NO Initial ITS Start location: __init 0: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 1: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (2+arg1-arg1P1 == 0 /\ 3+arg1 > 0 /\ arg1 < 0), cost: 1 2: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, (-3+arg1 < 0 /\ arg1 > 0 /\ -2+arg1-arg1P2 == 0), cost: 1 3: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, (-2-arg1P3-arg1 == 0 /\ 1+arg1 < 0 /\ 2+arg1 < 0 /\ arg1 < 0), cost: 1 4: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, (-2+arg1 > 0 /\ 2-arg1-arg1P4 == 0), cost: 1 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (2+arg1-arg1P1 == 0 /\ 3+arg1 > 0 /\ arg1 < 0), cost: 1 New rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, arg1'=2+arg1, (3+arg1 > 0 /\ -arg1 > 0), cost: 1 Applied preprocessing Original rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, (-3+arg1 < 0 /\ arg1 > 0 /\ -2+arg1-arg1P2 == 0), cost: 1 New rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg1, (arg1 > 0 /\ 3-arg1 > 0), cost: 1 Applied preprocessing Original rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, (-2-arg1P3-arg1 == 0 /\ 1+arg1 < 0 /\ 2+arg1 < 0 /\ arg1 < 0), cost: 1 New rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P3, arg1'=-2-arg1, -2-arg1 > 0, cost: 1 Applied preprocessing Original rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, (-2+arg1 > 0 /\ 2-arg1-arg1P4 == 0), cost: 1 New rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P4, arg1'=2-arg1, -2+arg1 > 0, cost: 1 Simplified rules Start location: __init 6: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 7: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, arg1'=2+arg1, (3+arg1 > 0 /\ -arg1 > 0), cost: 1 8: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg1, (arg1 > 0 /\ 3-arg1 > 0), cost: 1 9: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P3, arg1'=-2-arg1, -2-arg1 > 0, cost: 1 10: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P4, arg1'=2-arg1, -2+arg1 > 0, cost: 1 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Applied chaining First rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg1, (arg1 > 0 /\ 3-arg1 > 0), cost: 1 Second rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, arg1'=2+arg1, (3+arg1 > 0 /\ -arg1 > 0), cost: 1 New rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, -1+arg1 == 0, cost: 2 Applied nonterm Original rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, -1+arg1 == 0, cost: 2 New rule: f81_0_loop_EQ -> [3] : (-1+n5 >= 0 /\ 1-arg1 >= 0 /\ -1+arg1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_PMNIpc.txt Applied chaining First rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, arg1'=2+arg1, (3+arg1 > 0 /\ -arg1 > 0), cost: 1 Second rule: f81_0_loop_EQ -> [3] : (-1+n5 >= 0 /\ 1-arg1 >= 0 /\ -1+arg1 >= 0), cost: NONTERM New rule: f81_0_loop_EQ -> [3] : (1+arg1 >= 0 /\ -1-arg1 >= 0 /\ -1+n5 >= 0 /\ 3+arg1 > 0 /\ -arg1 > 0), cost: NONTERM Applied chaining First rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, arg1'=2+arg1, (3+arg1 > 0 /\ -arg1 > 0), cost: 1 Second rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg1, (arg1 > 0 /\ 3-arg1 > 0), cost: 1 New rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, 1+arg1 == 0, cost: 2 Applied nonterm Original rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, 1+arg1 == 0, cost: 2 New rule: f81_0_loop_EQ -> [3] : (1+arg1 >= 0 /\ -1-arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_FAKgfj.txt Applied chaining First rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg1, (arg1 > 0 /\ 3-arg1 > 0), cost: 1 Second rule: f81_0_loop_EQ -> [3] : (1+arg1 >= 0 /\ -1-arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM New rule: