NO Initial ITS Start location: l9 0: l0 -> l1 : x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, (-Result_4^post0+Result_4^0 == 0 /\ -x_5^post0+x_5^0 == 0), cost: 1 1: l1 -> l3 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, (1-x_5^0+x_5^post1 == 0 /\ Result_4^0-Result_4^post1 == 0), cost: 1 6: l1 -> l6 : x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, (-Result_4^post6+Result_4^0 == 0 /\ 1-x_5^0+x_5^post6 == 0), cost: 1 10: l1 -> l8 : x_5^0'=x_5^post10, Result_4^0'=Result_4^post10, (0 == 0 /\ -Result_4^post10+Result_4^0 == 0 /\ 13-x_5^10 <= 0 /\ -x_5^post10 <= 0 /\ -13+x_5^10 <= 0 /\ 1-x_5^0+x_5^10 == 0), cost: 1 12: l1 -> l5 : x_5^0'=x_5^post12, Result_4^0'=Result_4^post12, (0 == 0 /\ 13-x_5^11 <= 0 /\ 1+x_5^post12 <= 0 /\ -13+x_5^11 <= 0 /\ 1-x_5^0+x_5^11 == 0), cost: 1 2: l3 -> l4 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, (-12+x_5^0 <= 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 3: l3 -> l4 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, (14-x_5^0 <= 0 /\ x_5^0-x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0), cost: 1 4: l4 -> l2 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, (x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ -x_5^0 <= 0), cost: 1 5: l2 -> l1 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, (x_5^0-x_5^post5 == 0 /\ -Result_4^post5+Result_4^0 == 0), cost: 1 7: l6 -> l7 : x_5^0'=x_5^post7, Result_4^0'=Result_4^post7, (Result_4^0-Result_4^post7 == 0 /\ x_5^0-x_5^post7 == 0 /\ -12+x_5^0 <= 0), cost: 1 8: l6 -> l7 : x_5^0'=x_5^post8, Result_4^0'=Result_4^post8, (-Result_4^post8+Result_4^0 == 0 /\ 14-x_5^0 <= 0 /\ -x_5^post8+x_5^0 == 0), cost: 1 9: l7 -> l5 : x_5^0'=x_5^post9, Result_4^0'=Result_4^post9, (0 == 0 /\ x_5^0-x_5^post9 == 0 /\ 1+x_5^0 <= 0), cost: 1 11: l8 -> l1 : x_5^0'=x_5^post11, Result_4^0'=Result_4^post11, (-Result_4^post11+Result_4^0 == 0 /\ x_5^0-x_5^post11 == 0), cost: 1 13: l9 -> l0 : x_5^0'=x_5^post13, Result_4^0'=Result_4^post13, (Result_4^0-Result_4^post13 == 0 /\ x_5^0-x_5^post13 == 0), cost: 1 Removed unreachable rules and leafs Start location: l9 0: l0 -> l1 : x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, (-Result_4^post0+Result_4^0 == 0 /\ -x_5^post0+x_5^0 == 0), cost: 1 1: l1 -> l3 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, (1-x_5^0+x_5^post1 == 0 /\ Result_4^0-Result_4^post1 == 0), cost: 1 10: l1 -> l8 : x_5^0'=x_5^post10, Result_4^0'=Result_4^post10, (0 == 0 /\ -Result_4^post10+Result_4^0 == 0 /\ 13-x_5^10 <= 0 /\ -x_5^post10 <= 0 /\ -13+x_5^10 <= 0 /\ 1-x_5^0+x_5^10 == 0), cost: 1 2: l3 -> l4 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, (-12+x_5^0 <= 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 3: l3 -> l4 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, (14-x_5^0 <= 0 /\ x_5^0-x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0), cost: 1 4: l4 -> l2 