NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l8 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 -> l2 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, [ -x_5^0<=0 && x_5^0<=0 && Result_4^0==Result_4^post_2 && x_5^0==x_5^post_2 ], cost: 1 2: l1 -> l2 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ -x_5^0<=0 && 0<=-1+x_5^0 && x_5^1_1==x_5^1_1 && x_5^post_3==1+x_5^1_1 && -x_5^post_3<=0 && x_5^post_3<=0 && Result_4^0==Result_4^post_3 ], cost: 1 3: l1 -> l2 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ 0<=-1-x_5^0 && x_5^1_2==x_5^1_2 && x_5^post_4==-1+x_5^1_2 && -x_5^post_4<=0 && x_5^post_4<=0 && Result_4^0==Result_4^post_4 ], cost: 1 4: l1 -> l3 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ -x_5^0<=0 && 0<=-1+x_5^0 && x_5^1_3==x_5^1_3 && x_5^2_1==1+x_5^1_3 && -x_5^2_1<=0 && 0<=-1+x_5^2_1 && x_5^3_1==x_5^3_1 && x_5^post_5==1+x_5^3_1 && Result_4^0==Result_4^post_5 ], cost: 1 6: l1 -> l4 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, [ -x_5^0<=0 && 0<=-1+x_5^0 && x_5^1_4==x_5^1_4 && x_5^2_2_1==1+x_5^1_4 && 0<=-1-x_5^2_2_1 && x_5^3_2_1==x_5^3_2_1 && x_5^post_7==-1+x_5^3_2_1 && Result_4^0==Result_4^post_7 ], cost: 1 8: l1 -> l5 : Result_4^0'=Result_4^post_9, x_5^0'=x_5^post_9, [ 0<=-1-x_5^0 && x_5^1_5==x_5^1_5 && x_5^2_3_1==-1+x_5^1_5 && -x_5^2_3_1<=0 && 0<=-1+x_5^2_3_1 && x_5^3_3_1==x_5^3_3_1 && x_5^post_9==1+x_5^3_3_1 && Result_4^0==Result_4^post_9 ], cost: 1 10: l1 -> l6 : Result_4^0'=Result_4^post_11, x_5^0'=x_5^post_11, [ 0<=-1-x_5^0 && x_5^1_6==x_5^1_6 && x_5^2_4_1==-1+x_5^1_6 && 0<=-1-x_5^2_4_1 && x_5^3_4_1==x_5^3_4_1 && x_5^post_11==-1+x_5^3_4_1 && Result_4^0==Result_4^post_11 ], cost: 1 12: l2 -> l7 : Result_4^0'=Result_4^post_13, x_5^0'=x_5^post_13, [ Result_4^post_13==Result_4^post_13 && x_5^0==x_5^post_13 ], cost: 1 5: l3 -> 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: l4 -> l1 : Result_4^0'=Result_4^post_8, x_5^0'=x_5^post_8, [ Result_4^0==Result_4^post_8 && x_5^0==x_5^post_8 ], cost: 1 9: l5 -> l1 : Result_4^0'=Result_4^post_10, x_5^0'=x_5^post_10, [ Result_4^0==Result_4^post_10 && x_5^0==x_5^post_10 ], cost: 1 11: l6 -> 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: l8 -> 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: l8 -> 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: l8 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 4: l1 -> l3 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ -x_5^0<=0 && 0<=-1+x_5^0 && x_5^1_3==x_5^1_3 && x_5^2_1==1+x_5^1_3 && -x_5^2_1<=0 && 0<=-1+x_5^2_1 && x_5^3_1==x_5^3_1 && x_5^post_5==1+x_5^3_1 && Result_4^0==Result_4^post_5 ], cost: 1 6: l1 -> l4 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, [ -x_5^0<=0 && 0<=-1+x_5^0 && x_5^1_4==x_5^1_4 && x_5^2_2_1==1+x_5^1_4 && 0<=-1-x_5^2_2_1 && x_5^3_2_1==x_5^3_2_1 && x_5^post_7==-1+x_5^3_2_1 && Result_4^0==Result_4^post_7 ], cost: 1 8: l1 -> l5 : Result_4^0'=Result_4^post_9, x_5^0'=x_5^post_9, [ 0<=-1-x_5^0 && x_5^1_5==x_5^1_5 && x_5^2_3_1==-1+x_5^1_5 && -x_5^2_3_1<=0 && 0<=-1+x_5^2_3_1 && x_5^3_3_1==x_5^3_3_1 && x_5^post_9==1+x_5^3_3_1 && Result_4^0==Result_4^post_9 ], cost: 1 10: l1 -> l6 : Result_4^0'=Result_4^post_11, x_5^0'=x_5^post_11, [ 0<=-1-x_5^0 && x_5^1_6==x_5^1_6 && x_5^2_4_1==-1+x_5^1_6 && 0<=-1-x_5^2_4_1 && x_5^3_4_1==x_5^3_4_1 && x_5^post_11==-1+x_5^3_4_1 && Result_4^0==Result_4^post_11 ], cost: 1 5: l3 -> 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: l4 -> l1 : Result_4^0'=Result_4^post_8, x_5^0'=x_5^post_8, [ Result_4^0==Result_4^post_8 && x_5^0==x_5^post_8 ], cost: 1 9: l5 -> l1 : Result_4^0'=Result_4^post_10, x_5^0'=x_5^post_10, [ Result_4^0==Result_4^post_10 && x_5^0==x_5^post_10 ], cost: 1 11: l6 -> 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: l8 -> 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: l8 0: l0 -> l1 : [], cost: 1 4: l1 -> l3 : x_5^0'=1+x_5^3_1, [ 0<=-1+x_5^0 ], cost: 1 6: l1 -> l4 : x_5^0'=-1+x_5^3_2_1, [ 0<=-1+x_5^0 ], cost: 1 8: l1 -> l5 : x_5^0'=1+x_5^3_3_1, [ 0<=-1-x_5^0 ], cost: 1 10: l1 -> l6 : x_5^0'=-1+x_5^3_4_1, [ 0<=-1-x_5^0 ], cost: 1 5: l3 -> l1 : [], cost: 1 7: l4 -> l1 : [], cost: 1 9: l5 -> l1 : [], cost: 1 11: l6 -> l1 : [], cost: 1 13: l8 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l8 15: l1 -> l1 : x_5^0'=1+x_5^3_1, [ 0<=-1+x_5^0 ], cost: 2 16: l1 -> l1 : x_5^0'=-1+x_5^3_2_1, [ 0<=-1+x_5^0 ], cost: 2 17: l1 -> l1 : x_5^0'=1+x_5^3_3_1, [ 0<=-1-x_5^0 ], cost: 2 18: l1 -> l1 : x_5^0'=-1+x_5^3_4_1, [ 0<=-1-x_5^0 ], cost: 2 14: l8 -> l1 : [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 15: l1 -> l1 : x_5^0'=1+x_5^3_1, [ 0<=-1+x_5^0 ], cost: 2 16: l1 -> l1 : x_5^0'=-1+x_5^3_2_1, [ 0<=-1+x_5^0 ], cost: 2 17: l1 -> l1 : x_5^0'=1+x_5^3_3_1, [ 0<=-1-x_5^0 ], cost: 2 18: l1 -> l1 : x_5^0'=-1+x_5^3_4_1, [ 0<=-1-x_5^0 ], cost: 2 [test] deduced pseudo-invariant -1+x_5^0-x_5^3_1<=0, also trying 1-x_5^0+x_5^3_1<=-1 Accelerated rule 15 with non-termination, yielding the new rule 19. Accelerated rule 15 with non-termination, yielding the new rule 20. Accelerated rule 15 with backward acceleration, yielding the new rule 21. [test] deduced pseudo-invariant 1-x_5^3_2_1+x_5^0<=0, also trying -1+x_5^3_2_1-x_5^0<=-1 Accelerated rule 16 with non-termination, yielding the new rule 22. Accelerated rule 16 with non-termination, yielding the new rule 23. Accelerated rule 16 with backward acceleration, yielding the new rule 24. [test] deduced pseudo-invariant 2+x_5^3_3_1<=0, also trying -2-x_5^3_3_1<=-1 Accelerated rule 17 with non-termination, yielding the new rule 25. Accelerated rule 17 with non-termination, yielding the new rule 