NO Initial ITS Start location: l7 0: l0 -> l1 : j^0'=j^post0, i^0'=i^post0, (-i^post0+i^0 == 0 /\ j^post0-i^0 == 0), cost: 1 1: l1 -> l2 : j^0'=j^post1, i^0'=i^post1, (j^0-j^post1 == 0 /\ -1-i^0+i^post1 == 0), cost: 1 7: l2 -> l4 : j^0'=j^post7, i^0'=i^post7, (i^0-i^post7 == 0 /\ j^0-j^post7 == 0), cost: 1 2: l3 -> l0 : j^0'=j^post2, i^0'=i^post2, (6-i^0 <= 0 /\ i^0-i^post2 == 0 /\ j^0-j^post2 == 0), cost: 1 3: l3 -> l0 : j^0'=j^post3, i^0'=i^post3, (-4+i^0 <= 0 /\ j^0-j^post3 == 0 /\ -i^post3+i^0 == 0), cost: 1 4: l3 -> l1 : j^0'=j^post4, i^0'=i^post4, (0 == 0 /\ j^0-j^post4 == 0 /\ -5+i^0 <= 0 /\ 5-i^0 <= 0), cost: 1 5: l4 -> l5 : j^0'=j^post5, i^0'=i^post5, (10-i^0 <= 0 /\ j^0-j^post5 == 0 /\ -i^post5+i^0 == 0), cost: 1 6: l4 -> l3 : j^0'=j^post6, i^0'=i^post6, (-9+i^0 <= 0 /\ -i^post6+i^0 == 0 /\ j^0-j^post6 == 0), cost: 1 8: l6 -> l2 : j^0'=j^post8, i^0'=i^post8, (i^post8 == 0 /\ -j^post8+j^0 == 0), cost: 1 9: l7 -> l6 : j^0'=j^post9, i^0'=i^post9, (j^0-j^post9 == 0 /\ -i^post9+i^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l7 0: l0 -> l1 : j^0'=j^post0, i^0'=i^post0, (-i^post0+i^0 == 0 /\ j^post0-i^0 == 0), cost: 1 1: l1 -> l2 : j^0'=j^post1, i^0'=i^post1, (j^0-j^post1 == 0 /\ -1-i^0+i^post1 == 0), cost: 1 7: l2 -> l4 : j^0'=j^post7, i^0'=i^post7, (i^0-i^post7 == 0 /\ j^0-j^post7 == 0), cost: 1 2: l3 -> l0 : j^0'=j^post2, i^0'=i^post2, (6-i^0 <= 0 /\ i^0-i^post2 == 0 /\ j^0-j^post2 == 0), cost: 1 3: l3 -> l0 : j^0'=j^post3, i^0'=i^post3, (-4+i^0 <= 0 /\ j^0-j^post3 == 0 /\ -i^post3+i^0 == 0), cost: 1 4: l3 -> l1 : j^0'=j^post4, i^0'=i^post4, (0 == 0 /\ j^0-j^post4 == 0 /\ -5+i^0 <= 0 /\ 5-i^0 <= 0), cost: 1 6: l4 -> l3 : j^0'=j^post6, i^0'=i^post6, (-9+i^0 <= 0 /\ -i^post6+i^0 == 0 /\ j^0-j^post6 == 0), cost: 1 8: l6 -> l2 : j^0'=j^post8, i^0'=i^post8, (i^post8 == 0 /\ -j^post8+j^0 == 0), cost: 1 9: l7 -> l6 : j^0'=j^post9, i^0'=i^post9, (j^0-j^post9 == 0 /\ -i^post9+i^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : j^0'=j^post0, i^0'=i^post0, (-i^post0+i^0 == 0 /\ j^post0-i^0 == 0), cost: 1 New rule: l0 -> l1 : j^0'=i^0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l2 : j^0'=j^post1, i^0'=i^post1, (j^0-j^post1 == 0 /\ -1-i^0+i^post1 == 0), cost: 1 New rule: l1 -> l2 : i^0'=1+i^0, TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : j^0'=j^post2, i^0'=i^post2, (6-i^0 <= 0 /\ i^0-i^post2 == 0 /\ j^0-j^post2 == 0), cost: 1 New rule: l3 -> l0 : -6+i^0 >= 0, cost: 1 Applied preprocessing Original rule: l3 -> l0 : j^0'=j^post3, i^0'=i^post3, (-4+i^0 <= 0 /\ j^0-j^post3 == 0 /\ -i^post3+i^0 == 0), cost: 1 New rule: l3 -> l0 : -4+i^0 <= 0, cost: 1 Applied preprocessing Original rule: l3 -> l1 : j^0'=j^post4, i^0'=i^post4, (0 == 0 /\ j^0-j^post4 == 0 /\ -5+i^0 <= 0 /\ 5-i^0 <= 0), cost: 1 New rule: l3 -> l1 : i^0'=i^post4, -5+i^0 == 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : j^0'=j^post6, i^0'=i^post6, (-9+i^0 <= 0 /\ -i^post6+i^0 == 0 /\ j^0-j^post6 == 0), cost: 1 New rule: l4 -> l3 : -9+i^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l4 : j^0'=j^post7, i^0'=i^post7, (i^0-i^post7 == 0 /\ j^0-j^post7 == 0), cost: 1 New rule: l2 -> l4 : TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l2 : j^0'=j^post8, i^0'=i^post8, (i^post8 == 0 /\ -j^post8+j^0 == 0), cost: 1 New rule: l6 -> l2 : i^0'=0, TRUE, cost: 1 Applied preprocessing Original rule: l7 -> l6 : j^0'=j^post9, i^0'=i^post9, (j^0-j^post9 == 0 /\ -i^post9+i^0 == 0), cost: 1 New rule: l7 -> l6 : TRUE, cost: 1 Simplified rules Start location: l7 10: l0 -> l1 : j^0'=i^0, TRUE, cost: 1 11: l1 -> l2 : i^0'=1+i^0, TRUE, cost: 1 16: l2 -> l4 : TRUE, cost: 1 12: l3 -> l0 : -6+i^0 >= 0, cost: 1 13: l3 -> l0 : -4+i^0 <= 0, cost: 1 14: l3 -> l1 : i^0'=i^post4, -5+i^0 == 0, cost: 1 15: l4 -> l3 : -9+i^0 <= 0, cost: 1 17: l6 -> l2 : i^0'=0, TRUE, cost: 1 18: l7 -> l6 : TRUE, cost: 1 Eliminating location l6 by chaining: Applied chaining First rule: l7 -> l6 : TRUE, cost: 1 Second rule: l6 -> l2 : i^0'=0, TRUE, cost: 1 New rule: l7 -> l2 : i^0'=0, TRUE, cost: 2 Applied deletion Removed the following rules: 17 18 Eliminating location l4 by chaining: Applied chaining First rule: l2 -> l4 : TRUE, cost: 1 Second rule: l4 -> l3 : -9+i^0 <= 0, cost: 1 New rule: l2 -> l3 : -9+i^0 <= 0, cost: 2 Applied deletion Removed the following rules: 15 16 Eliminated locations on linear paths Start location: l7 10: l0 -> l1 : j^0'=i^0, TRUE, cost: 1 11: l1 -> l2 : i^0'=1+i^0, TRUE, cost: 1 20: l2 -> l3 : -9+i^0 <= 0, cost: 2 12: l3 -> l0 : -6+i^0 >= 0, cost: 1 13: l3 -> l0 : -4+i^0 <= 0, cost: 1 14: l3 -> l1 : i^0'=i^post4, -5+i^0 == 0, cost: 1 19: l7 -> l2 : i^0'=0, TRUE, cost: 2 Eliminating location l3 by chaining: Applied chaining First rule: l2 -> l3 : -9+i^0 <= 0, cost: 2 Second rule: l3 -> l0 : -6+i^0 >= 0, cost: 1 New rule: l2 -> l0 : (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 3 Applied chaining First rule: l2 -> l3 : -9+i^0 <= 0, cost: 2 Second rule: l3 -> l0 : -4+i^0 <= 0, cost: 1 New rule: l2 -> l0 : (-9+i^0 <= 0 /\ -4+i^0 <= 0), cost: 3 Applied simplification Original rule: l2 -> l0 : (-9+i^0 <= 0 /\ -4+i^0 <= 0), cost: 3 New rule: l2 -> l0 : -4+i^0 <= 0, cost: 3 Applied chaining First rule: l2 -> l3 : -9+i^0 <= 0, cost: 2 Second rule: l3 -> l1 : i^0'=i^post4, -5+i^0 == 0, cost: 1 New rule: l2 -> l1 : i^0'=i^post4, (-9+i^0 <= 0 /\ -5+i^0 == 0), cost: 3 Applied simplification Original rule: l2 -> l1 : i^0'=i^post4, (-9+i^0 <= 0 /\ -5+i^0 == 0), cost: 3 New rule: l2 -> l1 : i^0'=i^post4, -5+i^0 == 0, cost: 3 Applied deletion Removed the following rules: 12 13 14 20 Eliminated locations on tree-shaped paths Start location: l7 10: l0 -> l1 : j^0'=i^0, TRUE, cost: 1 11: l1 -> l2 : i^0'=1+i^0, TRUE, cost: 1 21: l2 -> l0 : (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 3 22: l2 -> l0 : -4+i^0 <= 0, cost: 3 23: l2 -> l1 : i^0'=i^post4, -5+i^0 == 0, cost: 3 19: l7 -> l2 : i^0'=0, TRUE, cost: 2 Eliminating location l0 by chaining: Applied chaining First rule: l2 -> l0 : (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 3 Second rule: l0 -> l1 : j^0'=i^0, TRUE, cost: 1 New rule: l2 -> l1 : j^0'=i^0, (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 4 Applied chaining First rule: l2 -> l0 : -4+i^0 <= 0, cost: 3 Second rule: l0 -> l1 : j^0'=i^0, TRUE, cost: 1 New rule: l2 -> l1 : j^0'=i^0, -4+i^0 <= 0, cost: 4 Applied deletion Removed the following rules: 10 21 22 Eliminating location l1 by chaining: Applied chaining First rule: l2 -> l1 : i^0'=i^post4, -5+i^0 == 0, cost: 3 Second rule: l1 -> l2 : i^0'=1+i^0, TRUE, cost: 1 New rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 Applied chaining First rule: l2 -> l1 : j^0'=i^0, (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 4 Second rule: l1 -> l2 : i^0'=1+i^0, TRUE, cost: 1 New rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 5 Applied chaining First rule: l2 -> l1 : j^0'=i^0, -4+i^0 <= 0, cost: 4 Second rule: l1 -> l2 : i^0'=1+i^0, TRUE, cost: 1 New rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, -4+i^0 <= 0, cost: 5 Applied deletion Removed the following rules: 11 23 24 25 Eliminated locations on tree-shaped paths Start location: l7 26: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 27: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 5 28: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, -4+i^0 <= 0, cost: 5 19: l7 -> l2 : i^0'=0, TRUE, cost: 2 Applied acceleration Original rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 New rule: l2 -> l2 : i^0'=1+i^post4, (-5+i^0 >= 0 /\ 5-i^0 >= 0 /\ -4+i^post4 >= 0 /\ 4-i^post4 >= 0 /\ -1+n >= 0), cost: 4*n Sub-proof via acceration calculus written to file:///tmp/tmpnam_gdpale.txt Applied nonterm Original rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 New rule: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ -5+i^0 >= 0 /\ 5-i^0 >= 0 /\ -1+i^0-i^post4 <= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_OkoMhg.txt Applied acceleration Original rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 5 New rule: l2 -> l2 : j^0'=-1+n0+i^0, i^0'=n0+i^0, (-6+i^0 >= 0 /\ 10-n0-i^0 >= 0 /\ -1+n0 >= 0), cost: 5*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_lkdlhm.txt Applied instantiation Original rule: l2 -> l2 : j^0'=-1+n0+i^0, i^0'=n0+i^0, (-6+i^0 >= 0 /\ 10-n0-i^0 >= 0 /\ -1+n0 >= 0), cost: 5*n0 New rule: l2 -> l2 : j^0'=9, i^0'=10, (0 >= 0 /\ -6+i^0 >= 0 /\ 9-i^0 >= 0), cost: 50-5*i^0 Applied acceleration Original rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, -4+i^0 <= 0, cost: 5 New rule: l2 -> l2 : j^0'=-1+i^0+n1, i^0'=i^0+n1, (5-i^0-n1 >= 0 /\ -1+n1 >= 0), cost: 5*n1 Sub-proof via acceration calculus written to file:///tmp/tmpnam_dLKgIO.txt Applied instantiation Original rule: l2 -> l2 : j^0'=-1+i^0+n1, i^0'=i^0+n1, (5-i^0-n1 >= 0 /\ -1+n1 >= 0), cost: 5*n1 New rule: