NO Initial ITS Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ -arg2P0+arg2 == 0 /\ 5-arg1P0 == 0), cost: 1 1: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (arg2 < 0 /\ 1+arg1-arg1P1 == 0 /\ 1-arg2-arg2P1 == 0 /\ arg2+arg1 < 0), cost: 1 2: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, (arg2 > 0 /\ 1-arg2-arg2P2 == 0 /\ 1+arg1-arg1P2 == 0 /\ arg2+arg1 < 0), cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, (-arg2P3 == 0 /\ arg2 < 0 /\ arg2-arg1 <= 0 /\ arg2+arg1 >= 0 /\ 1-arg1P3+arg1 == 0), cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, (arg2 > 0 /\ arg2-arg1 <= 0 /\ 1+arg1-arg1P4 == 0 /\ -arg2P4 == 0 /\ arg2+arg1 >= 0), cost: 1 5: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P5, arg1'=arg1P5, (-1-arg2-arg2P5 == 0 /\ arg2 < 0 /\ arg2-arg1 > 0 /\ 1-arg1P5+arg1 == 0 /\ arg2+arg1 >= 0), cost: 1 6: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P6, arg1'=arg1P6, (arg2 > 0 /\ arg2-arg1 > 0 /\ 1-arg1P6+arg1 == 0 /\ -1-arg2-arg2P6 == 0 /\ arg2+arg1 >= 0), cost: 1 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Removed rules with unsatisfiable guard Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ -arg2P0+arg2 == 0 /\ 5-arg1P0 == 0), cost: 1 1: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (arg2 < 0 /\ 1+arg1-arg1P1 == 0 /\ 1-arg2-arg2P1 == 0 /\ arg2+arg1 < 0), cost: 1 2: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, (arg2 > 0 /\ 1-arg2-arg2P2 == 0 /\ 1+arg1-arg1P2 == 0 /\ arg2+arg1 < 0), cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, (-arg2P3 == 0 /\ arg2 < 0 /\ arg2-arg1 <= 0 /\ arg2+arg1 >= 0 /\ 1-arg1P3+arg1 == 0), cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, (arg2 > 0 /\ arg2-arg1 <= 0 /\ 1+arg1-arg1P4 == 0 /\ -arg2P4 == 0 /\ arg2+arg1 >= 0), cost: 1 6: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P6, arg1'=arg1P6, (arg2 > 0 /\ arg2-arg1 > 0 /\ 1-arg1P6+arg1 == 0 /\ -1-arg2-arg2P6 == 0 /\ arg2+arg1 >= 0), cost: 1 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f142_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ -arg2P0+arg2 == 0 /\ 5-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (arg2 < 0 /\ 1+arg1-arg1P1 == 0 /\ 1-arg2-arg2P1 == 0 /\ arg2+arg1 < 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (-arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, (arg2 > 0 /\ 1-arg2-arg2P2 == 0 /\ 1+arg1-arg1P2 == 0 /\ arg2+arg1 < 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, (-arg2P3 == 0 /\ arg2 < 0 /\ arg2-arg1 <= 0 /\ arg2+arg1 >= 0 /\ 1-arg1P3+arg1 == 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=0, arg1'=1+arg1, (-arg2 > 0 /\ arg2+arg1 >= 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, (arg2 > 0 /\ arg2-arg1 <= 0 /\ 1+arg1-arg1P4 == 0 /\ -arg2P4 == 0 /\ arg2+arg1 >= 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=0, arg1'=1+arg1, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=arg2P6, arg1'=arg1P6, (arg2 > 0 /\ arg2-arg1 > 0 /\ 1-arg1P6+arg1 == 0 /\ -1-arg2-arg2P6 == 0 /\ arg2+arg1 >= 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=1+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 1 Simplified rules Start location: __init 8: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (1+arg2 > 0 /\ arg1 > 0), cost: 1 9: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (-arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 10: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 11: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=0, arg1'=1+arg1, (-arg2 > 0 /\ arg2+arg1 >= 0), cost: 1 12: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=0, arg1'=1+arg1, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 13: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=1+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 1 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=1+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (-arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=2+arg2, arg1'=2+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 2 Applied nonterm Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=2+arg2, arg1'=2+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 2 New