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, (x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ -x_5^0 <= 0), cost: 1 5: l2 -> l1 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, (x_5^0-x_5^post5 == 0 /\ -Result_4^post5+Result_4^0 == 0), cost: 1 11: l8 -> l1 : x_5^0'=x_5^post11, Result_4^0'=Result_4^post11, (-Result_4^post11+Result_4^0 == 0 /\ x_5^0-x_5^post11 == 0), cost: 1 13: l9 -> l0 : x_5^0'=x_5^post13, Result_4^0'=Result_4^post13, (Result_4^0-Result_4^post13 == 0 /\ x_5^0-x_5^post13 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, (-Result_4^post0+Result_4^0 == 0 /\ -x_5^post0+x_5^0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l3 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, (1-x_5^0+x_5^post1 == 0 /\ Result_4^0-Result_4^post1 == 0), cost: 1 New rule: l1 -> l3 : x_5^0'=-1+x_5^0, TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l4 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, (-12+x_5^0 <= 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 New rule: l3 -> l4 : -12+x_5^0 <= 0, cost: 1 Applied preprocessing Original rule: l3 -> l4 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, (14-x_5^0 <= 0 /\ x_5^0-x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0), cost: 1 New rule: l3 -> l4 : -14+x_5^0 >= 0, cost: 1 Applied preprocessing Original rule: l4 -> l2 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, (x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ -x_5^0 <= 0), cost: 1 New rule: l4 -> l2 : x_5^0 >= 0, cost: 1 Applied preprocessing Original rule: l2 -> l1 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, (x_5^0-x_5^post5 == 0 /\ -Result_4^post5+Result_4^0 == 0), cost: 1 New rule: l2 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l8 : x_5^0'=x_5^post10, Result_4^0'=Result_4^post10, (0 == 0 /\ -Result_4^post10+Result_4^0 == 0 /\ 13-x_5^10 <= 0 /\ -x_5^post10 <= 0 /\ -13+x_5^10 <= 0 /\ 1-x_5^0+x_5^10 == 0), cost: 1 New rule: l1 -> l8 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -14+x_5^0 == 0), cost: 1 Applied preprocessing Original rule: l8 -> l1 : x_5^0'=x_5^post11, Result_4^0'=Result_4^post11, (-Result_4^post11+Result_4^0 == 0 /\ x_5^0-x_5^post11 == 0), cost: 1 New rule: l8 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l9 -> l0 : x_5^0'=x_5^post13, Result_4^0'=Result_4^post13, (Result_4^0-Result_4^post13 == 0 /\ x_5^0-x_5^post13 == 0), cost: 1 New rule: l9 -> l0 : TRUE, cost: 1 Simplified rules Start location: l9 14: l0 -> l1 : TRUE, cost: 1 15: l1 -> l3 : x_5^0'=-1+x_5^0, TRUE, cost: 1 20: l1 -> l8 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -14+x_5^0 == 0), cost: 1 16: l3 -> l4 : -12+x_5^0 <= 0, cost: 1 17: l3 -> l4 : -14+x_5^0 >= 0, cost: 1 18: l4 -> l2 : x_5^0 >= 0, cost: 1 19: l2 -> l1 : TRUE, cost: 1 21: l8 -> l1 : TRUE, cost: 1 22: l9 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l9 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : