NO Initial ITS Start location: __init 0: f1_0_main_Load -> f50_0_increase_GE : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0 /\ -arg1P0+arg2 == 0), cost: 1 1: f50_0_increase_GE -> f79_0_increase_LE : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (arg1-arg2P1 == 0 /\ -10+arg1 < 0 /\ arg1-arg1P1 == 0 /\ arg1-arg3P1 == 0), cost: 1 2: f79_0_increase_LE -> f50_0_increase_GE : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, (-arg3 == 0 /\ -arg2 == 0 /\ 1+arg1-arg1P2 == 0), cost: 1 3: f79_0_increase_LE -> f79_0_increase_LE : arg1'=arg1P3, arg3'=arg3P3, arg2'=arg2P3, (1+arg2-arg2P3 == 0 /\ -arg3+arg2 == 0 /\ 1-arg3P3+arg2 == 0 /\ arg2 > 0 /\ arg1-arg1P3 == 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f50_0_increase_GE : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0 /\ -arg1P0+arg2 == 0), cost: 1 New rule: f1_0_main_Load -> f50_0_increase_GE : arg1'=arg2, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f50_0_increase_GE -> f79_0_increase_LE : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (arg1-arg2P1 == 0 /\ -10+arg1 < 0 /\ arg1-arg1P1 == 0 /\ arg1-arg3P1 == 0), cost: 1 New rule: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1, arg2'=arg1, 10-arg1 > 0, cost: 1 Applied preprocessing Original rule: f79_0_increase_LE -> f50_0_increase_GE : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, (-arg3 == 0 /\ -arg2 == 0 /\ 1+arg1-arg1P2 == 0), cost: 1 New rule: f79_0_increase_LE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 Applied preprocessing Original rule: f79_0_increase_LE -> f79_0_increase_LE : arg1'=arg1P3, arg3'=arg3P3, arg2'=arg2P3, (1+arg2-arg2P3 == 0 /\ -arg3+arg2 == 0 /\ 1-arg3P3+arg2 == 0 /\ arg2 > 0 /\ arg1-arg1P3 == 0), cost: 1 New rule: f79_0_increase_LE -> f79_0_increase_LE : arg3'=1+arg2, arg2'=1+arg2, (-arg3+arg2 == 0 /\ arg2 > 0), cost: 1 Simplified rules Start location: __init 5: f1_0_main_Load -> f50_0_increase_GE : arg1'=arg2, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 6: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1, arg2'=arg1, 10-arg1 > 0, cost: 1 7: f79_0_increase_LE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 8: f79_0_increase_LE -> f79_0_increase_LE : arg3'=1+arg2, arg2'=1+arg2, (-arg3+arg2 == 0 /\ arg2 > 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Applied nonterm Original rule: f79_0_increase_LE -> f79_0_increase_LE : arg3'=1+arg2, arg2'=1+arg2, (-arg3+arg2 == 0 /\ arg2 > 0), cost: 1 New rule: f79_0_increase_LE -> [4] : (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ arg2 > 0), cost: NONTERM Applied acceleration Original rule: f79_0_increase_LE -> f79_0_increase_LE : arg3'=1+arg2, arg2'=1+arg2, (-arg3+arg2 == 0 /\ arg2 > 0), cost: 1 New rule: f79_0_increase_LE -> f79_0_increase_LE : arg3'=n0+arg2, arg2'=n0+arg2, (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ arg2 > 0), cost: n0 Applied deletion Removed the following rules: 8 Accelerated simple loops Start location: __init 5: f1_0_main_Load -> f50_0_increase_GE : arg1'=arg2, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 6: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1, arg2'=arg1, 10-arg1 > 0, cost: 1 7: f79_0_increase_LE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 9: f79_0_increase_LE -> [4] : (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ arg2 > 0), cost: NONTERM 10: f79_0_increase_LE -> f79_0_increase_LE : arg3'=n0+arg2, arg2'=n0+arg2, (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ arg2 > 0), cost: n0 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Applied chaining First rule: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1, arg2'=arg1, 10-arg1 > 0, cost: 1 Second rule: f79_0_increase_LE -> [4] : (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ arg2 > 0), cost: NONTERM New rule: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM Applied chaining First rule: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1, arg2'=arg1, 10-arg1 > 0, cost: 1 Second rule: f79_0_increase_LE -> f79_0_increase_LE : arg3'=n0+arg2, arg2'=n0+arg2, (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ arg2 > 0), cost: n0 New