NO Initial ITS Start location: __init 0: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 1: f162_0_main_LT -> f162_0_main_LT : arg2'=arg2P1, arg1'=arg1P1, (1+arg1 > 0 /\ arg2-arg1 <= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 > 0 /\ arg2-arg2P1 == 0 /\ -1+arg1-arg1P1 == 0), cost: 1 2: f162_0_main_LT -> f162_0_main_LT : arg2'=arg2P2, arg1'=arg1P2, (1+arg1 > 0 /\ 1+2*arg1-arg1P2 == 0 /\ arg2-arg1 <= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 == 0 /\ 2*arg1 >= 0 /\ 1+arg2-arg2P2 == 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f162_0_main_LT -> f162_0_main_LT : arg2'=arg2P1, arg1'=arg1P1, (1+arg1 > 0 /\ arg2-arg1 <= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 > 0 /\ arg2-arg2P1 == 0 /\ -1+arg1-arg1P1 == 0), cost: 1 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+arg1, (1+arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 Applied preprocessing Original rule: f162_0_main_LT -> f162_0_main_LT : arg2'=arg2P2, arg1'=arg1P2, (1+arg1 > 0 /\ 1+2*arg1-arg1P2 == 0 /\ arg2-arg1 <= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 == 0 /\ 2*arg1 >= 0 /\ 1+arg2-arg2P2 == 0), cost: 1 New rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg1, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 4: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+arg1, (1+arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 5: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg1, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied acceleration Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+arg1, (1+arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg1-n, (1-arg2+arg1-n > 0 /\ 1+arg2 > 0 /\ n >= 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_OLfIja.txt Applied instantiation Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg1-n, (1-arg2+arg1-n > 0 /\ 1+arg2 > 0 /\ n >= 0), cost: n New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg1, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 New rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+arg2, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1-arg2+2*arg1 Applied nonterm Original rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+arg2, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1-arg2+2*arg1 New rule: f162_0_main_LT -> [3] : (arg2-arg1 >= 0 /\ -arg2+arg1 >= 0 /\ arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_idCDdd.txt Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 Second rule: f162_0_main_LT -> [3] : (arg2-arg1 >= 0 /\ -arg2+arg1 >= 0 /\ arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM New rule: f162_0_main_LT -> [3] : (0 >= 0 /\ 1 > 0 /\ arg2 >= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg1, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1 New rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg2, (1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: 1-arg2+arg1 Applied nonterm Original rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg2, (1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: 1-arg2+arg1 New rule: f162_0_main_LT -> [3] : (-1+n4 >= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_geiNdH.txt Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg1, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (-1+n4 >= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: NONTERM New rule: f162_0_main_LT -> [3] : (2+arg2 > 0 /\ -arg2+2*arg1 >= 0 /\ -1+n4 >= 0 /\ -arg2+arg1 == 0 /\ arg1 >= 0), cost: NONTERM Applied simplification Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 Applied simplification Original rule: f162_0_main_LT -> [3] : (0 >= 0 /\ 1 > 0 /\ arg2 >= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM New rule: f162_0_main_LT -> [3] : (1+arg2 > 0 /\ -arg2+arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM Applied simplification Original rule: f162_0_main_LT -> [3] : (2+arg2 > 0 /\ -arg2+2*arg1 >= 0 /\ -1+n4 >= 0 /\ -arg2+arg1 == 0 /\ arg1 >= 0), cost: NONTERM New rule: f162_0_main_LT -> [3] : (-1+n4 >= 0 /\ -arg2+arg1 == 0 /\ arg1 >= 0), cost: NONTERM Applied deletion Removed the following rules: 4 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 5: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg1, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1 7: f162_0_main_LT -> [3] : (arg2-arg1 >= 0 /\ -arg2+arg1 >= 0 /\ arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM 9: f162_0_main_LT -> [3] : (-1+n4 >= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: NONTERM 11: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 12: f162_0_main_LT -> [3] : (1+arg2 > 0 /\ -arg2+arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM 13: f162_0_main_LT -> [3] : (-1+n4 >= 0 /\ -arg2+arg1 == 0 /\ arg1 >= 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg2'=1+arg2, arg1'=1+2*arg1, (-arg2+arg1 == 0 /\ arg1 >= 0), cost: 1 New rule: f1_0_main_Load -> f162_0_main_LT : arg2'=1+arg1P0, arg1'=1+2*arg1P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (arg2-arg1 >= 0 /\ -arg2+arg1 >= 0 /\ arg1 >= 0 /\ -1+n3 >= 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 -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (-1+n4 >= 0 /\ 1+arg2 > 0 /\ -arg2+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 -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: -arg2+arg1 New rule: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg2P0, (1+arg2P0 > 0 /\ -arg2P0+arg1P0 >= 0 /\ arg1 > 0 /\ -1+arg2 > 0), cost: 1-arg2P0+arg1P0 Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (1+arg2 > 0 /\ -arg2+arg1 >= 0 /\ -1+n3 >= 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 -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (-1+n4 >= 0 /\ -arg2+arg1 == 0 /\ arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied deletion Removed the following rules: 5 7 9 11 12 13 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 14: f1_0_main_Load -> f162_0_main_LT : arg2'=1+arg1P0, arg1'=1+2*arg1P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 2 15: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 16: f1_0_main_Load -> f162_0_main_LT : arg2'=arg2P0, arg1'=arg2P0, (1+arg2P0 > 0 /\ -arg2P0+arg1P0 >= 0 /\ arg1 > 0 /\ -1+arg2 > 0), cost: 1-arg2P0+arg1P0 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 15: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 3 15 Eliminated locations on linear paths Start location: __init 17: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 17 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-1+arg2P3 > 0 /\ arg1P3 > 0)