rule: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ n1 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_dPnMnn.txt Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (-arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 Second rule: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ n1 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM New rule: f142_0_loop_EQ -> [3] : (2-arg2+arg1 >= 0 /\ -arg2 > 0 /\ n1 >= 0 /\ -arg2-arg1 > 0), cost: NONTERM Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (-arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=1+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-2+arg2, arg1'=2+arg1, (2-arg2+arg1 >= 0 /\ -arg2 > 0 /\ -arg2-arg1 > 0), cost: 2 Applied nonterm Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-2+arg2, arg1'=2+arg1, (2-arg2+arg1 >= 0 /\ -arg2 > 0 /\ -arg2-arg1 > 0), cost: 2 New rule: f142_0_loop_EQ -> [3] : (2-arg2+arg1 >= 0 /\ -arg2 > 0 /\ -arg2-arg1 > 0 /\ n3 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_fdpfCd.txt Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=1+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 1 Second rule: f142_0_loop_EQ -> [3] : (2-arg2+arg1 >= 0 /\ -arg2 > 0 /\ -arg2-arg1 > 0 /\ n3 >= 0), cost: NONTERM New rule: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ 4+arg2+arg1 >= 0 /\ 1+arg2 > 0 /\ n3 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ 4+arg2+arg1 >= 0 /\ 1+arg2 > 0 /\ n3 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM New rule: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ n3 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM Accelerated simple loops Start location: __init 8: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (1+arg2 > 0 /\ arg1 > 0), cost: 1 9: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (-arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 10: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=1-arg2, arg1'=1+arg1, (arg2 > 0 /\ -arg2-arg1 > 0), cost: 1 11: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=0, arg1'=1+arg1, (-arg2 > 0 /\ arg2+arg1 >= 0), cost: 1 12: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=0, arg1'=1+arg1, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 13: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=1+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 1 14: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ n1 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM 15: f142_0_loop_EQ -> [3] : (2-arg2+arg1 >= 0 /\ -arg2 > 0 /\ n1 >= 0 /\ -arg2-arg1 > 0), cost: NONTERM 16: f142_0_loop_EQ -> [3] : (2-arg2+arg1 >= 0 /\ -arg2 > 0 /\ -arg2-arg1 > 0 /\ n3 >= 0), cost: NONTERM 18: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ n3 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=0, arg1'=1+arg1, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 New rule: f1_0_main_Load -> f142_0_loop_EQ : arg2'=0, arg1'=6, (-5+arg2 <= 0 /\ arg2 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=1+arg1, (arg2-arg1 > 0 /\ arg2+arg1 >= 0), cost: 1 New rule: f1_0_main_Load -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=6, (-5+arg2 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ n1 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f142_0_loop_EQ -> [3] : (arg2-arg1 > 0 /\ n3 >= 0 /\ arg2+arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied deletion Removed the following rules: 9 10 11 12 13 14 15 16 18 Chained accelerated rules with incoming rules Start location: __init 8: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (1+arg2 > 0 /\ arg1 > 0), cost: 1 19: f1_0_main_Load -> f142_0_loop_EQ : arg2'=0, arg1'=6, (-5+arg2 <= 0 /\ arg2 > 0 /\ arg1 > 0), cost: 2 20: f1_0_main_Load -> f142_0_loop_EQ : arg2'=-1-arg2, arg1'=6, (-5+arg2 > 0 /\ arg1 > 0), cost: 2 21: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 21: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [3] : (-5+arg2P7 > 0 /\ arg1P7 > 0), cost: NONTERM Applied deletion Removed the following rules: 7 21 Eliminated locations on linear paths Start location: __init 22: __init -> [3] : (-5+arg2P7 > 0 /\ arg1P7 > 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: (-5+arg2P7 > 0 /\ arg1P7 > 0)