rule: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1+n0, arg2'=arg1+n0, (arg1 > 0 /\ 10-arg1 > 0), cost: 1+n0 Applied deletion Removed the following rules: 9 10 Chained accelerated rules with incoming rules Start location: __init 5: f1_0_main_Load -> f50_0_increase_GE : arg1'=arg2, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 6: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1, arg2'=arg1, 10-arg1 > 0, cost: 1 11: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM 12: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1+n0, arg2'=arg1+n0, (arg1 > 0 /\ 10-arg1 > 0), cost: 1+n0 7: f79_0_increase_LE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Second rule: f1_0_main_Load -> f50_0_increase_GE : arg1'=arg2, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 New rule: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 Applied deletion Removed the following rules: 4 5 Eliminated locations on linear paths Start location: __init 6: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1, arg2'=arg1, 10-arg1 > 0, cost: 1 11: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM 12: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1+n0, arg2'=arg1+n0, (arg1 > 0 /\ 10-arg1 > 0), cost: 1+n0 7: f79_0_increase_LE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 13: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 Eliminating location f79_0_increase_LE by chaining: Applied chaining First rule: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1, arg2'=arg1, 10-arg1 > 0, cost: 1 Second rule: f79_0_increase_LE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg1 == 0 /\ 10-arg1 > 0), cost: 2 Applied simplification Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg1 == 0 /\ 10-arg1 > 0), cost: 2 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, arg1 == 0, cost: 2 Applied chaining First rule: f50_0_increase_GE -> f79_0_increase_LE : arg3'=arg1+n0, arg2'=arg1+n0, (arg1 > 0 /\ 10-arg1 > 0), cost: 1+n0 Second rule: f79_0_increase_LE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ arg1+n0 == 0 /\ 10-arg1 > 0), cost: 2+n0 Applied deletion Removed the following rules: 6 7 12 Eliminated locations on tree-shaped paths Start location: __init 11: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM 14: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, arg1 == 0, cost: 2 15: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ arg1+n0 == 0 /\ 10-arg1 > 0), cost: 2+n0 13: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 Applied simplification Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ arg1+n0 == 0 /\ 10-arg1 > 0), cost: 2+n0 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ 10-arg1 > 0), cost: 2-arg1 Simplified simple loops Start location: __init 11: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM 14: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, arg1 == 0, cost: 2 16: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ 10-arg1 > 0), cost: 2-arg1 13: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 Applied acceleration Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, arg1 == 0, cost: 2 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=arg1+n4, arg3'=arg3P2, arg2'=arg2P2, (arg1 >= 0 /\ -arg1 >= 0 /\ -1+n4 >= 0 /\ 1-arg1-n4 >= 0), cost: 2*n4 Applied instantiation Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=arg1+n4, arg3'=arg3P2, arg2'=arg2P2, (arg1 >= 0 /\ -arg1 >= 0 /\ -1+n4 >= 0 /\ 1-arg1-n4 >= 0), cost: 2*n4 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1, arg3'=arg3P2, arg2'=arg2P2, (0 >= 0 /\ arg1 >= 0 /\ -arg1 >= 0), cost: 2-2*arg1 Applied acceleration Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ 10-arg1 > 0), cost: 2-arg1 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=arg1+n6, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ 11-arg1-n6 > 0 /\ -1+n6 >= 0), cost: -1/2*n6^2+5/2*n6-arg1*n6 Applied instantiation Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=arg1+n6, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ 11-arg1-n6 > 0 /\ -1+n6 >= 0), cost: -1/2*n6^2+5/2*n6-arg1*n6 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=10, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ 1 > 0 /\ 9-arg1 >= 0), cost: 25-5/2*arg1+arg1*(-10+arg1)-1/2*(-10+arg1)^2 Applied simplification Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1, arg3'=arg3P2, arg2'=arg2P2, (0 >= 0 /\ arg1 >= 0 /\ -arg1 >= 0), cost: 2-2*arg1 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1, arg3'=arg3P2, arg2'=arg2P2, (arg1 <= 0 /\ arg1 >= 0), cost: 2-2*arg1 Applied simplification Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=10, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ 1 > 0 /\ 9-arg1 >= 0), cost: 25-5/2*arg1+arg1*(-10+arg1)-1/2*(-10+arg1)^2 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=10, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ -9+arg1 <= 0), cost: 25-5/2*arg1+arg1*(-10+arg1)-1/2*(-10+arg1)^2 Applied deletion Removed the following rules: 14 16 Accelerated simple loops Start location: __init 11: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM 19: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1, arg3'=arg3P2, arg2'=arg2P2, (arg1 <= 0 /\ arg1 >= 0), cost: 2-2*arg1 20: f50_0_increase_GE -> f50_0_increase_GE : arg1'=10, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ -9+arg1 <= 0), cost: 25-5/2*arg1+arg1*(-10+arg1)-1/2*(-10+arg1)^2 13: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 Applied chaining First rule: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 Second rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=1, arg3'=arg3P2, arg2'=arg2P2, (arg1 <= 0 /\ arg1 >= 0), cost: 2-2*arg1 New rule: __init -> f50_0_increase_GE : arg1'=1, arg3'=arg3P2, arg2'=arg2P2, 1 > 0, cost: 4 Applied chaining First rule: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 Second rule: f50_0_increase_GE -> f50_0_increase_GE : arg1'=10, arg3'=arg3P2, arg2'=arg2P2, (arg1 > 0 /\ -9+arg1 <= 0), cost: 25-5/2*arg1+arg1*(-10+arg1)-1/2*(-10+arg1)^2 New rule: __init -> f50_0_increase_GE : arg1'=10, arg3'=arg3P2, arg2'=arg2P2, (arg2P4 > 0 /\ -9+arg2P4 <= 0), cost: 27+(-10+arg2P4)*arg2P4-1/2*(-10+arg2P4)^2-5/2*arg2P4 Applied deletion Removed the following rules: 19 20 Chained accelerated rules with incoming rules Start location: __init 11: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM 13: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 21: __init -> f50_0_increase_GE : arg1'=1, arg3'=arg3P2, arg2'=arg2P2, 1 > 0, cost: 4 22: __init -> f50_0_increase_GE : arg1'=10, arg3'=arg3P2, arg2'=arg2P2, (arg2P4 > 0 /\ -9+arg2P4 <= 0), cost: 27+(-10+arg2P4)*arg2P4-1/2*(-10+arg2P4)^2-5/2*arg2P4 Eliminating location f50_0_increase_GE by chaining: Applied chaining First rule: __init -> f50_0_increase_GE : arg1'=arg2P4, arg3'=arg3P0, arg2'=arg2P0, (arg1P4 > 0 /\ 1+arg2P4 > 0), cost: 2 Second rule: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM New rule: __init -> [4] : (arg1P4 > 0 /\ arg2P4 > 0 /\ 10-arg2P4 > 0 /\ 1+arg2P4 > 0), cost: NONTERM Applied simplification Original rule: __init -> [4] : (arg1P4 > 0 /\ arg2P4 > 0 /\ 10-arg2P4 > 0 /\ 1+arg2P4 > 0), cost: NONTERM New rule: __init -> [4] : (arg1P4 > 0 /\ arg2P4 > 0 /\ 10-arg2P4 > 0), cost: NONTERM Applied chaining First rule: __init -> f50_0_increase_GE : arg1'=1, arg3'=arg3P2, arg2'=arg2P2, 1 > 0, cost: 4 Second rule: f50_0_increase_GE -> [4] : (arg1 > 0 /\ 10-arg1 > 0), cost: NONTERM New rule: __init -> [4] : (1 > 0 /\ 9 > 0), cost: NONTERM Applied partial deletion Original rule: __init -> f50_0_increase_GE : arg1'=10, arg3'=arg3P2, arg2'=arg2P2, (arg2P4 > 0 /\ -9+arg2P4 <= 0), cost: 27+(-10+arg2P4)*arg2P4-1/2*(-10+arg2P4)^2-5/2*arg2P4 New rule: __init -> [6] : (arg2P4 > 0 /\ -9+arg2P4 <= 0), cost: 27+(-10+arg2P4)*arg2P4-1/2*(-10+arg2P4)^2-5/2*arg2P4 Applied deletion Removed the following rules: 11 13 21 22 Eliminated locations on tree-shaped paths Start location: __init 23: __init -> [4] : (arg1P4 > 0 /\ arg2P4 > 0 /\ 10-arg2P4 > 0), cost: NONTERM 24: __init -> [4] : (1 > 0 /\ 9 > 0), cost: NONTERM 25: __init -> [6] : (arg2P4 > 0 /\ -9+arg2P4 <= 0), cost: 27+(-10+arg2P4)*arg2P4-1/2*(-10+arg2P4)^2-5/2*arg2P4 Computing asymptotic complexity Proved nontermination of rule 23 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P4 > 0 /\ arg2P4 > 0 /\ 10-arg2P4 > 0)