NO Initial ITS Start location: __init 0: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=arg1P0, (20 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 20+arg2-arg1P0 == 0), cost: 1 1: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=arg1P1, (-25+arg1 < 0 /\ -10+arg1 > 0 /\ -1+arg1-arg1P1 == 0 /\ -31+arg1 < 0), cost: 1 2: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=arg1P2, (-25+arg1 > 0 /\ -1+arg1-arg1P2 == 0 /\ -31+arg1 < 0), cost: 1 3: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P3, arg1'=arg1P3, (20-arg1P3 == 0 /\ -30+arg1 > 0), cost: 1 4: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=arg1P4, (29-arg1P4 == 0 /\ 25-arg1 == 0), cost: 1 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=arg1P0, (20 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 20+arg2-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=arg1P1, (-25+arg1 < 0 /\ -10+arg1 > 0 /\ -1+arg1-arg1P1 == 0 /\ -31+arg1 < 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=-1+arg1, (-10+arg1 > 0 /\ 25-arg1 > 0), cost: 1 Applied preprocessing Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=arg1P2, (-25+arg1 > 0 /\ -1+arg1-arg1P2 == 0 /\ -31+arg1 < 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=-1+arg1, (-25+arg1 > 0 /\ 31-arg1 > 0), cost: 1 Applied preprocessing Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P3, arg1'=arg1P3, (20-arg1P3 == 0 /\ -30+arg1 > 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P3, arg1'=20, -30+arg1 > 0, cost: 1 Applied preprocessing Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=arg1P4, (29-arg1P4 == 0 /\ 25-arg1 == 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, -25+arg1 == 0, cost: 1 Simplified rules Start location: __init 6: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 7: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=-1+arg1, (-10+arg1 > 0 /\ 25-arg1 > 0), cost: 1 8: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=-1+arg1, (-25+arg1 > 0 /\ 31-arg1 > 0), cost: 1 9: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P3, arg1'=20, -30+arg1 > 0, cost: 1 10: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, -25+arg1 == 0, cost: 1 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Applied acceleration Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=-1+arg1, (-10+arg1 > 0 /\ 25-arg1 > 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=arg1-n, (-9+arg1-n > 0 /\ -1+n >= 0 /\ 25-arg1 > 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_jeDGmO.txt Applied instantiation Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=arg1-n, (-9+arg1-n > 0 /\ -1+n >= 0 /\ 25-arg1 > 0), cost: n New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=10, (1 > 0 /\ -11+arg1 >= 0 /\ 25-arg1 > 0), cost: -10+arg1 Applied acceleration Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=-1+arg1, (-25+arg1 > 0 /\ 31-arg1 > 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=-n0+arg1, (31-arg1 > 0 /\ -24-n0+arg1 > 0 /\ -1+n0 >= 0), cost: n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_JnOLPA.txt Applied instantiation Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=-n0+arg1, (31-arg1 > 0 /\ -24-n0+arg1 > 0 /\ -1+n0 >= 0), cost: n0 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, -25+arg1 == 0, cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, -25+arg1 == 0, cost: 5 Applied nonterm Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, -25+arg1 == 0, cost: 5 New rule: f121_0_loop_LE -> [3] : (-25+arg1 >= 0 /\ 25-arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_hMBnJM.txt Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 Second rule: f121_0_loop_LE -> [3] : (-25+arg1 >= 0 /\ 25-arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (0 >= 0 /\ 1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, -25+arg1 == 0, cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -24+arg1 Applied nonterm Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -24+arg1 New rule: f121_0_loop_LE -> [3] : (-1+n7 >= 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_PminFd.txt Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, -25+arg1 == 0, cost: 1 Second rule: f121_0_loop_LE -> [3] : (-1+n7 >= 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (-25+arg1 == 0 /\ -1+n7 >= 0 /\ 3 >= 0 /\ 2 > 0), cost: NONTERM Applied simplification Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=10, (1 > 0 /\ -11+arg1 >= 0 /\ 25-arg1 > 0), cost: -10+arg1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=10, (-11+arg1 >= 0 /\ 25-arg1 > 0), cost: -10+arg1 Applied simplification Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 Applied