l2 -> l2 : j^0'=4, i^0'=5, (0 >= 0 /\ 4-i^0 >= 0), cost: 25-5*i^0 Applied chaining First rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, -4+i^0 <= 0, cost: 5 Second rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 New rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^post4, -4+i^0 == 0, cost: 9 Applied acceleration Original rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^post4, -4+i^0 == 0, cost: 9 New rule: l2 -> l2 : j^0'=1+i^post4, i^0'=1+i^post4, (-4+i^0 >= 0 /\ 4-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -3+i^post4 >= 0 /\ -2+n2 >= 0), cost: 9*n2 Sub-proof via acceration calculus written to file:///tmp/tmpnam_EgkbOP.txt Applied nonterm Original rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^post4, -4+i^0 == 0, cost: 9 New rule: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ -4+i^0 >= 0 /\ 4-i^0 >= 0 /\ -1+i^0-i^post4 <= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_FBfoeD.txt Applied chaining First rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 Second rule: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ -4+i^0 >= 0 /\ 4-i^0 >= 0 /\ -1+i^0-i^post4 <= 0), cost: NONTERM New rule: l2 -> [8] : (0 <= 0 /\ -5+i^0 == 0 /\ 3-i^post4 >= 0 /\ -3+i^post4 >= 0), cost: NONTERM Applied chaining First rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 Second rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, -4+i^0 <= 0, cost: 5 New rule: l2 -> l2 : j^0'=1+i^post4, i^0'=2+i^post4, (-5+i^0 == 0 /\ -3+i^post4 <= 0), cost: 9 Applied acceleration Original rule: l2 -> l2 : j^0'=1+i^post4, i^0'=2+i^post4, (-5+i^0 == 0 /\ -3+i^post4 <= 0), cost: 9 New rule: l2 -> l2 : j^0'=1+i^post4, i^0'=2+i^post4, (-5+i^0 >= 0 /\ 5-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+n3 >= 0 /\ -3+i^post4 >= 0), cost: 9*n3 Sub-proof via acceration calculus written to file:///tmp/tmpnam_flfbFC.txt Applied nonterm Original rule: l2 -> l2 : j^0'=1+i^post4, i^0'=2+i^post4, (-5+i^0 == 0 /\ -3+i^post4 <= 0), cost: 9 New rule: l2 -> [8] : (-2+i^0-i^post4 <= 0 /\ 2-i^0+i^post4 <= 0 /\ -5+i^0 >= 0 /\ 5-i^0 >= 0 /\ 3-i^post4 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_dIeAOB.txt Applied chaining First rule: l2 -> l2 : j^0'=i^0, i^0'=1+i^0, -4+i^0 <= 0, cost: 5 Second rule: l2 -> [8] : (-2+i^0-i^post4 <= 0 /\ 2-i^0+i^post4 <= 0 /\ -5+i^0 >= 0 /\ 5-i^0 >= 0 /\ 3-i^post4 >= 0), cost: NONTERM New rule: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ -4+i^0 <= 0 /\ -4+i^0 >= 0 /\ 4-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+i^0-i^post4 <= 0), cost: NONTERM Applied chaining First rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 Second rule: l2 -> l2 : j^0'=4, i^0'=5, (0 >= 0 /\ 4-i^0 >= 0), cost: 25-5*i^0 New rule: l2 -> l2 : j^0'=4, i^0'=5, (-5+i^0 == 0 /\ -3+i^post4 <= 0), cost: 24-5*i^post4 Applied nonterm Original rule: l2 -> l2 : j^0'=4, i^0'=5, (-5+i^0 == 0 /\ -3+i^post4 <= 0), cost: 24-5*i^post4 New rule: l2 -> [8] : (-5+i^0 >= 0 /\ 5-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+n7 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_ioDdMo.txt Applied chaining First rule: l2 -> l2 : j^0'=4, i^0'=5, (0 >= 0 /\ 4-i^0 >= 0), cost: 25-5*i^0 Second rule: l2 -> [8] : (-5+i^0 >= 0 /\ 5-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+n7 >= 0), cost: NONTERM New rule: l2 -> [8] : (0 >= 0 /\ 4-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+n7 >= 0), cost: NONTERM Applied chaining First rule: l2 -> l2 : j^0'=4, i^0'=5, (0 >= 0 /\ 4-i^0 >= 0), cost: 25-5*i^0 Second rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 New rule: l2 -> l2 : j^0'=4, i^0'=1+i^post4, -4+i^0 <= 0, cost: 29-5*i^0 Applied acceleration Original rule: l2 -> l2 : j^0'=4, i^0'=1+i^post4, -4+i^0 <= 0, cost: 29-5*i^0 New rule: l2 -> l2 : j^0'=4, i^0'=1+i^post4, (4-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+n8 >= 0), cost: 24*n8-5*n8*i^post4 Sub-proof via acceration calculus written to file:///tmp/tmpnam_DhHMkG.txt Applied nonterm Original rule: l2 -> l2 : j^0'=4, i^0'=1+i^post4, -4+i^0 <= 0, cost: 29-5*i^0 New rule: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ 4-i^0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_AclNAO.txt Applied chaining First rule: l2 -> l2 : i^0'=1+i^post4, -5+i^0 == 0, cost: 4 Second rule: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ 4-i^0 >= 0), cost: NONTERM New rule: l2 -> [8] : (0 <= 0 /\ -5+i^0 == 0 /\ 3-i^post4 >= 0), cost: NONTERM Applied simplification Original rule: l2 -> l2 : i^0'=1+i^post4, (-5+i^0 >= 0 /\ 5-i^0 >= 0 /\ -4+i^post4 >= 0 /\ 4-i^post4 >= 0 /\ -1+n >= 0), cost: 4*n New rule: l2 -> l2 : i^0'=1+i^post4, (-5+i^0 <= 0 /\ -5+i^0 >= 0 /\ -4+i^post4 <= 0 /\ -4+i^post4 >= 0 /\ -1+n >= 0), cost: 4*n Applied simplification Original rule: l2 -> l2 : j^0'=9, i^0'=10, (0 >= 0 /\ -6+i^0 >= 0 /\ 9-i^0 >= 0), cost: 50-5*i^0 New rule: l2 -> l2 : j^0'=9, i^0'=10, (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 50-5*i^0 Applied simplification Original rule: l2 -> l2 : j^0'=4, i^0'=5, (0 >= 0 /\ 4-i^0 >= 0), cost: 25-5*i^0 New rule: l2 -> l2 : j^0'=4, i^0'=5, -4+i^0 <= 0, cost: 25-5*i^0 Applied simplification Original rule: l2 -> [8] : (0 <= 0 /\ -5+i^0 == 0 /\ 3-i^post4 >= 0 /\ -3+i^post4 >= 0), cost: NONTERM New rule: l2 -> [8] : (-5+i^0 == 0 /\ -3+i^post4 <= 0 /\ -3+i^post4 >= 0), cost: NONTERM Applied simplification Original rule: l2 -> [8] : (-2+i^0-i^post4 <= 0 /\ 2-i^0+i^post4 <= 0 /\ -5+i^0 >= 0 /\ 5-i^0 >= 0 /\ 3-i^post4 >= 0), cost: NONTERM New rule: l2 -> [8] : (-2+i^0-i^post4 <= 0 /\ -5+i^0 >= 0 /\ 3-i^post4 >= 0), cost: NONTERM Applied simplification Original rule: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ -4+i^0 <= 0 /\ -4+i^0 >= 0 /\ 4-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+i^0-i^post4 <= 0), cost: NONTERM New rule: l2 -> [8] : (-4+i^0 >= 0 /\ -1+i^0-i^post4 <= 0 /\ -3+i^post4 <= 0), cost: NONTERM Applied simplification Original rule: l2 -> [8] : (-5+i^0 >= 0 /\ 5-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+n7 >= 0), cost: NONTERM New rule: l2 -> [8] : (-5+i^0 <= 0 /\ -5+i^0 >= 0 /\ -1+n7 >= 0 /\ -3+i^post4 <= 0), cost: NONTERM Applied simplification Original rule: l2 -> [8] : (0 >= 0 /\ 4-i^0 >= 0 /\ 3-i^post4 >= 0 /\ -1+n7 >= 0), cost: NONTERM New rule: l2 -> [8] : (-4+i^0 <= 0 /\ -1+n7 >= 0 /\ -3+i^post4 <= 0), cost: NONTERM Applied simplification Original rule: l2 -> [8] : (0 <= 0 /\ -5+i^0 == 0 /\ 3-i^post4 >= 0), cost: NONTERM New rule: l2 -> [8] : (-5+i^0 == 0 /\ -3+i^post4 <= 0), cost: NONTERM Applied deletion Removed the following rules: 26 27 28 Accelerated simple loops Start location: l7 30: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ -5+i^0 >= 0 /\ 5-i^0 >= 0 /\ -1+i^0-i^post4 <= 0), cost: NONTERM 33: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ -4+i^0 >= 0 /\ 4-i^0 >= 0 /\ -1+i^0-i^post4 <= 0), cost: NONTERM 39: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ 4-i^0 >= 0), cost: NONTERM 41: l2 -> l2 : i^0'=1+i^post4, (-5+i^0 <= 0 /\ -5+i^0 >= 0 /\ -4+i^post4 <= 0 /\ -4+i^post4 >= 0 /\ -1+n >= 0), cost: 4*n 42: l2 -> l2 : j^0'=9, i^0'=10, (-9+i^0 <= 0 /\ -6+i^0 >= 0), cost: 50-5*i^0 43: l2 -> l2 : j^0'=4, i^0'=5, -4+i^0 <= 0, cost: 25-5*i^0 44: l2 -> [8] : (-5+i^0 == 0 /\ -3+i^post4 <= 0 /\ -3+i^post4 >= 0), cost: NONTERM 45: l2 -> [8] : (-2+i^0-i^post4 <= 0 /\ -5+i^0 >= 0 /\ 3-i^post4 >= 0), cost: NONTERM 46: l2 -> [8] : (-4+i^0 >= 0 /\ -1+i^0-i^post4 <= 0 /\ -3+i^post4 <= 0), cost: NONTERM 47: l2 -> [8] : (-5+i^0 <= 0 /\ -5+i^0 >= 0 /\ -1+n7 >= 0 /\ -3+i^post4 <= 0), cost: NONTERM 48: l2 -> [8] : (-4+i^0 <= 0 /\ -1+n7 >= 0 /\ -3+i^post4 <= 0), cost: NONTERM 49: l2 -> [8] : (-5+i^0 == 0 /\ -3+i^post4 <= 0), cost: NONTERM 19: l7 -> l2 : i^0'=0, TRUE, cost: 2 Applied chaining First rule: l7 -> l2 : i^0'=0, TRUE, cost: 2 Second rule: l2 -> [8] : (1-i^0+i^post4 <= 0 /\ 4-i^0 >= 0), cost: NONTERM New rule: l7 -> [8] : 4 >= 0, cost: NONTERM Applied chaining First rule: l7 -> l2 : i^0'=0, TRUE, cost: 2 Second rule: l2 -> l2 : j^0'=4, i^0'=5, -4+i^0 <= 0, cost: 25-5*i^0 New rule: l7 -> l2 : j^0'=4, i^0'=5, -4 <= 0, cost: 27 Applied chaining First rule: l7 -> l2 : i^0'=0, TRUE, cost: 2 Second rule: l2 -> [8] : (-4+i^0 <= 0 /\ -1+n7 >= 0 /\ -3+i^post4 <= 0), cost: NONTERM New rule: l7 -> [8] : -4 <= 0, cost: NONTERM Applied deletion Removed the following rules: 30 33 39 41 42 43 44 45 46 47 48 49 Chained accelerated rules with incoming rules Start location: l7 19: l7 -> l2 : i^0'=0, TRUE, cost: 2 50: l7 -> [8] : 4 >= 0, cost: NONTERM 51: l7 -> l2 : j^0'=4, i^0'=5, -4 <= 0, cost: 27 52: l7 -> [8] : -4 <= 0, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l7 50: l7 -> [8] : 4 >= 0, cost: NONTERM 52: l7 -> [8] : -4 <= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 50 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: 4 >= 0