TRUE, cost: 1 New rule: l9 -> l1 : TRUE, cost: 2 Applied deletion Removed the following rules: 14 22 Eliminating location l8 by chaining: Applied chaining First rule: l1 -> l8 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -14+x_5^0 == 0), cost: 1 Second rule: l8 -> l1 : TRUE, cost: 1 New rule: l1 -> l1 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -14+x_5^0 == 0), cost: 2 Applied deletion Removed the following rules: 20 21 Eliminating location l2 by chaining: Applied chaining First rule: l4 -> l2 : x_5^0 >= 0, cost: 1 Second rule: l2 -> l1 : TRUE, cost: 1 New rule: l4 -> l1 : x_5^0 >= 0, cost: 2 Applied deletion Removed the following rules: 18 19 Eliminated locations on linear paths Start location: l9 15: l1 -> l3 : x_5^0'=-1+x_5^0, TRUE, cost: 1 24: l1 -> l1 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -14+x_5^0 == 0), cost: 2 16: l3 -> l4 : -12+x_5^0 <= 0, cost: 1 17: l3 -> l4 : -14+x_5^0 >= 0, cost: 1 25: l4 -> l1 : x_5^0 >= 0, cost: 2 23: l9 -> l1 : TRUE, cost: 2 Applied acceleration Original rule: l1 -> l1 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -14+x_5^0 == 0), cost: 2 New rule: l1 -> l1 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -1+n >= 0 /\ 14-x_5^0 >= 0 /\ 14-x_5^post10 >= 0 /\ -14+x_5^0 >= 0 /\ -14+x_5^post10 >= 0), cost: 2*n Sub-proof via acceration calculus written to file:///tmp/tmpnam_ffiice.txt Applied nonterm Original rule: l1 -> l1 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -14+x_5^0 == 0), cost: 2 New rule: l1 -> [10] : (-x_5^post10+x_5^0 <= 0 /\ x_5^post10 >= 0 /\ x_5^post10-x_5^0 <= 0 /\ 14-x_5^0 >= 0 /\ -14+x_5^0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_anbcCG.txt Applied simplification Original rule: l1 -> l1 : x_5^0'=x_5^post10, (x_5^post10 >= 0 /\ -1+n >= 0 /\ 14-x_5^0 >= 0 /\ 14-x_5^post10 >= 0 /\ -14+x_5^0 >= 0 /\ -14+x_5^post10 >= 0), cost: 2*n New rule: l1 -> l1 : x_5^0'=x_5^post10, (-1+n >= 0 /\ -14+x_5^0 <= 0 /\ -14+x_5^0 >= 0 /\ -14+x_5^post10 <= 0 /\ -14+x_5^post10 >= 0), cost: 2*n Applied simplification Original rule: l1 -> [10] : (-x_5^post10+x_5^0 <= 0 /\ x_5^post10 >= 0 /\ x_5^post10-x_5^0 <= 0 /\ 14-x_5^0 >= 0 /\ -14+x_5^0 >= 0), cost: NONTERM New rule: l1 -> [10] : (-x_5^post10+x_5^0 <= 0 /\ x_5^post10-x_5^0 <= 0 /\ 14-x_5^0 >= 0 /\ -14+x_5^0 >= 0), cost: NONTERM Applied deletion Removed the following rules: 24 Accelerated simple loops Start location: l9 15: l1 -> l3 : x_5^0'=-1+x_5^0, TRUE, cost: 1 28: l1 -> l1 : x_5^0'=x_5^post10, (-1+n >= 0 /\ -14+x_5^0 <= 0 /\ -14+x_5^0 >= 0 /\ -14+x_5^post10 <= 0 /\ -14+x_5^post10 >= 0), cost: 2*n 29: l1 -> [10] : (-x_5^post10+x_5^0 <= 0 /\ x_5^post10-x_5^0 <= 0 /\ 14-x_5^0 >= 0 /\ -14+x_5^0 >= 0), cost: NONTERM 16: l3 -> l4 : -12+x_5^0 <= 0, cost: 1 17: l3 -> l4 : -14+x_5^0 >= 0, cost: 1 25: l4 -> l1 : x_5^0 >= 0, cost: 2 23: l9 -> l1 : TRUE, cost: 2 Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : x_5^0'=x_5^post10, (-1+n >= 0 /\ -14+x_5^0 <= 0 /\ -14+x_5^0 >= 0 /\ -14+x_5^post10 <= 0 /\ -14+x_5^post10 >= 0), cost: 2*n New rule: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n Applied chaining First rule: l4 -> l1 : x_5^0 >= 0, cost: 2 Second rule: l1 -> l1 : x_5^0'=x_5^post10, (-1+n >= 0 /\ -14+x_5^0 <= 0 /\ -14+x_5^0 >= 0 /\ -14+x_5^post10 <= 0 /\ -14+x_5^post10 >= 0), cost: 2*n New rule: l4 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> [10] : (-x_5^post10+x_5^0 <= 0 /\ x_5^post10-x_5^0 <= 0 /\ 14-x_5^0 >= 0 /\ -14+x_5^0 >= 0), cost: NONTERM New rule: l9 -> [10] : -14+x_5^0 == 0, cost: NONTERM Applied chaining First rule: l4 -> l1 : x_5^0 >= 0, cost: 2 Second rule: l1 -> [10] : (-x_5^post10+x_5^0 <= 0 /\ x_5^post10-x_5^0 <= 0 /\ 14-x_5^0 >= 0 /\ -14+x_5^0 >= 0), cost: NONTERM New rule: l4 -> [10] : -14+x_5^0 == 0, cost: NONTERM Applied deletion Removed the following rules: 28 29 Chained accelerated rules with incoming rules Start location: l9 15: l1 -> l3 : x_5^0'=-1+x_5^0, TRUE, cost: 1 16: l3 -> l4 : -12+x_5^0 <= 0, cost: 1 17: l3 -> l4 : -14+x_5^0 >= 0, cost: 1 25: l4 -> l1 : x_5^0 >= 0, cost: 2 31: l4 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n 33: l4 -> [10] : -14+x_5^0 == 0, cost: NONTERM 23: l9 -> l1 : TRUE, cost: 2 30: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n 32: l9 -> [10] : -14+x_5^0 == 0, cost: NONTERM Eliminating location l3 by chaining: Applied chaining First rule: l1 -> l3 : x_5^0'=-1+x_5^0, TRUE, cost: 1 Second rule: l3 -> l4 : -12+x_5^0 <= 0, cost: 1 New rule: l1 -> l4 : x_5^0'=-1+x_5^0, -13+x_5^0 <= 0, cost: 2 Applied chaining First rule: l1 -> l3 : x_5^0'=-1+x_5^0, TRUE, cost: 1 Second rule: l3 -> l4 : -14+x_5^0 >= 0, cost: 1 New rule: l1 -> l4 : x_5^0'=-1+x_5^0, -15+x_5^0 >= 0, cost: 2 Applied deletion Removed the following rules: 15 16 17 Eliminated locations on tree-shaped paths Start location: l9 34: l1 -> l4 : x_5^0'=-1+x_5^0, -13+x_5^0 <= 0, cost: 2 35: l1 -> l4 : x_5^0'=-1+x_5^0, -15+x_5^0 >= 0, cost: 2 25: l4 -> l1 : x_5^0 >= 0, cost: 2 31: l4 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n 33: l4 -> [10] : -14+x_5^0 == 0, cost: NONTERM 23: l9 -> l1 : TRUE, cost: 2 30: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n 32: l9 -> [10] : -14+x_5^0 == 0, cost: NONTERM Eliminating location l4 by chaining: Applied chaining First rule: l1 -> l4 : x_5^0'=-1+x_5^0, -13+x_5^0 <= 0, cost: 2 Second rule: l4 -> l1 : x_5^0 >= 0, cost: 2 New rule: l1 -> l1 : x_5^0'=-1+x_5^0, (-13+x_5^0 <= 0 /\ -1+x_5^0 >= 0), cost: 4 Applied chaining First rule: l1 -> l4 : x_5^0'=-1+x_5^0, -15+x_5^0 >= 0, cost: 2 Second rule: l4 -> l1 : x_5^0 >= 0, cost: 2 New rule: l1 -> l1 : x_5^0'=-1+x_5^0, (-15+x_5^0 >= 0 /\ -1+x_5^0 >= 0), cost: 4 Applied simplification Original rule: l1 -> l1 : x_5^0'=-1+x_5^0, (-15+x_5^0 >= 0 /\ -1+x_5^0 >= 0), cost: 4 New rule: l1 -> l1 : x_5^0'=-1+x_5^0, -15+x_5^0 >= 0, cost: 4 Applied chaining First rule: l1 -> l4 : x_5^0'=-1+x_5^0, -15+x_5^0 >= 0, cost: 2 Second rule: l4 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n New rule: l1 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 >= 0 /\ -15+x_5^0 == 0), cost: 4+2*n Applied simplification Original rule: l1 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 >= 0 /\ -15+x_5^0 == 0), cost: 4+2*n New rule: l1 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 4+2*n Applied chaining First rule: l1 -> l4 : x_5^0'=-1+x_5^0, -15+x_5^0 >= 0, cost: 2 Second rule: l4 -> [10] : -14+x_5^0 == 0, cost: NONTERM New rule: l1 -> [10] : (-15+x_5^0 >= 0 /\ -15+x_5^0 == 0), cost: NONTERM Applied simplification Original rule: l1 -> [10] : (-15+x_5^0 >= 0 /\ -15+x_5^0 == 0), cost: NONTERM New rule: l1 -> [10] : -15+x_5^0 == 0, cost: NONTERM Applied deletion Removed the following rules: 25 31 33 34 35 Eliminated locations on tree-shaped paths Start location: l9 36: l1 -> l1 : x_5^0'=-1+x_5^0, (-13+x_5^0 <= 0 /\ -1+x_5^0 >= 0), cost: 4 37: l1 -> l1 : x_5^0'=-1+x_5^0, -15+x_5^0 >= 0, cost: 4 38: l1 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 4+2*n 39: l1 -> [10] : -15+x_5^0 == 0, cost: NONTERM 23: l9 -> l1 : TRUE, cost: 2 30: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n 32: l9 -> [10] : -14+x_5^0 == 0, cost: NONTERM Applied acceleration Original rule: l1 -> l1 : x_5^0'=-1+x_5^0, (-13+x_5^0 <= 0 /\ -1+x_5^0 >= 0), cost: 4 New rule: l1 -> l1 : x_5^0'=x_5^0-n0, (n0 >= 0 /\ 13-x_5^0 >= 0 /\ x_5^0-n0 >= 0), cost: 4*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_njmHBp.txt Applied instantiation Original rule: l1 -> l1 : x_5^0'=x_5^0-n0, (n0 >= 0 /\ 13-x_5^0 >= 0 /\ x_5^0-n0 >= 0), cost: 4*n0 New rule: l1 -> l1 : x_5^0'=0, (0 >= 0 /\ x_5^0 >= 0 /\ 13-x_5^0 >= 0), cost: 4*x_5^0 Applied acceleration Original rule: l1 -> l1 : x_5^0'=-1+x_5^0, -15+x_5^0 >= 0, cost: 4 New rule: l1 -> l1 : x_5^0'=x_5^0-n1, (-14+x_5^0-n1 >= 0 /\ n1 >= 0), cost: 4*n1 Sub-proof via acceration calculus written to file:///tmp/tmpnam_ddPFOe.txt Applied instantiation Original rule: l1 -> l1 : x_5^0'=x_5^0-n1, (-14+x_5^0-n1 >= 0 /\ n1 >= 0), cost: 4*n1 New rule: l1 -> l1 : x_5^0'=14, (0 >= 0 /\ -14+x_5^0 >= 0), cost: -56+4*x_5^0 Applied simplification Original rule: l1 -> l1 : x_5^0'=0, (0 >= 0 /\ x_5^0 >= 0 /\ 13-x_5^0 >= 0), cost: 4*x_5^0 New rule: l1 -> l1 : x_5^0'=0, (x_5^0 >= 0 /\ -13+x_5^0 <= 0), cost: 4*x_5^0 Applied simplification Original rule: l1 -> l1 : x_5^0'=14, (0 >= 0 /\ -14+x_5^0 >= 0), cost: -56+4*x_5^0 New rule: l1 -> l1 : x_5^0'=14, -14+x_5^0 >= 0, cost: -56+4*x_5^0 Applied deletion Removed the following rules: 36 37 Accelerated simple loops Start location: l9 38: l1 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 4+2*n 39: l1 -> [10] : -15+x_5^0 == 0, cost: NONTERM 42: l1 -> l1 : x_5^0'=0, (x_5^0 >= 0 /\ -13+x_5^0 <= 0), cost: 4*x_5^0 