l9 -> [11] : [ -14+x_5^0==0 ], cost: NONTERM 39: l9 -> [10] : [ -15+x_5^0==0 ], cost: NONTERM 40: l9 -> [10] : [ -14+x_5^0==0 && -15+x_5^post_11==0 ], cost: NONTERM 41: l9 -> [10] : [ -15+x_5^0==0 && -15+x_5^post_11==0 ], cost: NONTERM 42: l9 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM 43: l9 -> [12] : [ x_5^0<=13 && x_5^0>=0 ], cost: 2+4*x_5^0 44: l9 -> [12] : [ -14+x_5^0==0 && -x_5^post_11<=0 && x_5^post_11<=13 ], cost: 4+4*x_5^post_11 45: l9 -> [12] : [ -14+x_5^0>=0 ], cost: -54+4*x_5^0 46: l9 -> [12] : [ -14+x_5^0==0 && -14+x_5^post_11>=0 ], cost: -52+4*x_5^post_11 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l9 39: l9 -> [10] : [ -15+x_5^0==0 ], cost: NONTERM 40: l9 -> [10] : [ -14+x_5^0==0 && -15+x_5^post_11==0 ], cost: NONTERM 41: l9 -> [10] : [ -15+x_5^0==0 && -15+x_5^post_11==0 ], cost: NONTERM 42: l9 -> [10] : [ -14+x_5^0==0 ], cost: NONTERM 43: l9 -> [12] : [ x_5^0<=13 && x_5^0>=0 ], cost: 2+4*x_5^0 44: l9 -> [12] : [ -14+x_5^0==0 && -x_5^post_11<=0 && x_5^post_11<=13 ], cost: 4+4*x_5^post_11 45: l9 -> [12] : [ -14+x_5^0>=0 ], cost: -54+4*x_5^0 46: l9 -> [12] : [ -14+x_5^0==0 && -14+x_5^post_11>=0 ], cost: -52+4*x_5^post_11 Computing asymptotic complexity for rule 39 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: [ -15+x_5^0==0 ] NO