NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l9 0: l0 -> l1 : a4^0'=a4^post_1, a^0'=a^post_1, answer^0'=answer^post_1, b5^0'=b5^post_1, b^0'=b^post_1, ret_complex6^0'=ret_complex6^post_1, [ 30<=a4^0 && ret_complex6^post_1==1 && answer^post_1==ret_complex6^post_1 && a^0==a^post_1 && a4^0==a4^post_1 && b^0==b^post_1 && b5^0==b5^post_1 ], cost: 1 1: l0 -> l2 : a4^0'=a4^post_2, a^0'=a^post_2, answer^0'=answer^post_2, b5^0'=b5^post_2, b^0'=b^post_2, ret_complex6^0'=ret_complex6^post_2, [ 1+a4^0<=30 && a^0==a^post_2 && a4^0==a4^post_2 && answer^0==answer^post_2 && b^0==b^post_2 && b5^0==b5^post_2 && ret_complex6^0==ret_complex6^post_2 ], cost: 1 3: l2 -> l4 : a4^0'=a4^post_4, a^0'=a^post_4, answer^0'=answer^post_4, b5^0'=b5^post_4, b^0'=b^post_4, ret_complex6^0'=ret_complex6^post_4, [ a^0==a^post_4 && a4^0==a4^post_4 && answer^0==answer^post_4 && b^0==b^post_4 && b5^0==b5^post_4 && ret_complex6^0==ret_complex6^post_4 ], cost: 1 2: l3 -> l0 : a4^0'=a4^post_3, a^0'=a^post_3, answer^0'=answer^post_3, b5^0'=b5^post_3, b^0'=b^post_3, ret_complex6^0'=ret_complex6^post_3, [ a^0==a^post_3 && a4^0==a4^post_3 && answer^0==answer^post_3 && b^0==b^post_3 && b5^0==b5^post_3 && ret_complex6^0==ret_complex6^post_3 ], cost: 1 10: l4 -> l3 : a4^0'=a4^post_11, a^0'=a^post_11, answer^0'=answer^post_11, b5^0'=b5^post_11, b^0'=b^post_11, ret_complex6^0'=ret_complex6^post_11, [ a4^0<=b5^0 && a4^post_11==2+a4^0 && b5^post_11==-10+b5^0 && a^0==a^post_11 && answer^0==answer^post_11 && b^0==b^post_11 && ret_complex6^0==ret_complex6^post_11 ], cost: 1 11: l4 -> l7 : a4^0'=a4^post_12, a^0'=a^post_12, answer^0'=answer^post_12, b5^0'=b5^post_12, b^0'=b^post_12, ret_complex6^0'=ret_complex6^post_12, [ 1+b5^0<=a4^0 && a^0==a^post_12 && a4^0==a4^post_12 && answer^0==answer^post_12 && b^0==b^post_12 && b5^0==b5^post_12 && ret_complex6^0==ret_complex6^post_12 ], cost: 1 4: l5 -> l2 : a4^0'=a4^post_5, a^0'=a^post_5, answer^0'=answer^post_5, b5^0'=b5^post_5, b^0'=b^post_5, ret_complex6^0'=ret_complex6^post_5, [ 13<=b5^0 && a4^post_5==1+a4^0 && a^0==a^post_5 && answer^0==answer^post_5 && b^0==b^post_5 && b5^0==b5^post_5 && ret_complex6^0==ret_complex6^post_5 ], cost: 1 5: l5 -> l2 : a4^0'=a4^post_6, a^0'=a^post_6, answer^0'=answer^post_6, b5^0'=b5^post_6, b^0'=b^post_6, ret_complex6^0'=ret_complex6^post_6, [ b5^0<=12 && a4^post_6==10+a4^0 && a^0==a^post_6 && answer^0==answer^post_6 && b^0==b^post_6 && b5^0==b5^post_6 && ret_complex6^0==ret_complex6^post_6 ], cost: 1 6: l6 -> l2 : a4^0'=a4^post_7, a^0'=a^post_7, answer^0'=answer^post_7, b5^0'=b5^post_7, b^0'=b^post_7, ret_complex6^0'=ret_complex6^post_7, [ 1+b5^0<=10 && a4^post_7==1+a4^0 && a^0==a^post_7 && answer^0==answer^post_7 && b^0==b^post_7 && b5^0==b5^post_7 && ret_complex6^0==ret_complex6^post_7 ], cost: 1 7: l6 -> l5 : a4^0'=a4^post_8, a^0'=a^post_8, answer^0'=answer^post_8, b5^0'=b5^post_8, b^0'=b^post_8, ret_complex6^0'=ret_complex6^post_8, [ 10<=b5^0 && a^0==a^post_8 && a4^0==a4^post_8 && answer^0==answer^post_8 && b^0==b^post_8 && b5^0==b5^post_8 && ret_complex6^0==ret_complex6^post_8 ], cost: 1 8: l7 -> l6 : a4^0'=a4^post_9, a^0'=a^post_9, answer^0'=answer^post_9, b5^0'=b5^post_9, b^0'=b^post_9, ret_complex6^0'=ret_complex6^post_9, [ b5^0<=5 && b5^post_9==2+b5^0 && a^0==a^post_9 && a4^0==a4^post_9 && answer^0==answer^post_9 && b^0==b^post_9 && ret_complex6^0==ret_complex6^post_9 ], cost: 1 9: l7 -> l6 : a4^0'=a4^post_10, a^0'=a^post_10, answer^0'=answer^post_10, b5^0'=b5^post_10, b^0'=b^post_10, ret_complex6^0'=ret_complex6^post_10, [ 6<=b5^0 && b5^post_10==b5^post_10 && a^0==a^post_10 && a4^0==a4^post_10 && answer^0==answer^post_10 && b^0==b^post_10 && ret_complex6^0==ret_complex6^post_10 ], cost: 1 12: l8 -> l3 : a4^0'=a4^post_13, a^0'=a^post_13, answer^0'=answer^post_13, b5^0'=b5^post_13, b^0'=b^post_13, ret_complex6^0'=ret_complex6^post_13, [ a^post_13==1 && b^post_13==1 && answer^post_13==0 && a4^post_13==a^post_13 && b5^post_13==b^post_13 && ret_complex6^0==ret_complex6^post_13 ], cost: 1 13: l9 -> l8 : a4^0'=a4^post_14, a^0'=a^post_14, answer^0'=answer^post_14, b5^0'=b5^post_14, b^0'=b^post_14, ret_complex6^0'=ret_complex6^post_14, [ a^0==a^post_14 && a4^0==a4^post_14 && answer^0==answer^post_14 && b^0==b^post_14 && b5^0==b5^post_14 && ret_complex6^0==ret_complex6^post_14 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 13: l9 -> l8 : a4^0'=a4^post_14, a^0'=a^post_14, answer^0'=answer^post_14, b5^0'=b5^post_14, b^0'=b^post_14, ret_complex6^0'=ret_complex6^post_14, [ a^0==a^post_14 && a4^0==a4^post_14 && answer^0==answer^post_14 && b^0==b^post_14 && b5^0==b5^post_14 && ret_complex6^0==ret_complex6^post_14 ], cost: 1 Removed unreachable and leaf rules: Start location: l9 1: l0 -> l2 : a4^0'=a4^post_2, a^0'=a^post_2, answer^0'=answer^post_2, b5^0'=b5^post_2, b^0'=b^post_2, ret_complex6^0'=ret_complex6^post_2, [ 1+a4^0<=30 && a^0==a^post_2 && a4^0==a4^post_2 && answer^0==answer^post_2 && b^0==b^post_2 && b5^0==b5^post_2 && ret_complex6^0==ret_complex6^post_2 ], cost: 1 3: l2 -> l4 : a4^0'=a4^post_4, a^0'=a^post_4, answer^0'=answer^post_4, b5^0'=b5^post_4, b^0'=b^post_4, ret_complex6^0'=ret_complex6^post_4, [ a^0==a^post_4 && a4^0==a4^post_4 && answer^0==answer^post_4 && b^0==b^post_4 && b5^0==b5^post_4 && ret_complex6^0==ret_complex6^post_4 ], cost: 1 2: l3 -> l0 : a4^0'=a4^post_3, a^0'=a^post_3, answer^0'=answer^post_3, b5^0'=b5^post_3, b^0'=b^post_3, ret_complex6^0'=ret_complex6^post_3, [ a^0==a^post_3 && a4^0==a4^post_3 && answer^0==answer^post_3 && b^0==b^post_3 && b5^0==b5^post_3 && ret_complex6^0==ret_complex6^post_3 ], cost: 1 10: l4 -> l3 : a4^0'=a4^post_11, a^0'=a^post_11, answer^0'=answer^post_11, b5^0'=b5^post_11, b^0'=b^post_11, ret_complex6^0'=ret_complex6^post_11, [ a4^0<=b5^0 && a4^post_11==2+a4^0 && b5^post_11==-10+b5^0 && a^0==a^post_11 && answer^0==answer^post_11 && b^0==b^post_11 && ret_complex6^0==ret_complex6^post_11 ], cost: 1 11: l4 -> l7 : a4^0'=a4^post_12, a^0'=a^post_12, answer^0'=answer^post_12, b5^0'=b5^post_12, b^0'=b^post_12, ret_complex6^0'=ret_complex6^post_12, [ 1+b5^0<=a4^0 && a^0==a^post_12 && a4^0==a4^post_12 && answer^0==answer^post_12 && b^0==b^post_12 && b5^0==b5^post_12 && ret_complex6^0==ret_complex6^post_12 ], cost: 1 4: l5 -> l2 : a4^0'=a4^post_5, a^0'=a^post_5, answer^0'=answer^post_5, b5^0'=b5^post_5, b^0'=b^post_5, ret_complex6^0'=ret_complex6^post_5, [ 13<=b5^0 && a4^post_5==1+a4^0 && a^0==a^post_5 && answer^0==answer^post_5 && b^0==b^post_5 && b5^0==b5^post_5 && ret_complex6^0==ret_complex6^post_5 ], cost: 1 5: l5 -> l2 : a4^0'=a4^post_6, a^0'=a^post_6, answer^0'=answer^post_6, b5^0'=b5^post_6, b^0'=b^post_6, ret_complex6^0'=ret_complex6^post_6, [ b5^0<=12 && a4^post_6==10+a4^0 && a^0==a^post_6 && answer^0==answer^post_6 && b^0==b^post_6 && b5^0==b5^post_6 && ret_complex6^0==ret_complex6^post_6 ], cost: 1 6: l6 -> l2 : a4^0'=a4^post_7, a^0'=a^post_7, answer^0'=answer^post_7, b5^0'=b5^post_7, b^0'=b^post_7, ret_complex6^0'=ret_complex6^post_7, [ 1+b5^0<=10 && a4^post_7==1+a4^0 && a^0==a^post_7 && answer^0==answer^post_7 && b^0==b^post_7 && b5^0==b5^post_7 && ret_complex6^0==ret_complex6^post_7 ], cost: 1 7: l6 -> l5 : a4^0'=a4^post_8, a^0'=a^post_8, answer^0'=answer^post_8, b5^0'=b5^post_8, b^0'=b^post_8, ret_complex6^0'=ret_complex6^post_8, [ 10<=b5^0 && a^0==a^post_8 && a4^0==a4^post_8 && answer^0==answer^post_8 && b^0==b^post_8 && b5^0==b5^post_8 && ret_complex6^0==ret_complex6^post_8 ], cost: 1 8: l7 -> l6 : a4^0'=a4^post_9, a^0'=a^post_9, answer^0'=answer^post_9, b5^0'=b5^post_9, b^0'=b^post_9, ret_complex6^0'=ret_complex6^post_9, [ b5^0<=5 && b5^post_9==2+b5^0 && a^0==a^post_9 && a4^0==a4^post_9 && answer^0==answer^post_9 && b^0==b^post_9 && ret_complex6^0==ret_complex6^post_9 ], cost: 1 9: l7 -> l6 : a4^0'=a4^post_10, a^0'=a^post_10, answer^0'=answer^post_10, b5^0'=b5^post_10, b^0'=b^post_10, ret_complex6^0'=ret_complex6^post_10, [ 6<=b5^0 && b5^post_10==b5^post_10 && a^0==a^post_10 && a4^0==a4^post_10 && answer^0==answer^post_10 && b^0==b^post_10 && ret_complex6^0==ret_complex6^post_10 ], cost: 1 12: l8 -> l3 : a4^0'=a4^post_13, a^0'=a^post_13, answer^0'=answer^post_13, b5^0'=b5^post_13, b^0'=b^post_13, ret_complex6^0'=ret_complex6^post_13, [ a^post_13==1 && b^post_13==1 && answer^post_13==0 && a4^post_13==a^post_13 && b5^post_13==b^post_13 && ret_complex6^0==ret_complex6^post_13 ], cost: 1 13: l9 -> l8 : a4^0'=a4^post_14, a^0'=a^post_14, answer^0'=answer^post_14, b5^0'=b5^post_14, b^0'=b^post_14, ret_complex6^0'=ret_complex6^post_14, [ a^0==a^post_14 && a4^0==a4^post_14 && answer^0==answer^post_14 && b^0==b^post_14 && b5^0==b5^post_14 && ret_complex6^0==ret_complex6^post_14 ], cost: 1 Simplified all rules, resulting in: Start location: l9 1: l0 -> l2 : [ 1+a4^0<=30 ], cost: 1 3: l2 -> l4 : [], cost: 1 2: l3 -> l0 : [], cost: 1 10: l4 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 1 11: l4 -> l7 : [ 1+b5^0<=a4^0 ], cost: 1 4: l5 -> l2 : a4^0'=1+a4^0, [ 13<=b5^0 ], cost: 1 5: l5 -> l2 : a4^0'=10+a4^0, [ b5^0<=12 ], cost: 1 6: l6 -> l2 : a4^0'=1+a4^0, [ 1+b5^0<=10 ], cost: 1 7: l6 -> l5 : [ 10<=b5^0 ], cost: 1 8: l7 -> l6 : b5^0'=2+b5^0, [ b5^0<=5 ], cost: 1 9: l7 -> l6 : b5^0'=b5^post_10, [ 6<=b5^0 ], cost: 1 12: l8 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 1 13: l9 -> l8 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l9 3: l2 -> l4 : [], cost: 1 15: l3 -> l2 : [ 1+a4^0<=30 ], cost: 2 10: l4 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 1 11: l4 -> l7 : [ 1+b5^0<=a4^0 ], cost: 1 4: l5 -> l2 : a4^0'=1+a4^0, [ 13<=b5^0 ], cost: 1 5: l5 -> l2 : a4^0'=10+a4^0, [ b5^0<=12 ], cost: 1 6: l6 -> l2 : a4^0'=1+a4^0, [ 1+b5^0<=10 ], cost: 1 7: l6 -> l5 : [ 10<=b5^0 ], cost: 1 8: l7 -> l6 : b5^0'=2+b5^0, [ b5^0<=5 ], cost: 1 9: l7 -> l6 : b5^0'=b5^post_10, [ 6<=b5^0 ], cost: 1 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l9 16: l2 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 2 17: l2 -> l7 : [ 1+b5^0<=a4^0 ], cost: 2 15: l3 -> l2 : [ 1+a4^0<=30 ], cost: 2 4: l5 -> l2 : a4^0'=1+a4^0, [ 