WORST_CASE(Omega(0),?) Initial ITS Start location: __init 0: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 1: f152_0_gcd_EQ -> f207_0_mod_LE : arg2'=arg2P1, arg1'=arg1P1, (arg2 > 0 /\ arg2-arg1 > 0 /\ arg1-arg1P1 == 0 /\ arg2-arg2P1 == 0 /\ arg1 > 0), cost: 1 2: f152_0_gcd_EQ -> f207_0_mod_LE : arg2'=arg2P2, arg1'=arg1P2, (arg2 > 0 /\ arg2-arg1 < 0 /\ arg1 > 0 /\ arg1-arg1P2 == 0 /\ arg2-arg2P2 == 0), cost: 1 3: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg2P3, arg1'=arg1P3, (-arg2P3 == 0 /\ arg2 > 0 /\ arg2-arg1P3 == 0 /\ -arg1 == 0), cost: 1 4: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg2P4, arg1'=arg1P4, (arg1-arg1P4 == 0 /\ -arg2+arg1 == 0 /\ arg1 > 0 /\ -arg2P4 == 0), cost: 1 5: f207_0_mod_LE -> f207_0_mod_LE : arg2'=arg2P5, arg1'=arg1P5, (arg2 > 0 /\ arg2-arg1 < 0 /\ -arg2-arg1P5+arg1 == 0 /\ arg2-arg2P5 == 0 /\ arg1 > 0), cost: 1 6: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg2P6, arg1'=arg1P6, (arg1-arg2P6 == 0 /\ arg2-arg1 > 0 /\ -arg1P6+arg2 == 0), cost: 1 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Applied preprocessing Original rule: f152_0_gcd_EQ -> f207_0_mod_LE : arg2'=arg2P1, arg1'=arg1P1, (arg2 > 0 /\ arg2-arg1 > 0 /\ arg1-arg1P1 == 0 /\ arg2-arg2P1 == 0 /\ arg1 > 0), cost: 1 New rule: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2-arg1 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f152_0_gcd_EQ -> f207_0_mod_LE : arg2'=arg2P2, arg1'=arg1P2, (arg2 > 0 /\ arg2-arg1 < 0 /\ arg1 > 0 /\ arg1-arg1P2 == 0 /\ arg2-arg2P2 == 0), cost: 1 New rule: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 Applied preprocessing Original rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg2P3, arg1'=arg1P3, (-arg2P3 == 0 /\ arg2 > 0 /\ arg2-arg1P3 == 0 /\ -arg1 == 0), cost: 1 New rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2, (arg2 > 0 /\ arg1 == 0), cost: 1 Applied preprocessing Original rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg2P4, arg1'=arg1P4, (arg1-arg1P4 == 0 /\ -arg2+arg1 == 0 /\ arg1 > 0 /\ -arg2P4 == 0), cost: 1 New rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, (-arg2+arg1 == 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f207_0_mod_LE -> f207_0_mod_LE : arg2'=arg2P5, arg1'=arg1P5, (arg2 > 0 /\ arg2-arg1 < 0 /\ -arg2-arg1P5+arg1 == 0 /\ arg2-arg2P5 == 0 /\ arg1 > 0), cost: 1 New rule: f207_0_mod_LE -> f207_0_mod_LE : arg1'=-arg2+arg1, (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 Applied preprocessing Original rule: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg2P6, arg1'=arg1P6, (arg1-arg2P6 == 0 /\ arg2-arg1 > 0 /\ -arg1P6+arg2 == 0), cost: 1 New rule: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, arg2-arg1 > 0, cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 8: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2-arg1 > 0 /\ arg1 > 0), cost: 1 9: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 10: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2, (arg2 > 0 /\ arg1 == 0), cost: 1 11: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, (-arg2+arg1 == 0 /\ arg1 > 0), cost: 1 12: f207_0_mod_LE -> f207_0_mod_LE : arg1'=-arg2+arg1, (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 13: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, arg2-arg1 > 0, cost: 1 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Applied acceleration Original rule: f207_0_mod_LE -> f207_0_mod_LE : arg1'=-arg2+arg1, (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 New rule: f207_0_mod_LE -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0), cost: n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_mBAFgJ.txt Applied deletion Removed the following rules: 12 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 8: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2-arg1 > 0 /\ arg1 > 0), cost: 1 9: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 10: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2, (arg2 > 0 /\ arg1 == 0), cost: 1 11: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, (-arg2+arg1 == 0 /\ arg1 > 0), cost: 1 13: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, arg2-arg1 > 0, cost: 1 14: f207_0_mod_LE -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0), cost: n0 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2, (arg2 > 0 /\ arg1 == 0), cost: 1 New rule: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2P0, (arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, (-arg2+arg1 == 0 /\ arg1 > 0), cost: 1 New rule: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2P0, (arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 2 Applied deletion Removed the following rules: 10 11 Applied chaining First rule: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2-arg1 > 0 /\ arg1 > 0), cost: 1 Second rule: f207_0_mod_LE -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0), cost: n0 New rule: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2-arg1 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0), cost: 1+n0 Applied chaining First rule: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 Second rule: f207_0_mod_LE -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0), cost: n0 New rule: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0), cost: 1+n0 Applied deletion Removed the following rules: 14 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 15: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2P0, (arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 2 8: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2-arg1 > 0 /\ arg1 > 0), cost: 1 9: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1 16: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2-arg1 