43: l1 -> l1 : x_5^0'=14, -14+x_5^0 >= 0, cost: -56+4*x_5^0 23: l9 -> l1 : TRUE, cost: 2 30: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n 32: l9 -> [10] : -14+x_5^0 == 0, cost: NONTERM Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 4+2*n New rule: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 6+2*n Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : x_5^0'=0, (x_5^0 >= 0 /\ -13+x_5^0 <= 0), cost: 4*x_5^0 New rule: l9 -> l1 : x_5^0'=0, (x_5^0 >= 0 /\ -13+x_5^0 <= 0), cost: 2+4*x_5^0 Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : x_5^0'=14, -14+x_5^0 >= 0, cost: -56+4*x_5^0 New rule: l9 -> l1 : x_5^0'=14, -14+x_5^0 >= 0, cost: -54+4*x_5^0 Applied chaining First rule: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n Second rule: l1 -> l1 : x_5^0'=14, -14+x_5^0 >= 0, cost: -56+4*x_5^0 New rule: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n Applied deletion Removed the following rules: 38 42 43 Chained accelerated rules with incoming rules Start location: l9 39: l1 -> [10] : -15+x_5^0 == 0, cost: NONTERM 23: l9 -> l1 : TRUE, cost: 2 30: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n 32: l9 -> [10] : -14+x_5^0 == 0, cost: NONTERM 44: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 6+2*n 45: l9 -> l1 : x_5^0'=0, (x_5^0 >= 0 /\ -13+x_5^0 <= 0), cost: 2+4*x_5^0 46: l9 -> l1 : x_5^0'=14, -14+x_5^0 >= 0, cost: -54+4*x_5^0 Eliminating location l1 by chaining: Applied chaining First rule: l9 -> l1 : TRUE, cost: 2 Second rule: l1 -> [10] : -15+x_5^0 == 0, cost: NONTERM New rule: l9 -> [10] : -15+x_5^0 == 0, cost: NONTERM Applied partial deletion Original rule: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n New rule: l9 -> [12] : (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n Applied partial deletion Original rule: l9 -> l1 : x_5^0'=14, (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 6+2*n New rule: l9 -> [12] : (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 6+2*n Applied partial deletion Original rule: l9 -> l1 : x_5^0'=0, (x_5^0 >= 0 /\ -13+x_5^0 <= 0), cost: 2+4*x_5^0 New rule: l9 -> [12] : (x_5^0 >= 0 /\ -13+x_5^0 <= 0), cost: 2+4*x_5^0 Applied partial deletion Original rule: l9 -> l1 : x_5^0'=14, -14+x_5^0 >= 0, cost: -54+4*x_5^0 New rule: l9 -> [12] : -14+x_5^0 >= 0, cost: -54+4*x_5^0 Applied deletion Removed the following rules: 23 30 39 44 45 46 Eliminated locations on tree-shaped paths Start location: l9 32: l9 -> [10] : -14+x_5^0 == 0, cost: NONTERM 47: l9 -> [10] : -15+x_5^0 == 0, cost: NONTERM 48: l9 -> [12] : (-1+n >= 0 /\ -14+x_5^0 == 0), cost: 2+2*n 49: l9 -> [12] : (-1+n >= 0 /\ -15+x_5^0 == 0), cost: 6+2*n 50: l9 -> [12] : (x_5^0 >= 0 /\ -13+x_5^0 <= 0), cost: 2+4*x_5^0 51: l9 -> [12] : -14+x_5^0 >= 0, cost: -54+4*x_5^0 Computing asymptotic complexity Proved nontermination of rule 32 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -14+x_5^0 == 0