13<=b5^0 ], cost: 1 5: l5 -> l2 : a4^0'=10+a4^0, [ b5^0<=12 ], cost: 1 18: l7 -> l2 : a4^0'=1+a4^0, b5^0'=2+b5^0, [ b5^0<=5 ], cost: 2 19: l7 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 6<=b5^0 && 1+b5^post_10<=10 ], cost: 2 20: l7 -> l5 : b5^0'=b5^post_10, [ 6<=b5^0 && 10<=b5^post_10 ], cost: 2 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l9 16: l2 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 2 21: l2 -> l2 : a4^0'=1+a4^0, b5^0'=2+b5^0, [ 1+b5^0<=a4^0 && b5^0<=5 ], cost: 4 22: l2 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 ], cost: 4 23: l2 -> l5 : b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 ], cost: 4 15: l3 -> l2 : [ 1+a4^0<=30 ], cost: 2 4: l5 -> l2 : a4^0'=1+a4^0, [ 13<=b5^0 ], cost: 1 5: l5 -> l2 : a4^0'=10+a4^0, [ b5^0<=12 ], cost: 1 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Accelerating simple loops of location 2. Accelerating the following rules: 21: l2 -> l2 : a4^0'=1+a4^0, b5^0'=2+b5^0, [ 1+b5^0<=a4^0 && b5^0<=5 ], cost: 4 22: l2 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 ], cost: 4 Accelerated rule 21 with backward acceleration, yielding the new rule 24. Accelerated rule 22 with non-termination, yielding the new rule 25. [accelerate] Nesting with 1 inner and 2 outer candidates Removing the simple loops: 21. Accelerated all simple loops using metering functions (where possible): Start location: l9 16: l2 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 2 22: l2 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 ], cost: 4 23: l2 -> l5 : b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 ], cost: 4 24: l2 -> l2 : a4^0'=k+a4^0, b5^0'=2*k+b5^0, [ k>=0 && -1+2*k+b5^0<=-1+k+a4^0 && -2+2*k+b5^0<=5 ], cost: 4*k 25: l2 -> [10] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 && 1+b5^post_10<=1+a4^0 && 6<=b5^post_10 ], cost: NONTERM 15: l3 -> l2 : [ 1+a4^0<=30 ], cost: 2 4: l5 -> l2 : a4^0'=1+a4^0, [ 13<=b5^0 ], cost: 1 5: l5 -> l2 : a4^0'=10+a4^0, [ b5^0<=12 ], cost: 1 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l9 16: l2 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 2 23: l2 -> l5 : b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 ], cost: 4 15: l3 -> l2 : [ 1+a4^0<=30 ], cost: 2 28: l3 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 ], cost: 6 30: l3 -> l2 : a4^0'=k+a4^0, b5^0'=2*k+b5^0, [ 1+a4^0<=30 && k>=0 && -1+2*k+b5^0<=-1+k+a4^0 && -2+2*k+b5^0<=5 ], cost: 2+4*k 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 4: l5 -> l2 : a4^0'=1+a4^0, [ 13<=b5^0 ], cost: 1 5: l5 -> l2 : a4^0'=10+a4^0, [ b5^0<=12 ], cost: 1 26: l5 -> l2 : a4^0'=2+a4^0, b5^0'=b5^post_10, [ 13<=b5^0 && 1+b5^0<=1+a4^0 && 1+b5^post_10<=10 ], cost: 5 27: l5 -> l2 : a4^0'=11+a4^0, b5^0'=b5^post_10, [ b5^0<=12 && 1+b5^0<=10+a4^0 && 6<=b5^0 && 1+b5^post_10<=10 ], cost: 5 29: l5 -> l2 : a4^0'=10+k+a4^0, b5^0'=2*k+b5^0, [ b5^0<=12 && k>=0 && -1+2*k+b5^0<=9+k+a4^0 && -2+2*k+b5^0<=5 ], cost: 1+4*k 31: l5 -> [10] : [ 13<=b5^0 && 1+b5^0<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 32: l5 -> [10] : [ b5^0<=12 && 1+b5^0<=10+a4^0 && 6<=b5^0 && 6<=10+a4^0 ], cost: NONTERM 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l9 16: l2 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 2 34: l2 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 ], cost: 5 35: l2 -> l2 : a4^0'=10+a4^0, b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 ], cost: 5 36: l2 -> [10] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 37: l2 -> [10] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+a4^0 && 6<=10+a4^0 ], cost: NONTERM 15: l3 -> l2 : [ 1+a4^0<=30 ], cost: 2 28: l3 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 ], cost: 6 30: l3 -> l2 : a4^0'=k+a4^0, b5^0'=2*k+b5^0, [ 1+a4^0<=30 && k>=0 && -1+2*k+b5^0<=-1+k+a4^0 && -2+2*k+b5^0<=5 ], cost: 2+4*k 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Accelerating simple loops of location 2. Accelerating the following rules: 34: l2 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 ], cost: 5 35: l2 -> l2 : a4^0'=10+a4^0, b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 ], cost: 5 Accelerated rule 34 with non-termination, yielding the new rule 38. Accelerated rule 35 with non-termination, yielding the new rule 39. [accelerate] Nesting with 0 inner and 1 outer candidates Removing the simple loops: 35. Accelerated all simple loops using metering functions (where possible): Start location: l9 16: l2 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 2 34: l2 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 ], cost: 5 36: l2 -> [10] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 37: l2 -> [10] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+a4^0 && 6<=10+a4^0 ], cost: NONTERM 38: l2 -> [11] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 ], cost: NONTERM 39: l2 -> [11] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 ], cost: NONTERM 15: l3 -> l2 : [ 1+a4^0<=30 ], cost: 2 28: l3 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 ], cost: 6 30: l3 -> l2 : a4^0'=k+a4^0, b5^0'=2*k+b5^0, [ 1+a4^0<=30 && k>=0 && -1+2*k+b5^0<=-1+k+a4^0 && -2+2*k+b5^0<=5 ], cost: 2+4*k 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l9 16: l2 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ a4^0<=b5^0 ], cost: 2 36: l2 -> [10] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 37: l2 -> [10] : [ 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+a4^0 && 6<=10+a4^0 ], cost: NONTERM 15: l3 -> l2 : [ 1+a4^0<=30 ], cost: 2 28: l3 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 ], cost: 6 30: l3 -> l2 : a4^0'=k+a4^0, b5^0'=2*k+b5^0, [ 1+a4^0<=30 && k>=0 && -1+2*k+b5^0<=-1+k+a4^0 && -2+2*k+b5^0<=5 ], cost: 2+4*k 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 40: l3 -> l2 : a4^0'=1+a4^0, b5^0'=b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 ], cost: 7 41: l3 -> l2 : a4^0'=1+k+a4^0, b5^0'=b5^post_10, [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 ], cost: 7+4*k 42: l3 -> [11] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=a4^0 ], cost: NONTERM 43: l3 -> [11] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=k+a4^0 ], cost: NONTERM 44: l3 -> [11] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 ], cost: NONTERM 45: l3 -> [11] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 ], cost: NONTERM 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l9 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 42: l3 -> [11] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=a4^0 ], cost: NONTERM 43: l3 -> [11] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=k+a4^0 ], cost: NONTERM 44: l3 -> [11] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 ], cost: NONTERM 45: l3 -> [11] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 ], cost: NONTERM 46: l3 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ 1+a4^0<=30 && a4^0<=b5^0 ], cost: 4 47: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 48: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+a4^0 && 6<=10+a4^0 ], cost: NONTERM 49: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 && 1+a4^0<=b5^post_10 ], cost: 8 50: l3 -> l3 : a4^0'=2+k+a4^0, b5^0'=-10+2*k+b5^0, [ 1+a4^0<=30 && k>=0 && -1+2*k+b5^0<=-1+k+a4^0 && -2+2*k+b5^0<=5 && k+a4^0<=2*k+b5^0 ], cost: 4+4*k 51: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+k+a4^0 && 6<=1+k+a4^0 ], cost: NONTERM 52: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+k+a4^0 && 6<=10+k+a4^0 ], cost: NONTERM 53: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+a4^0<=b5^post_10 ], cost: 9 54: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=2+a4^0 ], cost: NONTERM 55: l3 -> l3 : a4^0'=3+k+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+k+a4^0<=b5^post_10 ], cost: 9+4*k 56: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+k+a4^0 && 6<=2+k+a4^0 ], cost: NONTERM 57: l3 -> [12] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 ], cost: 7+4*k 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Merged rules: Start location: l9 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 46: l3 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ 1+a4^0<=30 && a4^0<=b5^0 ], cost: 4 47: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 48: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+a4^0 && 6<=10+a4^0 ], cost: NONTERM 49: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 && 1+a4^0<=b5^post_10 ], cost: 8 50: l3 -> l3 : a4^0'=2+k+a4^0, b5^0'=-10+2*k+b5^0, [ 1+a4^0<=30 && k>=0 && -1+2*k+b5^0<=-1+k+a4^0 && -2+2*k+b5^0<=5 && k+a4^0<=2*k+b5^0 ], cost: 4+4*k 51: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+k+a4^0 && 6<=1+k+a4^0 ], cost: NONTERM 52: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+k+a4^0 && 6<=10+k+a4^0 ], cost: NONTERM 53: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+a4^0<=b5^post_10 ], cost: 9 54: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=2+a4^0 ], cost: NONTERM 55: l3 -> l3 : a4^0'=3+k+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+k+a4^0<=b5^post_10 ], cost: 9+4*k 56: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+k+a4^0 && 6<=2+k+a4^0 ], cost: NONTERM 57: l3 -> [12] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 ], cost: 7+4*k 58: l3 -> [11] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 ], cost: NONTERM 59: l3 -> [11] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 ], cost: NONTERM 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Applied pruning (of leafs and parallel rules): Start location: l9 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 46: l3 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ 1+a4^0<=30 && a4^0<=b5^0 ], cost: 4 47: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 48: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+a4^0 && 6<=10+a4^0 ], cost: NONTERM 49: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 && 1+a4^0<=b5^post_10 ], cost: 8 50: l3 -> l3 : a4^0'=2+k+a4^0, b5^0'=-10+2*k+b5^0, [ 1+a4^0<=30 && k>=0 && -1+2*k+b5^0<=-1+k+a4^0 && -2+2*k+b5^0<=5 && k+a4^0<=2*k+b5^0 ], cost: 4+4*k 51: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+k+a4^0 && 6<=1+k+a4^0 ], cost: NONTERM 52: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+k+a4^0 && 6<=10+k+a4^0 ], cost: NONTERM 53: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+a4^0<=b5^post_10 ], cost: 9 55: l3 -> l3 : a4^0'=3+k+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+k+a4^0<=b5^post_10 ], cost: 9+4*k 57: l3 -> [12] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 ], cost: 7+4*k 58: l3 -> [11] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 ], cost: NONTERM 59: l3 -> [11] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 ], cost: NONTERM 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Accelerating simple loops of location 3. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 46: l3 -> l3 : a4^0'=2+a4^0, b5^0'=-10+b5^0, [ 1+a4^0<=30 && a4^0<=b5^0 ], cost: 4 49: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 && 1+a4^0<=b5^post_10 ], cost: 8 50: l3 -> l3 : a4^0'=2-b5^0+2*a4^0, b5^0'=-10-b5^0+2*a4^0, [ 1+a4^0<=30 && -b5^0+a4^0>=0 && -2-b5^0+2*a4^0<=5 ], cost: 4-4*b5^0+4*a4^0 53: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+a4^0<=b5^post_10 ], cost: 9 55: l3 -> l3 : a4^0'=3+k+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+k+a4^0<=b5^post_10 ], cost: 9+4*k Accelerated rule 46 with backward acceleration, yielding the new rule 60. Failed to prove monotonicity of the guard of rule 49. Found no closed form for 50. Failed to prove monotonicity of the guard of rule 53. Failed to prove monotonicity of the guard of rule 55. [accelerate] Nesting with 4 inner and 5 outer candidates Removing the simple loops: 46. Accelerated all simple loops using metering functions (where possible): Start location: l9 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 47: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 48: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+a4^0 && 6<=10+a4^0 ], cost: NONTERM 49: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 1+b5^post_10<=10 && 1+a4^0<=b5^post_10 ], cost: 8 50: l3 -> l3 : a4^0'=2-b5^0+2*a4^0, b5^0'=-10-b5^0+2*a4^0, [ 1+a4^0<=30 && -b5^0+a4^0>=0 && -2-b5^0+2*a4^0<=5 ], cost: 4-4*b5^0+4*a4^0 51: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+k+a4^0 && 6<=1+k+a4^0 ], cost: NONTERM 52: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+k+a4^0 && 6<=10+k+a4^0 ], cost: NONTERM 53: l3 -> l3 : a4^0'=3+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+a4^0<=b5^post_10 ], cost: 9 55: l3 -> l3 : a4^0'=3+k+a4^0, b5^0'=-10+b5^post_10, [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+k+a4^0<=b5^post_10 ], cost: 9+4*k 57: l3 -> [12] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 ], cost: 7+4*k 58: l3 -> [11] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 ], cost: NONTERM 59: l3 -> [11] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 ], cost: NONTERM 60: l3 -> l3 : a4^0'=2*k_3+a4^0, b5^0'=-10*k_3+b5^0, [ k_3>=0 && -1+2*k_3+a4^0<=30 && -2+2*k_3+a4^0<=10-10*k_3+b5^0 ], cost: 4*k_3 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l9 33: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 6<=a4^0 ], cost: NONTERM 47: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+a4^0 && 6<=1+a4^0 ], cost: NONTERM 48: l3 -> [10] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+a4^0 && 6<=10+a4^0 ], cost: NONTERM 51: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 && 1+b5^post_10<=1+k+a4^0 && 6<=1+k+a4^0 ], cost: NONTERM 52: l3 -> [10] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=10+k+a4^0 && 6<=10+k+a4^0 ], cost: NONTERM 57: l3 -> [12] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 && 13<=b5^post_10 ], cost: 7+4*k 58: l3 -> [11] : [ 1+a4^0<=30 && 1+b5^0<=a4^0 && 6<=b5^0 ], cost: NONTERM 59: l3 -> [11] : [ 1+a4^0<=30 && k>=0 && -2+2*k+b5^0<=5 && 1+2*k+b5^0<=k+a4^0 && 6<=2*k+b5^0 ], cost: NONTERM 14: l9 -> l3 : a4^0'=1, a^0'=1, answer^0'=0, b5^0'=1, b^0'=1, [], cost: 2 61: l9 -> l3 : a4^0'=3, a^0'=1, answer^0'=0, b5^0'=-9, b^0'=1, [], cost: 6 62: l9 -> l3 : a4^0'=1+2*k_3, a^0'=1, answer^0'=0, b5^0'=1-10*k_3, b^0'=1, [ k_3>=0 && 2*k_3<=30 && -1+2*k_3<=11-10*k_3 ], cost: 2+4*k_3 Eliminated locations (on tree-shaped paths): Start location: l9 63: l9 -> [10] : [ k>=0 && -11+2*k<=5 && -8+2*k<=3+k && 6<=-9+2*k && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=13+k ], cost: NONTERM 64: l9 -> [12] : a4^0'=3, a^0'=1, answer^0'=0, b5^0'=-9, b^0'=1, [ k>=0 && -11+2*k<=5 && -8+2*k<=3+k && 6<=-9+2*k && 13<=b5^post_10 ], cost: 13+4*k 65: l9 -> [11] : [ k>=0 && -11+2*k<=5 && -8+2*k<=3+k && 6<=-9+2*k ], cost: NONTERM 66: l9 -> [10] : [ k_3>=0 && -1+2*k_3<=11-10*k_3 && 2+2*k_3<=30 && k>=0 && -1-10*k_3+2*k<=5 && 2-10*k_3+2*k<=1+2*k_3+k && 6<=1-10*k_3+2*k && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=11+2*k_3+k && 6<=11+2*k_3+k ], cost: NONTERM 67: l9 -> [12] : a4^0'=1+2*k_3, a^0'=1, answer^0'=0, b5^0'=1-10*k_3, b^0'=1, [ k_3>=0 && -1+2*k_3<=11-10*k_3 && 2+2*k_3<=30 && k>=0 && -1-10*k_3+2*k<=5 && 2-10*k_3+2*k<=1+2*k_3+k && 6<=1-10*k_3+2*k && 13<=b5^post_10 ], cost: 9+4*k_3+4*k 68: l9 -> [11] : [ k_3>=0 && -1+2*k_3<=11-10*k_3 && 2+2*k_3<=30 && k>=0 && -1-10*k_3+2*k<=5 && 2-10*k_3+2*k<=1+2*k_3+k && 6<=1-10*k_3+2*k ], cost: NONTERM 69: l9 -> [14] : [ k_3>=0 && 2*k_3<=30 && -1+2*k_3<=11-10*k_3 ], cost: 2+4*k_3 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l9 63: l9 -> [10] : [ k>=0 && -11+2*k<=5 && -8+2*k<=3+k && 6<=-9+2*k && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=13+k ], cost: NONTERM 64: l9 -> [12] : a4^0'=3, a^0'=1, answer^0'=0, b5^0'=-9, b^0'=1, [ k>=0 && -11+2*k<=5 && -8+2*k<=3+k && 6<=-9+2*k && 13<=b5^post_10 ], cost: 13+4*k 65: l9 -> [11] : [ k>=0 && -11+2*k<=5 && -8+2*k<=3+k && 6<=-9+2*k ], cost: NONTERM 66: l9 -> [10] : [ k_3>=0 && -1+2*k_3<=11-10*k_3 && 2+2*k_3<=30 && k>=0 && -1-10*k_3+2*k<=5 && 2-10*k_3+2*k<=1+2*k_3+k && 6<=1-10*k_3+2*k && 10<=b5^post_10 && b5^post_10<=12 && 1+b5^post_10<=11+2*k_3+k && 6<=11+2*k_3+k ], cost: NONTERM 67: l9 -> [12] : a4^0'=1+2*k_3, a^0'=1, answer^0'=0, b5^0'=1-10*k_3, b^0'=1, [ k_3>=0 && -1+2*k_3<=11-10*k_3 && 2+2*k_3<=30 && k>=0 && -1-10*k_3+2*k<=5 && 2-10*k_3+2*k<=1+2*k_3+k && 6<=1-10*k_3+2*k && 13<=b5^post_10 ], cost: 9+4*k_3+4*k 68: l9 -> [11] : [ k_3>=0 && -1+2*k_3<=11-10*k_3 && 2+2*k_3<=30 && k>=0 && -1-10*k_3+2*k<=5 && 2-10*k_3+2*k<=1+2*k_3+k && 6<=1-10*k_3+2*k ], cost: NONTERM 69: l9 -> [14] : [ k_3>=0 && 2*k_3<=30 && -1+2*k_3<=11-10*k_3 ], cost: 2+4*k_3 Computing asymptotic complexity for rule 65 Simplified the guard: 65: l9 -> [11] : [ -11+2*k<=5 && 6<=-9+2*k ], cost: NONTERM 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: [ -11+2*k<=5 && 6<=-9+2*k ] NO