f81_0_loop_EQ -> [3] : (arg1 > 0 /\ -1+n6 >= 0 /\ 3-arg1 > 0 /\ 1-arg1 >= 0 /\ -1+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f81_0_loop_EQ -> [3] : (-1+n5 >= 0 /\ 1-arg1 >= 0 /\ -1+arg1 >= 0), cost: NONTERM New rule: f81_0_loop_EQ -> [3] : (-1+n5 >= 0 /\ -1+arg1 <= 0 /\ -1+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f81_0_loop_EQ -> [3] : (1+arg1 >= 0 /\ -1-arg1 >= 0 /\ -1+n5 >= 0 /\ 3+arg1 > 0 /\ -arg1 > 0), cost: NONTERM New rule: f81_0_loop_EQ -> [3] : (1+arg1 >= 0 /\ -1+n5 >= 0 /\ -arg1 > 0), cost: NONTERM Applied simplification Original rule: f81_0_loop_EQ -> [3] : (1+arg1 >= 0 /\ -1-arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM New rule: f81_0_loop_EQ -> [3] : (1+arg1 <= 0 /\ 1+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM Applied simplification Original rule: f81_0_loop_EQ -> [3] : (arg1 > 0 /\ -1+n6 >= 0 /\ 3-arg1 > 0 /\ 1-arg1 >= 0 /\ -1+arg1 >= 0), cost: NONTERM New rule: f81_0_loop_EQ -> [3] : (-1+n6 >= 0 /\ -1+arg1 <= 0 /\ -1+arg1 >= 0), cost: NONTERM Accelerated simple loops Start location: __init 6: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 7: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P1, arg1'=2+arg1, (3+arg1 > 0 /\ -arg1 > 0), cost: 1 8: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg1, (arg1 > 0 /\ 3-arg1 > 0), cost: 1 9: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P3, arg1'=-2-arg1, -2-arg1 > 0, cost: 1 10: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P4, arg1'=2-arg1, -2+arg1 > 0, cost: 1 15: f81_0_loop_EQ -> [3] : (-1+n5 >= 0 /\ -1+arg1 <= 0 /\ -1+arg1 >= 0), cost: NONTERM 16: f81_0_loop_EQ -> [3] : (1+arg1 >= 0 /\ -1+n5 >= 0 /\ -arg1 > 0), cost: NONTERM 17: f81_0_loop_EQ -> [3] : (1+arg1 <= 0 /\ 1+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM 18: f81_0_loop_EQ -> [3] : (-1+n6 >= 0 /\ -1+arg1 <= 0 /\ -1+arg1 >= 0), cost: NONTERM 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg1, (arg1 > 0 /\ 3-arg1 > 0), cost: 1 New rule: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg2, (arg2 > 0 /\ arg1 > 0 /\ 3-arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f81_0_loop_EQ -> f81_0_loop_EQ : arg2'=arg2P4, arg1'=2-arg1, -2+arg1 > 0, cost: 1 New rule: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P4, arg1'=2-arg2, (-2+arg2 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f81_0_loop_EQ -> [3] : (-1+n5 >= 0 /\ -1+arg1 <= 0 /\ -1+arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 == 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f81_0_loop_EQ -> [3] : (-1+n6 >= 0 /\ -1+arg1 <= 0 /\ -1+arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 == 0), cost: NONTERM Applied deletion Removed the following rules: 7 8 9 10 15 16 17 18 Chained accelerated rules with incoming rules Start location: __init 6: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 19: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P2, arg1'=-2+arg2, (arg2 > 0 /\ arg1 > 0 /\ 3-arg2 > 0), cost: 2 20: f1_0_main_Load -> f81_0_loop_EQ : arg2'=arg2P4, arg1'=2-arg2, (-2+arg2 > 0 /\ arg1 > 0), cost: 2 21: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 == 0), cost: NONTERM 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 21: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 == 0), cost: NONTERM 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 == 0), cost: NONTERM New rule: __init -> [3] : (-1+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM Applied deletion Removed the following rules: 5 21 Eliminated locations on linear paths Start location: __init 22: __init -> [3] : (-1+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 22 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-1+arg2P5 == 0 /\ arg1P5 > 0)