WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l9 0: l0 -> l1 : N^0'=N^post_1, choice^0'=choice^post_1, i^0'=i^post_1, pos^0'=pos^post_1, seq^0'=seq^post_1, walker^0'=walker^post_1, z^0'=z^post_1, [ N^0==N^post_1 && choice^0==choice^post_1 && i^0==i^post_1 && pos^0==pos^post_1 && seq^0==seq^post_1 && walker^0==walker^post_1 && z^0==z^post_1 ], cost: 1 1: l2 -> l3 : N^0'=N^post_2, choice^0'=choice^post_2, i^0'=i^post_2, pos^0'=pos^post_2, seq^0'=seq^post_2, walker^0'=walker^post_2, z^0'=z^post_2, [ 1<=choice^0 && walker^post_2==1+walker^0 && N^0==N^post_2 && choice^0==choice^post_2 && i^0==i^post_2 && pos^0==pos^post_2 && seq^0==seq^post_2 && z^0==z^post_2 ], cost: 1 2: l2 -> l3 : N^0'=N^post_3, choice^0'=choice^post_3, i^0'=i^post_3, pos^0'=pos^post_3, seq^0'=seq^post_3, walker^0'=walker^post_3, z^0'=z^post_3, [ choice^0<=0 && walker^post_3==-1+walker^0 && N^0==N^post_3 && choice^0==choice^post_3 && i^0==i^post_3 && pos^0==pos^post_3 && seq^0==seq^post_3 && z^0==z^post_3 ], cost: 1 12: l3 -> l8 : N^0'=N^post_13, choice^0'=choice^post_13, i^0'=i^post_13, pos^0'=pos^post_13, seq^0'=seq^post_13, walker^0'=walker^post_13, z^0'=z^post_13, [ N^0==N^post_13 && choice^0==choice^post_13 && i^0==i^post_13 && pos^0==pos^post_13 && seq^0==seq^post_13 && walker^0==walker^post_13 && z^0==z^post_13 ], cost: 1 3: l4 -> l3 : N^0'=N^post_4, choice^0'=choice^post_4, i^0'=i^post_4, pos^0'=pos^post_4, seq^0'=seq^post_4, walker^0'=walker^post_4, z^0'=z^post_4, [ seq^post_4==1 && i^post_4==seq^post_4 && z^post_4==z^post_4 && 0<=z^post_4 && pos^post_4==0 && N^post_4==N^post_4 && N^post_4<=2 && 2<=N^post_4 && walker^post_4==1 && choice^0==choice^post_4 ], cost: 1 4: l5 -> l2 : N^0'=N^post_5, choice^0'=choice^post_5, i^0'=i^post_5, pos^0'=pos^post_5, seq^0'=seq^post_5, walker^0'=walker^post_5, z^0'=z^post_5, [ i^0<=0 && seq^post_5==1+seq^0 && i^post_5==seq^post_5 && z^post_5==z^post_5 && 0<=z^post_5 && N^0==N^post_5 && choice^0==choice^post_5 && pos^0==pos^post_5 && walker^0==walker^post_5 ], cost: 1 5: l5 -> l2 : N^0'=N^post_6, choice^0'=choice^post_6, i^0'=i^post_6, pos^0'=pos^post_6, seq^0'=seq^post_6, walker^0'=walker^post_6, z^0'=z^post_6, [ 1<=i^0 && choice^0<=0 && i^post_6==-1+i^0 && N^0==N^post_6 && choice^0==choice^post_6 && pos^0==pos^post_6 && seq^0==seq^post_6 && walker^0==walker^post_6 && z^0==z^post_6 ], cost: 1 6: l6 -> l2 : N^0'=N^post_7, choice^0'=choice^post_7, i^0'=i^post_7, pos^0'=pos^post_7, seq^0'=seq^post_7, walker^0'=walker^post_7, z^0'=z^post_7, [ 1<=z^0 && z^post_7==-1+z^0 && N^0==N^post_7 && choice^0==choice^post_7 && i^0==i^post_7 && pos^0==pos^post_7 && seq^0==seq^post_7 && walker^0==walker^post_7 ], cost: 1 7: l6 -> l5 : N^0'=N^post_8, choice^0'=choice^post_8, i^0'=i^post_8, pos^0'=pos^post_8, seq^0'=seq^post_8, walker^0'=walker^post_8, z^0'=z^post_8, [ z^0<=0 && N^0==N^post_8 && choice^0==choice^post_8 && i^0==i^post_8 && pos^0==pos^post_8 && seq^0==seq^post_8 && walker^0==walker^post_8 && z^0==z^post_8 ], cost: 1 8: l7 -> l0 : N^0'=N^post_9, choice^0'=choice^post_9, i^0'=i^post_9, pos^0'=pos^post_9, seq^0'=seq^post_9, walker^0'=walker^post_9, z^0'=z^post_9, [ 1+walker^0<=1 && N^0==N^post_9 && choice^0==choice^post_9 && i^0==i^post_9 && pos^0==pos^post_9 && seq^0==seq^post_9 && walker^0==walker^post_9 && z^0==z^post_9 ], cost: 1 9: l7 -> l6 : N^0'=N^post_10, choice^0'=choice^post_10, i^0'=i^post_10, pos^0'=pos^post_10, seq^0'=seq^post_10, walker^0'=walker^post_10, z^0'=z^post_10, [ 1<=walker^0 && choice^post_10==choice^post_10 && 0<=choice^post_10 && choice^post_10<=1 && N^0==N^post_10 && i^0==i^post_10 && pos^0==pos^post_10 && seq^0==seq^post_10 && walker^0==walker^post_10 && z^0==z^post_10 ], cost: 1 10: l8 -> l0 : N^0'=N^post_11, choice^0'=choice^post_11, i^0'=i^post_11, pos^0'=pos^post_11, seq^0'=seq^post_11, walker^0'=walker^post_11, z^0'=z^post_11, [ 1+N^0<=walker^0 && N^0==N^post_11 && choice^0==choice^post_11 && i^0==i^post_11 && pos^0==pos^post_11 && seq^0==seq^post_11 && walker^0==walker^post_11 && z^0==z^post_11 ], cost: 1 11: l8 -> l7 : N^0'=N^post_12, choice^0'=choice^post_12, i^0'=i^post_12, pos^0'=pos^post_12, seq^0'=seq^post_12, walker^0'=walker^post_12, z^0'=z^post_12, [ walker^0<=N^0 && N^0==N^post_12 && choice^0==choice^post_12 && i^0==i^post_12 && pos^0==pos^post_12 && seq^0==seq^post_12 && walker^0==walker^post_12 && z^0==z^post_12 ], cost: 1 13: l9 -> l4 : N^0'=N^post_14, choice^0'=choice^post_14, i^0'=i^post_14, pos^0'=pos^post_14, seq^0'=seq^post_14, walker^0'=walker^post_14, z^0'=z^post_14, [ N^0==N^post_14 && choice^0==choice^post_14 && i^0==i^post_14 && pos^0==pos^post_14 && seq^0==seq^post_14 && walker^0==walker^post_14 && z^0==z^post_14 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 13: l9 -> l4 : N^0'=N^post_14, choice^0'=choice^post_14, i^0'=i^post_14, pos^0'=pos^post_14, seq^0'=seq^post_14, walker^0'=walker^post_14, z^0'=z^post_14, [ N^0==N^post_14 && choice^0==choice^post_14 && i^0==i^post_14 && pos^0==pos^post_14 && seq^0==seq^post_14 && walker^0==walker^post_14 && z^0==z^post_14 ], cost: 1 Removed unreachable and leaf rules: Start location: l9 1: l2 -> l3 : N^0'=N^post_2, choice^0'=choice^post_2, i^0'=i^post_2, pos^0'=pos^post_2, seq^0'=seq^post_2, walker^0'=walker^post_2, z^0'=z^post_2, [ 1<=choice^0 && walker^post_2==1+walker^0 && N^0==N^post_2 && choice^0==choice^post_2 && i^0==i^post_2 && pos^0==pos^post_2 && seq^0==seq^post_2 && z^0==z^post_2 ], cost: 1 2: l2 -> l3 : N^0'=N^post_3, choice^0'=choice^post_3, i^0'=i^post_3, pos^0'=pos^post_3, seq^0'=seq^post_3, walker^0'=walker^post_3, z^0'=z^post_3, [ choice^0<=0 && walker^post_3==-1+walker^0 && N^0==N^post_3 && choice^0==choice^post_3 && i^0==i^post_3 && pos^0==pos^post_3 && seq^0==seq^post_3 && z^0==z^post_3 ], cost: 1 12: l3 -> l8 : N^0'=N^post_13, choice^0'=choice^post_13, i^0'=i^post_13, pos^0'=pos^post_13, seq^0'=seq^post_13, walker^0'=walker^post_13, z^0'=z^post_13, [ N^0==N^post_13 && choice^0==choice^post_13 && i^0==i^post_13 && pos^0==pos^post_13 && seq^0==seq^post_13 && walker^0==walker^post_13 && z^0==z^post_13 ], cost: 1 3: l4 -> l3 : N^0'=N^post_4, choice^0'=choice^post_4, i^0'=i^post_4, pos^0'=pos^post_4, seq^0'=seq^post_4, walker^0'=walker^post_4, z^0'=z^post_4, [ seq^post_4==1 && i^post_4==seq^post_4 && z^post_4==z^post_4 && 0<=z^post_4 && pos^post_4==0 && N^post_4==N^post_4 && N^post_4<=2 && 2<=N^post_4 && walker^post_4==1 && choice^0==choice^post_4 ], cost: 1 4: l5 -> l2 : N^0'=N^post_5, choice^0'=choice^post_5, i^0'=i^post_5, pos^0'=pos^post_5, seq^0'=seq^post_5, walker^0'=walker^post_5, z^0'=z^post_5, [ i^0<=0 && seq^post_5==1+seq^0 && i^post_5==seq^post_5 && z^post_5==z^post_5 && 0<=z^post_5 && N^0==N^post_5 && choice^0==choice^post_5 && pos^0==pos^post_5 && walker^0==walker^post_5 ], cost: 1 5: l5 -> l2 : N^0'=N^post_6, choice^0'=choice^post_6, i^0'=i^post_6, pos^0'=pos^post_6, seq^0'=seq^post_6, walker^0'=walker^post_6, z^0'=z^post_6, [ 1<=i^0 && choice^0<=0 && i^post_6==-1+i^0 && N^0==N^post_6 && choice^0==choice^post_6 && pos^0==pos^post_6 && seq^0==seq^post_6 && walker^0==walker^post_6 && z^0==z^post_6 ], cost: 1 6: l6 -> l2 : N^0'=N^post_7, choice^0'=choice^post_7, i^0'=i^post_7, pos^0'=pos^post_7, seq^0'=seq^post_7, walker^0'=walker^post_7, z^0'=z^post_7, [ 1<=z^0 && z^post_7==-1+z^0 && N^0==N^post_7 && choice^0==choice^post_7 && i^0==i^post_7 && pos^0==pos^post_7 && seq^0==seq^post_7 && walker^0==walker^post_7 ], cost: 1 7: l6 -> l5 : N^0'=N^post_8, choice^0'=choice^post_8, i^0'=i^post_8, pos^0'=pos^post_8, seq^0'=seq^post_8, walker^0'=walker^post_8, z^0'=z^post_8, [ z^0<=0 && N^0==N^post_8 && choice^0==choice^post_8 && i^0==i^post_8 && pos^0==pos^post_8 && seq^0==seq^post_8 && walker^0==walker^post_8 && z^0==z^post_8 ], cost: 1 9: l7 -> l6 : N^0'=N^post_10, choice^0'=choice^post_10, i^0'=i^post_10, pos^0'=pos^post_10, seq^0'=seq^post_10, walker^0'=walker^post_10, z^0'=z^post_10, [ 1<=walker^0 && choice^post_10==choice^post_10 && 0<=choice^post_10 && choice^post_10<=1 && N^0==N^post_10 && i^0==i^post_10 && pos^0==pos^post_10 && seq^0==seq^post_10 && walker^0==walker^post_10 && z^0==z^post_10 ], cost: 1 11: l8 -> l7 : N^0'=N^post_12, choice^0'=choice^post_12, i^0'=i^post_12, pos^0'=pos^post_12, seq^0'=seq^post_12, walker^0'=walker^post_12, z^0'=z^post_12, [ walker^0<=N^0 && N^0==N^post_12 && choice^0==choice^post_12 && i^0==i^post_12 && pos^0==pos^post_12 && seq^0==seq^post_12 && walker^0==walker^post_12 && z^0==z^post_12 ], cost: 1 13: l9 -> l4 : N^0'=N^post_14, choice^0'=choice^post_14, i^0'=i^post_14, pos^0'=pos^post_14, seq^0'=seq^post_14, walker^0'=walker^post_14, z^0'=z^post_14, [ N^0==N^post_14 && choice^0==choice^post_14 && i^0==i^post_14 && pos^0==pos^post_14 && seq^0==seq^post_14 && walker^0==walker^post_14 && z^0==z^post_14 ], cost: 1 Simplified all rules, resulting in: Start location: l9 1: l2 -> l3 : walker^0'=1+walker^0, [ 1<=choice^0 ], cost: 1 2: l2 -> l3 : walker^0'=-1+walker^0, [ choice^0<=0 ], cost: 1 12: l3 -> l8 : [], cost: 1 3: l4 -> l3 : N^0'=2, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1, z^0'=z^post_4, [ 0<=z^post_4 ], cost: 1 4: l5 -> l2 : i^0'=1+seq^0, seq^0'=1+seq^0, z^0'=z^post_5, [ i^0<=0 && 0<=z^post_5 ], cost: 1 5: l5 -> l2 : i^0'=-1+i^0, [ 1<=i^0 && choice^0<=0 ], cost: 1 6: l6 -> l2 : z^0'=-1+z^0, [ 1<=z^0 ], cost: 1 7: l6 -> l5 : [ z^0<=0 ], cost: 1 9: l7 -> l6 : choice^0'=choice^post_10, [ 1<=walker^0 && 0<=choice^post_10 && choice^post_10<=1 ], cost: 1 11: l8 -> l7 : [ walker^0<=N^0 ], cost: 1 13: l9 -> l4 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l9 1: l2 -> l3 : walker^0'=1+walker^0, [ 1<=choice^0 ], cost: 1 2: l2 -> l3 : walker^0'=-1+walker^0, [ choice^0<=0 ], cost: 1 16: l3 -> l6 : choice^0'=choice^post_10, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && choice^post_10<=1 ], cost: 3 4: l5 -> l2 : i^0'=1+seq^0, seq^0'=1+seq^0, z^0'=z^post_5, [ i^0<=0 && 0<=z^post_5 ], cost: 1 5: l5 -> l2 : i^0'=-1+i^0, [ 1<=i^0 && choice^0<=0 ], cost: 1 6: l6 -> l2 : z^0'=-1+z^0, [ 1<=z^0 ], cost: 1 7: l6 -> l5 : [ z^0<=0 ], cost: 1 14: l9 -> l3 : N^0'=2, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1, z^0'=z^post_4, [ 0<=z^post_4 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l9 1: l2 -> l3 : walker^0'=1+walker^0, [ 1<=choice^0 ], cost: 1 2: l2 -> l3 : walker^0'=-1+walker^0, [ choice^0<=0 ], cost: 1 17: l3 -> l2 : choice^0'=choice^post_10, z^0'=-1+z^0, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && choice^post_10<=1 && 1<=z^0 ], cost: 4 18: l3 -> l5 : choice^0'=choice^post_10, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && choice^post_10<=1 && z^0<=0 ], cost: 4 4: l5 -> l2 : i^0'=1+seq^0, seq^0'=1+seq^0, z^0'=z^post_5, [ i^0<=0 && 0<=z^post_5 ], cost: 1 5: l5 -> l2 : i^0'=-1+i^0, [ 1<=i^0 && choice^0<=0 ], cost: 1 14: l9 -> l3 : N^0'=2, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1, z^0'=z^post_4, [ 0<=z^post_4 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l9 1: l2 -> l3 : walker^0'=1+walker^0, [ 1<=choice^0 ], cost: 1 2: l2 -> l3 : walker^0'=-1+walker^0, [ choice^0<=0 ], cost: 1 17: l3 -> l2 : choice^0'=choice^post_10, z^0'=-1+z^0, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && choice^post_10<=1 && 1<=z^0 ], cost: 4 19: l3 -> l2 : choice^0'=choice^post_10, i^0'=1+seq^0, seq^0'=1+seq^0, z^0'=z^post_5, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && choice^post_10<=1 && z^0<=0 && i^0<=0 && 0<=z^post_5 ], cost: 5 20: l3 -> l2 : choice^0'=choice^post_10, i^0'=-1+i^0, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && z^0<=0 && 1<=i^0 && choice^post_10<=0 ], cost: 5 14: l9 -> l3 : N^0'=2, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1, z^0'=z^post_4, [ 0<=z^post_4 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l9 21: l3 -> l3 : choice^0'=choice^post_10, walker^0'=1+walker^0, z^0'=-1+z^0, [ walker^0<=N^0 && 1<=walker^0 && choice^post_10<=1 && 1<=z^0 && 1<=choice^post_10 ], cost: 5 22: l3 -> l3 : choice^0'=choice^post_10, walker^0'=-1+walker^0, z^0'=-1+z^0, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && 1<=z^0 && choice^post_10<=0 ], cost: 5 23: l3 -> l3 : choice^0'=choice^post_10, i^0'=1+seq^0, seq^0'=1+seq^0, walker^0'=1+walker^0, z^0'=z^post_5, [ walker^0<=N^0 && 1<=walker^0 && choice^post_10<=1 && z^0<=0 && i^0<=0 && 0<=z^post_5 && 1<=choice^post_10 ], cost: 6 24: l3 -> l3 : choice^0'=choice^post_10, i^0'=1+seq^0, seq^0'=1+seq^0, walker^0'=-1+walker^0, z^0'=z^post_5, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && z^0<=0 && i^0<=0 && 0<=z^post_5 && choice^post_10<=0 ], cost: 6 25: l3 -> l3 : choice^0'=choice^post_10, i^0'=-1+i^0, walker^0'=-1+walker^0, [ walker^0<=N^0 && 1<=walker^0 && 0<=choice^post_10 && z^0<=0 && 1<=i^0 && choice^post_10<=0 ], cost: 6 14: l9 -> l3 : N^0'=2, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1, z^0'=z^post_4, [ 0<=z^post_4 ], cost: 2 Accelerating simple loops of location 3. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 21: l3 -> l3 : choice^0'=1, walker^0'=1+walker^0, z^0'=-1+z^0, [ walker^0<=N^0 && 1<=walker^0 && 1<=z^0 ], cost: 5 22: l3 -> l3 : choice^0'=0, walker^0'=-1+walker^0, z^0'=-1+z^0, [ walker^0<=N^0 && 1<=walker^0 && 1<=z^0 ], cost: 5 23: l3 -> l3 : choice^0'=1, i^0'=1+seq^0, seq^0'=1+seq^0, walker^0'=1+walker^0, z^0'=z^post_5, [ walker^0<=N^0 && 1<=walker^0 && z^0<=0 && i^0<=0 && 0<=z^post_5 ], cost: 6 24: l3 -> l3 : choice^0'=0, i^0'=1+seq^0, seq^0'=1+seq^0, walker^0'=-1+walker^0, z^0'=z^post_5, [ walker^0<=N^0 && 1<=walker^0 && z^0<=0 && i^0<=0 && 0<=z^post_5 ], cost: 6 25: l3 -> l3 : choice^0'=0, i^0'=-1+i^0, walker^0'=-1+walker^0, [ walker^0<=N^0 && 1<=walker^0 && z^0<=0 && 1<=i^0 ], cost: 6 Accelerated rule 21 with backward acceleration, yielding the new rule 26. Accelerated rule 21 with backward acceleration, yielding the new rule 27. Accelerated rule 22 with backward acceleration, yielding the new rule 28. Accelerated rule 22 with backward acceleration, yielding the new rule 29. Failed to prove monotonicity of the guard of rule 23. Failed to prove monotonicity of the guard of rule 24. Accelerated rule 25 with backward acceleration, yielding the new rule 30. Accelerated rule 25 with backward acceleration, yielding the new rule 31. [accelerate] Nesting with 8 inner and 5 outer candidates Removing the simple loops: 21 22 25. Accelerated all simple loops using metering functions (where possible): Start location: l9 23: l3 -> l3 : choice^0'=1, i^0'=1+seq^0, seq^0'=1+seq^0, walker^0'=1+walker^0, z^0'=z^post_5, [ walker^0<=N^0 && 1<=walker^0 && z^0<=0 && i^0<=0 && 0<=z^post_5 ], cost: 6 24: l3 -> l3 : choice^0'=0, i^0'=1+seq^0, seq^0'=1+seq^0, walker^0'=-1+walker^0, z^0'=z^post_5, [ walker^0<=N^0 && 1<=walker^0 && z^0<=0 && i^0<=0 && 0<=z^post_5 ], cost: 6 26: l3 -> l3 : choice^0'=1, walker^0'=1+N^0, z^0'=-1+walker^0+z^0-N^0, [ 1<=walker^0 && 1-walker^0+N^0>=1 && 1<=walker^0+z^0-N^0 ], cost: 5-5*walker^0+5*N^0 27: l3 -> l3 : choice^0'=1, walker^0'=walker^0+z^0, z^0'=0, [ 1<=walker^0 && z^0>=1 && -1+walker^0+z^0<=N^0 ], cost: 5*z^0 28: l3 -> l3 : choice^0'=0, walker^0'=0, z^0'=-walker^0+z^0, [ walker^0<=N^0 && walker^0>=1 && 1<=1-walker^0+z^0 ], cost: 5*walker^0 29: l3 -> l3 : choice^0'=0, walker^0'=walker^0-z^0, z^0'=0, [ walker^0<=N^0 && z^0>=1 && 1<=1+walker^0-z^0 ], cost: 5*z^0 30: l3 -> l3 : choice^0'=0, i^0'=-walker^0+i^0, walker^0'=0, [ walker^0<=N^0 && z^0<=0 && walker^0>=1 && 1<=1-walker^0+i^0 ], cost: 6*walker^0 31: l3 -> l3 : choice^0'=0, i^0'=0, walker^0'=walker^0-i^0, [ walker^0<=N^0 && z^0<=0 && i^0>=1 && 1<=1+walker^0-i^0 ], cost: 6*i^0 14: l9 -> l3 : N^0'=2, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1, z^0'=z^post_4, [ 0<=z^post_4 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: l9 14: l9 -> l3 : N^0'=2, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1, z^0'=z^post_4, [ 0<=z^post_4 ], cost: 2 32: l9 -> l3 : N^0'=2, choice^0'=1, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=3, z^0'=-2+z^post_4, [ 1<=-1+z^post_4 ], cost: 12 33: l9 -> l3 : N^0'=2, choice^0'=1, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1+z^post_4, z^0'=0, [ z^post_4>=1 && z^post_4<=2 ], cost: 2+5*z^post_4 34: l9 -> l3 : N^0'=2, choice^0'=0, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=0, z^0'=-1+z^post_4, [ 1<=z^post_4 ], cost: 7 35: l9 -> l3 : N^0'=2, choice^0'=0, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=0, z^0'=0, [], cost: 7 36: l9 -> l3 : N^0'=2, choice^0'=0, i^0'=0, pos^0'=0, seq^0'=1, walker^0'=0, z^0'=0, [], cost: 8 37: l9 -> l3 : N^0'=2, choice^0'=0, i^0'=0, pos^0'=0, seq^0'=1, walker^0'=0, z^0'=0, [], cost: 8 Removed unreachable locations (and leaf rules with constant cost): Start location: l9 33: l9 -> l3 : N^0'=2, choice^0'=1, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1+z^post_4, z^0'=0, [ z^post_4>=1 && z^post_4<=2 ], cost: 2+5*z^post_4 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l9 33: l9 -> l3 : N^0'=2, choice^0'=1, i^0'=1, pos^0'=0, seq^0'=1, walker^0'=1+z^post_4, z^0'=0, [ z^post_4>=1 && z^post_4<=2 ], cost: 2+5*z^post_4 Computing asymptotic complexity for rule 33 Resulting cost 0 has complexity: Unknown Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [ N^0==N^post_14 && choice^0==choice^post_14 && i^0==i^post_14 && pos^0==pos^post_14 && seq^0==seq^post_14 && walker^0==walker^post_14 && z^0==z^post_14 ] WORST_CASE(Omega(1),?)