26. Accelerated rule 17 with backward acceleration, yielding the new rule 27. [test] deduced pseudo-invariant -1-x_5^0+x_5^3_4_1<=0, also trying 1+x_5^0-x_5^3_4_1<=-1 Accelerated rule 18 with non-termination, yielding the new rule 28. Accelerated rule 18 with non-termination, yielding the new rule 29. Accelerated rule 18 with backward acceleration, yielding the new rule 30. [accelerate] Nesting with 0 inner and 4 outer candidates Also removing duplicate rules: 20 23 26 29. Accelerated all simple loops using metering functions (where possible): Start location: l8 15: l1 -> l1 : x_5^0'=1+x_5^3_1, [ 0<=-1+x_5^0 ], cost: 2 16: l1 -> l1 : x_5^0'=-1+x_5^3_2_1, [ 0<=-1+x_5^0 ], cost: 2 17: l1 -> l1 : x_5^0'=1+x_5^3_3_1, [ 0<=-1-x_5^0 ], cost: 2 18: l1 -> l1 : x_5^0'=-1+x_5^3_4_1, [ 0<=-1-x_5^0 ], cost: 2 19: l1 -> [9] : [ 0<=-1+x_5^0 && 0<=x_5^3_1 ], cost: NONTERM 21: l1 -> [9] : [ 0<=-1+x_5^0 && -1+x_5^0-x_5^3_1<=0 ], cost: NONTERM 22: l1 -> [9] : [ 0<=-1+x_5^0 && 0<=-2+x_5^3_2_1 ], cost: NONTERM 24: l1 -> [9] : [ 0<=-1+x_5^0 && 1-x_5^3_2_1+x_5^0<=0 ], cost: NONTERM 25: l1 -> [9] : [ 0<=-1-x_5^0 && 0<=-2-x_5^3_3_1 ], cost: NONTERM 27: l1 -> [9] : [ 0<=-1-x_5^0 && 2+x_5^3_3_1<=0 ], cost: NONTERM 28: l1 -> [9] : [ 0<=-1-x_5^0 && 0<=-x_5^3_4_1 ], cost: NONTERM 30: l1 -> [9] : [ 0<=-1-x_5^0 && -1-x_5^0+x_5^3_4_1<=0 ], cost: NONTERM 14: l8 -> l1 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l8 14: l8 -> l1 : [], cost: 2 31: l8 -> l1 : x_5^0'=1+x_5^3_1, [ 0<=-1+x_5^0 ], cost: 4 32: l8 -> l1 : x_5^0'=-1+x_5^3_2_1, [ 0<=-1+x_5^0 ], cost: 4 33: l8 -> l1 : x_5^0'=1+x_5^3_3_1, [ 0<=-1-x_5^0 ], cost: 4 34: l8 -> l1 : x_5^0'=-1+x_5^3_4_1, [ 0<=-1-x_5^0 ], cost: 4 35: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 36: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 37: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 38: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 39: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM 40: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM 41: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM 42: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l8 35: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 36: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 37: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 38: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 39: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM 40: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM 41: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM 42: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l8 38: l8 -> [9] : [ 0<=-1+x_5^0 ], cost: NONTERM 42: l8 -> [9] : [ 0<=-1-x_5^0 ], cost: NONTERM Computing asymptotic complexity for rule 38 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 ] NO