NO Initial ITS Start location: __init 0: f1_0_main_Load -> f121_0_loop_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 20-arg1P0+arg2 == 0 /\ 20 > 0 /\ 1+arg2 > 0), cost: 1 1: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P1, arg2'=arg2P1, (-31+arg1 < 0 /\ -1+arg1-arg1P1 == 0 /\ -10+arg1 > 0 /\ -25+arg1 < 0), cost: 1 2: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P2, arg2'=arg2P2, (-31+arg1 < 0 /\ -1+arg1-arg1P2 == 0 /\ -25+arg1 > 0), cost: 1 3: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P3, arg2'=arg2P3, (20-arg1P3 == 0 /\ -30+arg1 > 0), cost: 1 4: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P4, arg2'=arg2P4, (25-arg1 == 0 /\ 29-arg1P4 == 0), cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 20-arg1P0+arg2 == 0 /\ 20 > 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P1, arg2'=arg2P1, (-31+arg1 < 0 /\ -1+arg1-arg1P1 == 0 /\ -10+arg1 > 0 /\ -25+arg1 < 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P1, (-10+arg1 > 0 /\ 25-arg1 > 0), cost: 1 Applied preprocessing Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P2, arg2'=arg2P2, (-31+arg1 < 0 /\ -1+arg1-arg1P2 == 0 /\ -25+arg1 > 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P2, (31-arg1 > 0 /\ -25+arg1 > 0), cost: 1 Applied preprocessing Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P3, arg2'=arg2P3, (20-arg1P3 == 0 /\ -30+arg1 > 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=20, arg2'=arg2P3, -30+arg1 > 0, cost: 1 Applied preprocessing Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1P4, arg2'=arg2P4, (25-arg1 == 0 /\ 29-arg1P4 == 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1 Simplified rules Start location: __init 6: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 7: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P1, (-10+arg1 > 0 /\ 25-arg1 > 0), cost: 1 8: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P2, (31-arg1 > 0 /\ -25+arg1 > 0), cost: 1 9: f121_0_loop_LE -> f121_0_loop_LE : arg1'=20, arg2'=arg2P3, -30+arg1 > 0, cost: 1 10: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Applied acceleration Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P1, (-10+arg1 > 0 /\ 25-arg1 > 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1-n3, arg2'=arg2P1, (25-arg1 > 0 /\ -1+n3 >= 0 /\ -9+arg1-n3 > 0), cost: n3 Applied instantiation Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1-n3, arg2'=arg2P1, (25-arg1 > 0 /\ -1+n3 >= 0 /\ -9+arg1-n3 > 0), cost: n3 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=10, arg2'=arg2P1, (1 > 0 /\ 25-arg1 > 0 /\ -11+arg1 >= 0), cost: -10+arg1 Applied acceleration Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P2, (31-arg1 > 0 /\ -25+arg1 > 0), cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1-n5, arg2'=arg2P2, (31-arg1 > 0 /\ -24+arg1-n5 > 0 /\ -1+n5 >= 0), cost: n5 Applied instantiation Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=arg1-n5, arg2'=arg2P2, (31-arg1 > 0 /\ -24+arg1-n5 > 0 /\ -1+n5 >= 0), cost: n5 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, -25+arg1 == 0, cost: 5 Applied nonterm Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, -25+arg1 == 0, cost: 5 New rule: f121_0_loop_LE -> [3] : (25-arg1 >= 0 /\ -25+arg1 >= 0), cost: NONTERM Applied acceleration Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, -25+arg1 == 0, cost: 5 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (25-arg1 >= 0 /\ -25+arg1 >= 0), cost: 5*n13 Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 Second rule: f121_0_loop_LE -> [3] : (25-arg1 >= 0 /\ -25+arg1 >= 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (0 >= 0 /\ 1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM Heuristically decided not to add the following rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (25-arg1 >= 0 /\ -25+arg1 >= 0), cost: 5*n13 Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -24+arg1 Applied nonterm Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -24+arg1 New rule: f121_0_loop_LE -> [3] : (31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM Applied acceleration Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -24+arg1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: 5*n15 Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1 Second rule: f121_0_loop_LE -> [3] : (31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (3 >= 0 /\ 2 > 0 /\ -25+arg1 == 0), cost: NONTERM Applied chaining First rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: 5*n15 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (3 >= 0 /\ 2 > 0 /\ -25+arg1 == 0), cost: 1+5*n15 Applied simplification Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=10, arg2'=arg2P1, (1 > 0 /\ 25-arg1 > 0 /\ -11+arg1 >= 0), cost: -10+arg1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=10, arg2'=arg2P1, (25-arg1 > 0 /\ -11+arg1 >= 0), cost: -10+arg1 Applied simplification Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 Applied simplification Original rule: f121_0_loop_LE -> [3] : (25-arg1 >= 0 /\ -25+arg1 >= 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (-25+arg1 <= 0 /\ -25+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f121_0_loop_LE -> [3] : (0 >= 0 /\ 1 > 0 /\ 