simplification Original rule: f121_0_loop_LE -> [3] : (-25+arg1 >= 0 /\ 25-arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (-25+arg1 <= 0 /\ -25+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM Applied simplification Original rule: f121_0_loop_LE -> [3] : (0 >= 0 /\ 1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (31-arg1 > 0 /\ -26+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM Applied simplification Original rule: f121_0_loop_LE -> [3] : (-25+arg1 == 0 /\ -1+n7 >= 0 /\ 3 >= 0 /\ 2 > 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (-25+arg1 == 0 /\ -1+n7 >= 0), cost: NONTERM Applied deletion Removed the following rules: 7 8 Accelerated simple loops Start location: __init 6: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 9: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P3, arg1'=20, -30+arg1 > 0, cost: 1 10: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, -25+arg1 == 0, cost: 1 15: f121_0_loop_LE -> [3] : (-1+n7 >= 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM 17: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=10, (-11+arg1 >= 0 /\ 25-arg1 > 0), cost: -10+arg1 18: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 19: f121_0_loop_LE -> [3] : (-25+arg1 <= 0 /\ -25+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM 20: f121_0_loop_LE -> [3] : (31-arg1 > 0 /\ -26+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM 21: f121_0_loop_LE -> [3] : (-25+arg1 == 0 /\ -1+n7 >= 0), cost: NONTERM 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P3, arg1'=20, -30+arg1 > 0, cost: 1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P3, arg1'=20, (arg1 > 0 /\ -10+arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, -25+arg1 == 0, cost: 1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, (-5+arg2 == 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f121_0_loop_LE -> [3] : (-1+n7 >= 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (-6+arg2 >= 0 /\ arg1 > 0 /\ 11-arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P1, arg1'=10, (-11+arg1 >= 0 /\ 25-arg1 > 0), cost: -10+arg1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P1, arg1'=10, (5-arg2 > 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 11+arg2 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (-6+arg2 >= 0 /\ arg1 > 0 /\ 11-arg2 > 0), cost: -4+arg2 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f121_0_loop_LE -> [3] : (-25+arg1 <= 0 /\ -25+arg1 >= 0 /\ -1+n6 >= 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 -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f121_0_loop_LE -> [3] : (31-arg1 > 0 /\ -26+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (-6+arg2 >= 0 /\ arg1 > 0 /\ 11-arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f121_0_loop_LE -> [3] : (-25+arg1 == 0 /\ -1+n7 >= 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 15 17 18 19 20 21 Chained accelerated rules with incoming rules Start location: __init 6: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P0, arg1'=20+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 22: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P3, arg1'=20, (arg1 > 0 /\ -10+arg2 > 0), cost: 2 23: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P4, arg1'=29, (-5+arg2 == 0 /\ arg1 > 0), cost: 2 24: f1_0_main_Load -> [3] : (-6+arg2 >= 0 /\ arg1 > 0 /\ 11-arg2 > 0), cost: NONTERM 25: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P1, arg1'=10, (5-arg2 > 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 11+arg2 26: f1_0_main_Load -> f121_0_loop_LE : arg2'=arg2P2, arg1'=25, (-6+arg2 >= 0 /\ arg1 > 0 /\ 11-arg2 > 0), cost: -4+arg2 27: f1_0_main_Load -> [3] : (-5+arg2 == 0 /\ arg1 > 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 24: f1_0_main_Load -> [3] : (-6+arg2 >= 0 /\ arg1 > 0 /\ 11-arg2 > 0), cost: NONTERM 27: f1_0_main_Load -> [3] : (-5+arg2 == 0 /\ arg1 > 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] : (-6+arg2 >= 0 /\ arg1 > 0 /\ 11-arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-6+arg2P5 >= 0 /\ arg1P5 > 0 /\ 11-arg2P5 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (-5+arg2 == 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [3] : (-5+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM Applied deletion Removed the following rules: 5 24 27 Eliminated locations on tree-shaped paths Start location: __init 28: __init -> [3] : (-6+arg2P5 >= 0 /\ arg1P5 > 0 /\ 11-arg2P5 > 0), cost: NONTERM 29: __init -> [3] : (-5+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 28 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-6+arg2P5 >= 0 /\ arg1P5 > 0 /\ 11-arg2P5 > 0)