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0), cost: 1+n0 17: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0), cost: 1+n0 13: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, arg2-arg1 > 0, cost: 1 7: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Second rule: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1 New rule: __init -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 2 Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P7, arg1'=arg1P7, TRUE, cost: 1 Second rule: f1_0_main_Load -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2P0, (arg2P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 2 New rule: __init -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2P0, (arg2P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 3 Applied deletion Removed the following rules: 0 7 15 Eliminating location f207_0_mod_LE by chaining: Applied chaining First rule: f152_0_gcd_EQ -> f207_0_mod_LE : (arg2-arg1 > 0 /\ arg1 > 0), cost: 1 Second rule: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, arg2-arg1 > 0, cost: 1 New rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, (arg2-arg1 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2-arg1 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0), cost: 1+n0 Second rule: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, arg2-arg1 > 0, cost: 1 New rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (arg2-arg1 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 Applied simplification Original rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (arg2-arg1 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 New rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (arg2-arg1 > 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 Applied chaining First rule: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=arg1-arg2*n0, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0), cost: 1+n0 Second rule: f207_0_mod_LE -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, arg2-arg1 > 0, cost: 1 New rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 Applied simplification Original rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (arg2 > 0 /\ n0 >= 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 New rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (-arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 Applied deletion Removed the following rules: 8 9 13 16 17 Eliminated locations on tree-shaped paths Start location: __init 20: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, (arg2-arg1 > 0 /\ arg1 > 0), cost: 2 21: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (arg2-arg1 > 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 22: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (-arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 18: __init -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 2 19: __init -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2P0, (arg2P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 3 Accelerated simple loops Start location: __init 20: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, (arg2-arg1 > 0 /\ arg1 > 0), cost: 2 21: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (arg2-arg1 > 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 22: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (-arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 18: __init -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 2 19: __init -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2P0, (arg2P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 3 Applied chaining First rule: __init -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 2 Second rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1, arg1'=arg2, (arg2-arg1 > 0 /\ arg1 > 0), cost: 2 New rule: __init -> f152_0_gcd_EQ : arg2'=arg1P0, arg1'=arg2P0, (arg2P0-arg1P0 > 0 /\ arg1P0 > 0), cost: 4 Applied chaining First rule: __init -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 2 Second rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (arg2-arg1 > 0 /\ -arg2-arg2*(-1+n0)+arg1 > 0 /\ arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 New rule: __init -> f152_0_gcd_EQ : arg2'=arg1P0-arg2P0*n0, arg1'=arg2P0, (arg2P0-arg1P0 > 0 /\ 1+arg1P0 > 0 /\ -arg2P0-arg2P0*(-1+n0)+arg1P0 > 0 /\ arg2P0-arg1P0+arg2P0*n0 > 0), cost: 4+n0 Applied chaining First rule: __init -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 2 Second rule: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=arg1-arg2*n0, arg1'=arg2, (-arg2-arg2*(-1+n0)+arg1 > 0 /\ -arg2+arg1 > 0 /\ arg2-arg1+arg2*n0 > 0), cost: 2+n0 New rule: __init -> f152_0_gcd_EQ : arg2'=arg1P0-arg2P0*n0, arg1'=arg2P0, (-arg2P0+arg1P0 > 0 /\ -arg2P0-arg2P0*(-1+n0)+arg1P0 > 0 /\ arg2P0-arg1P0+arg2P0*n0 > 0), cost: 4+n0 Applied deletion Removed the following rules: 20 21 22 Chained accelerated rules with incoming rules Start location: __init 18: __init -> f152_0_gcd_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 2 19: __init -> f152_0_gcd_EQ : arg2'=0, arg1'=arg2P0, (arg2P0 > 0 /\ arg1P7 > 0 /\ 1+arg2P7 > 0), cost: 3 23: __init -> f152_0_gcd_EQ : arg2'=arg1P0, arg1'=arg2P0, (arg2P0-arg1P0 > 0 /\ arg1P0 > 0), cost: 4 24: __init -> f152_0_gcd_EQ : arg2'=arg1P0-arg2P0*n0, arg1'=arg2P0, (arg2P0-arg1P0 > 0 /\ 1+arg1P0 > 0 /\ -arg2P0-arg2P0*(-1+n0)+arg1P0 > 0 /\ arg2P0-arg1P0+arg2P0*n0 > 0), cost: 4+n0 25: __init -> f152_0_gcd_EQ : arg2'=arg1P0-arg2P0*n0, arg1'=arg2P0, (-arg2P0+arg1P0 > 0 /\ -arg2P0-arg2P0*(-1+n0)+arg1P0 > 0 /\ arg2P0-arg1P0+arg2P0*n0 > 0), cost: 4+n0 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