31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : (31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f121_0_loop_LE -> [3] : (3 >= 0 /\ 2 > 0 /\ -25+arg1 == 0), cost: NONTERM New rule: f121_0_loop_LE -> [3] : -25+arg1 == 0, cost: NONTERM Applied simplification Original rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (3 >= 0 /\ 2 > 0 /\ -25+arg1 == 0), cost: 1+5*n15 New rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1+5*n15 Applied deletion Removed the following rules: 7 8 Applied deletion Removed the following rules: 15 Accelerated simple loops Start location: __init 6: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 9: f121_0_loop_LE -> f121_0_loop_LE : arg1'=20, arg2'=arg2P3, -30+arg1 > 0, cost: 1 10: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1 17: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: 5*n15 19: f121_0_loop_LE -> f121_0_loop_LE : arg1'=10, arg2'=arg2P1, (25-arg1 > 0 /\ -11+arg1 >= 0), cost: -10+arg1 20: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 21: f121_0_loop_LE -> [3] : (-25+arg1 <= 0 /\ -25+arg1 >= 0), cost: NONTERM 22: f121_0_loop_LE -> [3] : (31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM 23: f121_0_loop_LE -> [3] : -25+arg1 == 0, cost: NONTERM 24: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1+5*n15 5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=20, arg2'=arg2P3, -30+arg1 > 0, cost: 1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20, arg2'=arg2P3, (arg1 > 0 /\ -10+arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (arg1 > 0 /\ -5+arg2 == 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: 5*n15 New rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (arg1 > 0 /\ 11-arg2 > 0 /\ -6+arg2 >= 0), cost: 1+5*n15 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=10, arg2'=arg2P1, (25-arg1 > 0 /\ -11+arg1 >= 0), cost: -10+arg1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=10, arg2'=arg2P1, (arg1 > 0 /\ 1+arg2 > 0 /\ 5-arg2 > 0), cost: 11+arg2 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (31-arg1 > 0 /\ -26+arg1 >= 0), cost: -25+arg1 New rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (arg1 > 0 /\ 11-arg2 > 0 /\ -6+arg2 >= 0), cost: -4+arg2 Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> [3] : (-25+arg1 <= 0 /\ -25+arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> [3] : (31-arg1 > 0 /\ -26+arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ 11-arg2 > 0 /\ -6+arg2 >= 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> [3] : -25+arg1 == 0, cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f121_0_loop_LE -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, -25+arg1 == 0, cost: 1+5*n15 New rule: f1_0_main_Load -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (arg1 > 0 /\ -5+arg2 == 0), cost: 2+5*n15 Applied deletion Removed the following rules: 9 10 17 19 20 21 22 23 24 Chained accelerated rules with incoming rules Start location: __init 6: f1_0_main_Load -> f121_0_loop_LE : arg1'=20+arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 25: f1_0_main_Load -> f121_0_loop_LE : arg1'=20, arg2'=arg2P3, (arg1 > 0 /\ -10+arg2 > 0), cost: 2 26: f1_0_main_Load -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (arg1 > 0 /\ -5+arg2 == 0), cost: 2 27: f1_0_main_Load -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (arg1 > 0 /\ 11-arg2 > 0 /\ -6+arg2 >= 0), cost: 1+5*n15 28: f1_0_main_Load -> f121_0_loop_LE : arg1'=10, arg2'=arg2P1, (arg1 > 0 /\ 1+arg2 > 0 /\ 5-arg2 > 0), cost: 11+arg2 29: f1_0_main_Load -> f121_0_loop_LE : arg1'=25, arg2'=arg2P2, (arg1 > 0 /\ 11-arg2 > 0 /\ -6+arg2 >= 0), cost: -4+arg2 30: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM 31: f1_0_main_Load -> [3] : (arg1 > 0 /\ 11-arg2 > 0 /\ -6+arg2 >= 0), cost: NONTERM 32: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM 33: f1_0_main_Load -> f121_0_loop_LE : arg1'=29, arg2'=arg2P4, (arg1 > 0 /\ -5+arg2 == 0), cost: 2+5*n15 5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 30: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM 31: f1_0_main_Load -> [3] : (arg1 > 0 /\ 11-arg2 > 0 /\ -6+arg2 >= 0), cost: NONTERM 32: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM 5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM New rule: __init -> [3] : (-5+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ 11-arg2 > 0 /\ -6+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 : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 == 0), cost: NONTERM New rule: __init -> [3] : (-5+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM Applied deletion Removed the following rules: 5 30 31 32 Eliminated locations on tree-shaped paths Start location: __init 34: __init -> [3] : (-5+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM 35: __init -> [3] : (-6+arg2P5 >= 0 /\ arg1P5 > 0 /\ 11-arg2P5 > 0), cost: NONTERM 36: __init -> [3] : (-5+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM Removed duplicate rules (ignoring updates) Start location: __init 35: __init -> [3] : (-6+arg2P5 >= 0 /\ arg1P5 > 0 /\ 11-arg2P5 > 0), cost: NONTERM 36: __init -> [3] : (-5+arg2P5 == 0 /\ arg1P5 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 35 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)