WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1 > 0 /\ -1+arg2 > 0), cost: 1 1: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg2P1, arg4'=arg4P1, arg1'=arg1P1, arg3'=arg3P1, (arg2 > 0 /\ arg2-arg1 <= 0 /\ -arg2P1+arg1 == 0 /\ -arg3P1+arg2 == 0 /\ arg2-arg1P1 == 0 /\ arg2-arg4P1 == 0), cost: 1 2: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg2P2, arg4'=arg4P2, arg1'=arg1P2, arg3'=arg3P2, (-arg4 == 0 /\ -arg3 == 0 /\ -arg1P2+arg2 == 0 /\ arg1-arg2P2 == 0), cost: 1 3: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2P3, arg4'=arg4P3, arg1'=arg1P3, arg3'=arg3P3, (-arg1P3+arg1 == 0 /\ 1-arg3P3+arg3 == 0 /\ -1+arg3 < 0 /\ 1+arg2-arg2P3 == 0 /\ arg3 < 0 /\ 1-arg4P3+arg3 == 0 /\ -arg4+arg3 == 0), cost: 1 4: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2P4, arg4'=arg4P4, arg1'=arg1P4, arg3'=arg3P4, (-arg1P4+arg1 == 0 /\ 1-arg4P4+arg3 == 0 /\ 1-arg3P4+arg3 == 0 /\ -1+arg3 < 0 /\ 1-arg2P4+arg2 == 0 /\ arg3 > 0 /\ -arg4+arg3 == 0), cost: 1 5: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2P5, arg4'=arg4P5, arg1'=arg1P5, arg3'=arg3P5, (-1+arg2-arg2P5 == 0 /\ -1+arg3-arg3P5 == 0 /\ arg3 > 0 /\ arg1-arg1P5 == 0 /\ -1-arg4P5+arg3 == 0 /\ -arg4+arg3 == 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg4'=arg4P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Removed rules with unsatisfiable guard Start location: __init 0: f1_0_main_Load -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1 > 0 /\ -1+arg2 > 0), cost: 1 1: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg2P1, arg4'=arg4P1, arg1'=arg1P1, arg3'=arg3P1, (arg2 > 0 /\ arg2-arg1 <= 0 /\ -arg2P1+arg1 == 0 /\ -arg3P1+arg2 == 0 /\ arg2-arg1P1 == 0 /\ arg2-arg4P1 == 0), cost: 1 2: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg2P2, arg4'=arg4P2, arg1'=arg1P2, arg3'=arg3P2, (-arg4 == 0 /\ -arg3 == 0 /\ -arg1P2+arg2 == 0 /\ arg1-arg2P2 == 0), cost: 1 3: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2P3, arg4'=arg4P3, arg1'=arg1P3, arg3'=arg3P3, (-arg1P3+arg1 == 0 /\ 1-arg3P3+arg3 == 0 /\ -1+arg3 < 0 /\ 1+arg2-arg2P3 == 0 /\ arg3 < 0 /\ 1-arg4P3+arg3 == 0 /\ -arg4+arg3 == 0), cost: 1 5: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2P5, arg4'=arg4P5, arg1'=arg1P5, arg3'=arg3P5, (-1+arg2-arg2P5 == 0 /\ -1+arg3-arg3P5 == 0 /\ arg3 > 0 /\ arg1-arg1P5 == 0 /\ -1-arg4P5+arg3 == 0 /\ -arg4+arg3 == 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg4'=arg4P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Applied preprocessing Original rule: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg2P1, arg4'=arg4P1, arg1'=arg1P1, arg3'=arg3P1, (arg2 > 0 /\ arg2-arg1 <= 0 /\ -arg2P1+arg1 == 0 /\ -arg3P1+arg2 == 0 /\ arg2-arg1P1 == 0 /\ arg2-arg4P1 == 0), cost: 1 New rule: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg1, arg4'=arg2, arg1'=arg2, arg3'=arg2, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 Applied preprocessing Original rule: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg2P2, arg4'=arg4P2, arg1'=arg1P2, arg3'=arg3P2, (-arg4 == 0 /\ -arg3 == 0 /\ -arg1P2+arg2 == 0 /\ arg1-arg2P2 == 0), cost: 1 New rule: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg1, arg4'=arg4P2, arg1'=arg2, arg3'=arg3P2, (arg4 == 0 /\ arg3 == 0), cost: 1 Applied preprocessing Original rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2P3, arg4'=arg4P3, arg1'=arg1P3, arg3'=arg3P3, (-arg1P3+arg1 == 0 /\ 1-arg3P3+arg3 == 0 /\ -1+arg3 < 0 /\ 1+arg2-arg2P3 == 0 /\ arg3 < 0 /\ 1-arg4P3+arg3 == 0 /\ -arg4+arg3 == 0), cost: 1 New rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=1+arg2, arg4'=1+arg3, arg3'=1+arg3, (-arg3 > 0 /\ -arg4+arg3 == 0), cost: 1 Applied preprocessing Original rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2P5, arg4'=arg4P5, arg1'=arg1P5, arg3'=arg3P5, (-1+arg2-arg2P5 == 0 /\ -1+arg3-arg3P5 == 0 /\ arg3 > 0 /\ arg1-arg1P5 == 0 /\ -1-arg4P5+arg3 == 0 /\ -arg4+arg3 == 0), cost: 1 New rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=-1+arg2, arg4'=-1+arg3, arg3'=-1+arg3, (arg3 > 0 /\ -arg4+arg3 == 0), cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1 > 0 /\ -1+arg2 > 0), cost: 1 7: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg1, arg4'=arg2, arg1'=arg2, arg3'=arg2, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 8: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg1, arg4'=arg4P2, arg1'=arg2, arg3'=arg3P2, (arg4 == 0 /\ arg3 == 0), cost: 1 9: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=1+arg2, arg4'=1+arg3, arg3'=1+arg3, (-arg3 > 0 /\ -arg4+arg3 == 0), cost: 1 10: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=-1+arg2, arg4'=-1+arg3, arg3'=-1+arg3, (arg3 > 0 /\ -arg4+arg3 == 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg4'=arg4P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Applied acceleration Original rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=1+arg2, arg4'=1+arg3, arg3'=1+arg3, (-arg3 > 0 /\ -arg4+arg3 == 0), cost: 1 New rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2+n, arg4'=n+arg3, arg3'=n+arg3, (-1+n >= 0 /\ 1-n-arg3 > 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_oChlOG.txt Applied instantiation Original rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2+n, arg4'=n+arg3, arg3'=n+arg3, (-1+n >= 0 /\ 1-n-arg3 > 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: n New rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (1 > 0 /\ -1-arg3 >= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: -arg3 Applied acceleration Original rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=-1+arg2, arg4'=-1+arg3, arg3'=-1+arg3, (arg3 > 0 /\ -arg4+arg3 == 0), cost: 1 New rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-n0, arg4'=-n0+arg3, arg3'=-n0+arg3, (1-n0+arg3 > 0 /\ arg4-arg3 >= 0 /\ -1+n0 >= 0 /\ -arg4+arg3 >= 0), cost: n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_fgHMej.txt Applied instantiation Original rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-n0, arg4'=-n0+arg3, arg3'=-n0+arg3, (1-n0+arg3 > 0 /\ arg4-arg3 >= 0 /\ -1+n0 >= 0 /\ -arg4+arg3 >= 0), cost: n0 New rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (1 > 0 /\ -1+arg3 >= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: arg3 Applied simplification Original rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (1 > 0 /\ -1-arg3 >= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: -arg3 New rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (1+arg3 <= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: -arg3 Applied simplification Original rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (1 > 0 /\ -1+arg3 >= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: arg3 New rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (-1+arg3 >= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: arg3 Applied deletion Removed the following rules: 9 10 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1 > 0 /\ -1+arg2 > 0), cost: 1 7: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg1, arg4'=arg2, arg1'=arg2, arg3'=arg2, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 8: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg1, arg4'=arg4P2, arg1'=arg2, arg3'=arg3P2, (arg4 == 0 /\ arg3 == 0), cost: 1 13: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (1+arg3 <= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: -arg3 14: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (-1+arg3 >= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: arg3 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg4'=arg4P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Applied chaining First rule: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg1, arg4'=arg2, arg1'=arg2, arg3'=arg2, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 Second rule: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg4'=0, arg3'=0, (-1+arg3 >= 0 /\ arg4-arg3 >= 0 /\ -arg4+arg3 >= 0), cost: arg3 New rule: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=-arg2+arg1, arg4'=0, arg1'=arg2, arg3'=0, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 1+arg2 Applied deletion Removed the following rules: 13 14 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1 > 0 /\ -1+arg2 > 0), cost: 1 7: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg1, arg4'=arg2, arg1'=arg2, arg3'=arg2, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 15: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=-arg2+arg1, arg4'=0, arg1'=arg2, arg3'=0, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 1+arg2 8: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg1, arg4'=arg4P2, arg1'=arg2, arg3'=arg3P2, (arg4 == 0 /\ arg3 == 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg4'=arg4P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P6, arg4'=arg4P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Second rule: f1_0_main_Load -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1 > 0 /\ -1+arg2 > 0), cost: 1 New rule: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1P6 > 0 /\ -1+arg2P6 > 0), cost: 2 Applied deletion Removed the following rules: 0 6 Eliminated locations on linear paths Start location: __init 7: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=arg1, arg4'=arg2, arg1'=arg2, arg3'=arg2, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1 15: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=-arg2+arg1, arg4'=0, arg1'=arg2, arg3'=0, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 1+arg2 8: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg1, arg4'=arg4P2, arg1'=arg2, arg3'=arg3P2, (arg4 == 0 /\ arg3 == 0), cost: 1 16: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1P6 > 0 /\ -1+arg2P6 > 0), cost: 2 Eliminating location f319_0_minus_EQ by chaining: Applied chaining First rule: f248_0_mod_LT -> f319_0_minus_EQ : arg2'=-arg2+arg1, arg4'=0, arg1'=arg2, arg3'=0, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 1+arg2 Second rule: f319_0_minus_EQ -> f248_0_mod_LT : arg2'=arg1, arg4'=arg4P2, arg1'=arg2, arg3'=arg3P2, (arg4 == 0 /\ arg3 == 0), cost: 1 New rule: f248_0_mod_LT -> f248_0_mod_LT : arg2'=arg2, arg4'=arg4P2, arg1'=-arg2+arg1, arg3'=arg3P2, (0 == 0 /\ arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 2+arg2 Applied simplification Original rule: f248_0_mod_LT -> f248_0_mod_LT : arg2'=arg2, arg4'=arg4P2, arg1'=-arg2+arg1, arg3'=arg3P2, (0 == 0 /\ arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 2+arg2 New rule: f248_0_mod_LT -> f248_0_mod_LT : arg2'=arg2, arg4'=arg4P2, arg1'=-arg2+arg1, arg3'=arg3P2, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 2+arg2 Applied deletion Removed the following rules: 7 8 15 Eliminated locations on tree-shaped paths Start location: __init 17: f248_0_mod_LT -> f248_0_mod_LT : arg2'=arg2, arg4'=arg4P2, arg1'=-arg2+arg1, arg3'=arg3P2, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 2+arg2 16: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1P6 > 0 /\ -1+arg2P6 > 0), cost: 2 Applied simplification Original rule: f248_0_mod_LT -> f248_0_mod_LT : arg2'=arg2, arg4'=arg4P2, arg1'=-arg2+arg1, arg3'=arg3P2, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 2+arg2 New rule: f248_0_mod_LT -> f248_0_mod_LT : arg4'=arg4P2, arg1'=-arg2+arg1, arg3'=arg3P2, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 2+arg2 Simplified simple loops Start location: __init 18: f248_0_mod_LT -> f248_0_mod_LT : arg4'=arg4P2, arg1'=-arg2+arg1, arg3'=arg3P2, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 2+arg2 16: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1P6 > 0 /\ -1+arg2P6 > 0), cost: 2 Applied acceleration Original rule: f248_0_mod_LT -> f248_0_mod_LT : arg4'=arg4P2, arg1'=-arg2+arg1, arg3'=arg3P2, (arg2-arg1 <= 0 /\ -1+arg2 >= 0), cost: 2+arg2 New rule: f248_0_mod_LT -> f248_0_mod_LT : arg4'=arg4P2, arg1'=arg1-n1*arg2, arg3'=arg3P2, (-arg2+arg1-arg2*(-1+n1) >= 0 /\ -1+arg2 >= 0 /\ -1+n1 >= 0), cost: 2*n1+n1*arg2 Sub-proof via acceration calculus written to file:///tmp/tmpnam_bNaMNO.txt Applied deletion Removed the following rules: 18 Accelerated simple loops Start location: __init 19: f248_0_mod_LT -> f248_0_mod_LT : arg4'=arg4P2, arg1'=arg1-n1*arg2, arg3'=arg3P2, (-arg2+arg1-arg2*(-1+n1) >= 0 /\ -1+arg2 >= 0 /\ -1+n1 >= 0), cost: 2*n1+n1*arg2 16: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1P6 > 0 /\ -1+arg2P6 > 0), cost: 2 Applied chaining First rule: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1P6 > 0 /\ -1+arg2P6 > 0), cost: 2 Second rule: f248_0_mod_LT -> f248_0_mod_LT : arg4'=arg4P2, arg1'=arg1-n1*arg2, arg3'=arg3P2, (-arg2+arg1-arg2*(-1+n1) >= 0 /\ -1+arg2 >= 0 /\ -1+n1 >= 0), cost: 2*n1+n1*arg2 New rule: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P2, arg1'=arg1P0-n1*arg2P0, arg3'=arg3P2, (-1+arg2P0 >= 0 /\ -1+n1 >= 0 /\ -arg2P0+arg1P0-arg2P0*(-1+n1) >= 0), cost: 2+2*n1+n1*arg2P0 Applied deletion Removed the following rules: 19 Chained accelerated rules with incoming rules Start location: __init 16: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (1+arg1P0 > 0 /\ 1+arg2P0 > 0 /\ arg1P6 > 0 /\ -1+arg2P6 > 0), cost: 2 20: __init -> f248_0_mod_LT : arg2'=arg2P0, arg4'=arg4P2, arg1'=arg1P0-n1*arg2P0, arg3'=arg3P2, (-1+arg2P0 >= 0 /\ -1+n1 >= 0 /\ -arg2P0+arg1P0-arg2P0*(-1+n1) >= 0), cost: 2+2*n1+n1*arg2P0 Removed unreachable locations and irrelevant leafs Start location: __init Computing asymptotic complexity Proved the following lower bound Complexity: Unknown Cpx degree: ? Solved cost: 0 Rule cost: 0