NO Initial ITS Start location: __init 0: f1_0_main_Load -> f104_0_main_LE : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x20 > 0 /\ -arg1P0+x20-x30 == 0 /\ 1+x30 > 0 /\ -1+arg2 > 0), cost: 1 1: f104_0_main_LE -> f157_0_main_LE : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (1+arg1-arg3P1 == 0 /\ arg1 > 0 /\ 1+arg1-arg2P1 == 0 /\ 1+arg1-arg1P1 == 0), cost: 1 2: f157_0_main_LE -> f104_0_main_LE : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, (-arg3 == 0 /\ -arg2 == 0 /\ arg1-arg1P2 == 0), cost: 1 3: f157_0_main_LE -> f157_0_main_LE : arg1'=arg1P3, arg3'=arg3P3, arg2'=arg2P3, (-1+arg2-arg2P3 == 0 /\ -1-arg3P3+arg2 == 0 /\ -arg3+arg2 == 0 /\ arg1-arg1P3 == 0 /\ arg2 > 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f104_0_main_LE : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x20 > 0 /\ -arg1P0+x20-x30 == 0 /\ 1+x30 > 0 /\ -1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x20 > 0 /\ 1+x30 > 0 /\ -1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f104_0_main_LE -> f157_0_main_LE : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (1+arg1-arg3P1 == 0 /\ arg1 > 0 /\ 1+arg1-arg2P1 == 0 /\ 1+arg1-arg1P1 == 0), cost: 1 New rule: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=1+arg1, arg2'=1+arg1, arg1 > 0, cost: 1 Applied preprocessing Original rule: f157_0_main_LE -> f104_0_main_LE : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, (-arg3 == 0 /\ -arg2 == 0 /\ arg1-arg1P2 == 0), cost: 1 New rule: f157_0_main_LE -> f104_0_main_LE : arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 Applied preprocessing Original rule: f157_0_main_LE -> f157_0_main_LE : arg1'=arg1P3, arg3'=arg3P3, arg2'=arg2P3, (-1+arg2-arg2P3 == 0 /\ -1-arg3P3+arg2 == 0 /\ -arg3+arg2 == 0 /\ arg1-arg1P3 == 0 /\ arg2 > 0), cost: 1 New rule: f157_0_main_LE -> f157_0_main_LE : arg3'=-1+arg2, arg2'=-1+arg2, (-arg3+arg2 == 0 /\ arg2 > 0), cost: 1 Simplified rules Start location: __init 5: f1_0_main_Load -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x20 > 0 /\ 1+x30 > 0 /\ -1+arg2 > 0), cost: 1 6: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=1+arg1, arg2'=1+arg1, arg1 > 0, cost: 1 7: f157_0_main_LE -> f104_0_main_LE : arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 8: f157_0_main_LE -> f157_0_main_LE : arg3'=-1+arg2, arg2'=-1+arg2, (-arg3+arg2 == 0 /\ arg2 > 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Applied acceleration Original rule: f157_0_main_LE -> f157_0_main_LE : arg3'=-1+arg2, arg2'=-1+arg2, (-arg3+arg2 == 0 /\ arg2 > 0), cost: 1 New rule: f157_0_main_LE -> f157_0_main_LE : arg3'=arg2-n0, arg2'=arg2-n0, (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ 1+arg2-n0 > 0 /\ -1+n0 >= 0), cost: n0 Applied instantiation Original rule: f157_0_main_LE -> f157_0_main_LE : arg3'=arg2-n0, arg2'=arg2-n0, (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ 1+arg2-n0 > 0 /\ -1+n0 >= 0), cost: n0 New rule: f157_0_main_LE -> f157_0_main_LE : arg3'=0, arg2'=0, (1 > 0 /\ arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ -1+arg2 >= 0), cost: arg2 Applied simplification Original rule: f157_0_main_LE -> f157_0_main_LE : arg3'=0, arg2'=0, (1 > 0 /\ arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ -1+arg2 >= 0), cost: arg2 New rule: f157_0_main_LE -> f157_0_main_LE : arg3'=0, arg2'=0, (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ -1+arg2 >= 0), cost: arg2 Applied deletion Removed the following rules: 8 Accelerated simple loops Start location: __init 5: f1_0_main_Load -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x20 > 0 /\ 1+x30 > 0 /\ -1+arg2 > 0), cost: 1 6: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=1+arg1, arg2'=1+arg1, arg1 > 0, cost: 1 7: f157_0_main_LE -> f104_0_main_LE : arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 10: f157_0_main_LE -> f157_0_main_LE : arg3'=0, arg2'=0, (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ -1+arg2 >= 0), cost: arg2 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Applied chaining First rule: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=1+arg1, arg2'=1+arg1, arg1 > 0, cost: 1 Second rule: f157_0_main_LE -> f157_0_main_LE : arg3'=0, arg2'=0, (arg3-arg2 >= 0 /\ -arg3+arg2 >= 0 /\ -1+arg2 >= 0), cost: arg2 New rule: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=0, arg2'=0, arg1 > 0, cost: 2+arg1 Applied deletion Removed the following rules: 10 Chained accelerated rules with incoming rules Start location: __init 5: f1_0_main_Load -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x20 > 0 /\ 1+x30 > 0 /\ -1+arg2 > 0), cost: 1 6: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=1+arg1, arg2'=1+arg1, arg1 > 0, cost: 1 11: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=0, arg2'=0, arg1 > 0, cost: 2+arg1 7: f157_0_main_LE -> f104_0_main_LE : arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P4, arg3'=arg3P4, arg2'=arg2P4, TRUE, cost: 1 Second rule: f1_0_main_Load -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x20 > 0 /\ 1+x30 > 0 /\ -1+arg2 > 0), cost: 1 New rule: __init -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (1+x20 > 0 /\ arg1P4 > 0 /\ 1+x30 > 0 /\ -1+arg2P4 > 0), cost: 2 Applied deletion Removed the following rules: 4 5 Eliminated locations on linear paths Start location: __init 6: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=1+arg1, arg2'=1+arg1, arg1 > 0, cost: 1 11: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=0, arg2'=0, arg1 > 0, cost: 2+arg1 7: f157_0_main_LE -> f104_0_main_LE : arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 12: __init -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (1+x20 > 0 /\ arg1P4 > 0 /\ 1+x30 > 0 /\ -1+arg2P4 > 0), cost: 2 Eliminating location f157_0_main_LE by chaining: Applied chaining First rule: f104_0_main_LE -> f157_0_main_LE : arg1'=1+arg1, arg3'=0, arg2'=0, arg1 > 0, cost: 2+arg1 Second rule: f157_0_main_LE -> f104_0_main_LE : arg3'=arg3P2, arg2'=arg2P2, (arg3 == 0 /\ arg2 == 0), cost: 1 New rule: f104_0_main_LE -> f104_0_main_LE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (0 == 0 /\ arg1 > 0), cost: 3+arg1 Applied simplification Original rule: f104_0_main_LE -> f104_0_main_LE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, (0 == 0 /\ arg1 > 0), cost: 3+arg1 New rule: f104_0_main_LE -> f104_0_main_LE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, arg1 > 0, cost: 3+arg1 Applied deletion Removed the following rules: 6 7 11 Eliminated locations on tree-shaped paths Start location: __init 13: f104_0_main_LE -> f104_0_main_LE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, arg1 > 0, cost: 3+arg1 12: __init -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (1+x20 > 0 /\ arg1P4 > 0 /\ 1+x30 > 0 /\ -1+arg2P4 > 0), cost: 2 Applied nonterm Original rule: f104_0_main_LE -> f104_0_main_LE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, arg1 > 0, cost: 3+arg1 New rule: f104_0_main_LE -> [5] : arg1 > 0, cost: NONTERM Applied acceleration Original rule: f104_0_main_LE -> f104_0_main_LE : arg1'=1+arg1, arg3'=arg3P2, arg2'=arg2P2, arg1 > 0, cost: 3+arg1 New rule: f104_0_main_LE -> f104_0_main_LE : arg1'=arg1+n3, arg3'=arg3P2, arg2'=arg2P2, arg1 > 0, cost: 5/2*n3+1/2*n3^2+arg1*n3 Applied deletion Removed the following rules: 13 Accelerated simple loops Start location: __init 14: f104_0_main_LE -> [5] : arg1 > 0, cost: NONTERM 15: f104_0_main_LE -> f104_0_main_LE : arg1'=arg1+n3, arg3'=arg3P2, arg2'=arg2P2, arg1 > 0, cost: 5/2*n3+1/2*n3^2+arg1*n3 12: __init -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (1+x20 > 0 /\ arg1P4 > 0 /\ 1+x30 > 0 /\ -1+arg2P4 > 0), cost: 2 Applied chaining First rule: __init -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (1+x20 > 0 /\ arg1P4 > 0 /\ 1+x30 > 0 /\ -1+arg2P4 > 0), cost: 2 Second rule: f104_0_main_LE -> [5] : arg1 > 0, cost: NONTERM New rule: __init -> [5] : TRUE, cost: NONTERM Applied chaining First rule: __init -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (1+x20 > 0 /\ arg1P4 > 0 /\ 1+x30 > 0 /\ -1+arg2P4 > 0), cost: 2 Second rule: f104_0_main_LE -> f104_0_main_LE : arg1'=arg1+n3, arg3'=arg3P2, arg2'=arg2P2, arg1 > 0, cost: 5/2*n3+1/2*n3^2+arg1*n3 New rule: __init -> f104_0_main_LE : arg1'=x20+n3-x30, arg3'=arg3P2, arg2'=arg2P2, (x20-x30 > 0 /\ 1+x30 > 0), cost: 2+(x20-x30)*n3+5/2*n3+1/2*n3^2 Applied deletion Removed the following rules: 14 15 Chained accelerated rules with incoming rules Start location: __init 12: __init -> f104_0_main_LE : arg1'=x20-x30, arg3'=arg3P0, arg2'=arg2P0, (1+x20 > 0 /\ arg1P4 > 0 /\ 1+x30 > 0 /\ -1+arg2P4 > 0), cost: 2 16: __init -> [5] : TRUE, cost: NONTERM 17: __init -> f104_0_main_LE : arg1'=x20+n3-x30, arg3'=arg3P2, arg2'=arg2P2, (x20-x30 > 0 /\ 1+x30 > 0), cost: 2+(x20-x30)*n3+5/2*n3+1/2*n3^2 Removed unreachable locations and irrelevant leafs Start location: __init 16: __init -> [5] : TRUE, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 16 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: TRUE