NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=arg2P0, arg1'=arg1P0, (-arg1P0 == 0 /\ 100-arg2P0 == 0), cost: 1 1: f162_0_main_GE -> f162_0_main_GE : arg2'=arg2P1, arg1'=arg1P1, (-2+arg2-arg1 > 0 /\ arg2-arg1 > 0 /\ 1+arg1-arg1P1 == 0 /\ arg2-arg2P1 == 0), cost: 1 2: f162_0_main_GE -> f162_0_main_GE : arg2'=arg2P2, arg1'=arg1P2, (2-arg2+arg1 == 0 /\ -2 < 0 /\ -1+arg2-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0), cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=arg2P0, arg1'=arg1P0, (-arg1P0 == 0 /\ 100-arg2P0 == 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 Applied preprocessing Original rule: f162_0_main_GE -> f162_0_main_GE : arg2'=arg2P1, arg1'=arg1P1, (-2+arg2-arg1 > 0 /\ arg2-arg1 > 0 /\ 1+arg1-arg1P1 == 0 /\ arg2-arg2P1 == 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, -2+arg2-arg1 > 0, cost: 1 Applied preprocessing Original rule: f162_0_main_GE -> f162_0_main_GE : arg2'=arg2P2, arg1'=arg1P2, (2-arg2+arg1 == 0 /\ -2 < 0 /\ -1+arg2-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0), cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, 2-arg2+arg1 == 0, cost: 1 Simplified rules Start location: __init 4: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 5: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, -2+arg2-arg1 > 0, cost: 1 6: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, 2-arg2+arg1 == 0, cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied acceleration Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=1+arg1, -2+arg2-arg1 > 0, cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1+n, (-1+arg2-arg1-n > 0 /\ n >= 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_BiBABa.txt Applied instantiation Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=arg1+n, (-1+arg2-arg1-n > 0 /\ n >= 0), cost: n New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (-2+arg2-arg1 >= 0 /\ 1 > 0), cost: -2+arg2-arg1 Applied nonterm Original rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, 2-arg2+arg1 == 0, cost: 1 New rule: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ 2-arg2+arg1 >= 0 /\ -1+n0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_JmiMpC.txt Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, 2-arg2+arg1 == 0, cost: 1 Second rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (-2+arg2-arg1 >= 0 /\ 1 > 0), cost: -2+arg2-arg1 New rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, 2-arg2+arg1 == 0, cost: 1 Applied nonterm Original rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, 2-arg2+arg1 == 0, cost: 1 New rule: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ 2-arg2+arg1 >= 0 /\ -1+n2 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_bJbCpa.txt Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (-2+arg2-arg1 >= 0 /\ 1 > 0), cost: -2+arg2-arg1 Second rule: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ 2-arg2+arg1 >= 0 /\ -1+n2 >= 0), cost: NONTERM New rule: f162_0_main_GE -> [3] : (0 >= 0 /\ -2+arg2-arg1 >= 0 /\ 1 > 0 /\ -1+n2 >= 0), cost: NONTERM Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (-2+arg2-arg1 >= 0 /\ 1 > 0), cost: -2+arg2-arg1 Second rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, 2-arg2+arg1 == 0, cost: 1 New rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, -2+arg2-arg1 >= 0, cost: -1+arg2-arg1 Applied nonterm Original rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, -2+arg2-arg1 >= 0, cost: -1+arg2-arg1 New rule: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_LFnAIl.txt Applied chaining First rule: f162_0_main_GE -> f162_0_main_GE : arg2'=1+arg2, arg1'=-1+arg2, 2-arg2+arg1 == 0, cost: 1 Second rule: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM New rule: f162_0_main_GE -> [3] : (0 >= 0 /\ 2-arg2+arg1 == 0 /\ -1+n3 >= 0), cost: NONTERM Applied simplification Original rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, (-2+arg2-arg1 >= 0 /\ 1 > 0), cost: -2+arg2-arg1 New rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, -2+arg2-arg1 >= 0, cost: -2+arg2-arg1 Applied simplification Original rule: f162_0_main_GE -> [3] : (0 >= 0 /\ -2+arg2-arg1 >= 0 /\ 1 > 0 /\ -1+n2 >= 0), cost: NONTERM New rule: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ -1+n2 >= 0), cost: NONTERM Applied simplification Original rule: f162_0_main_GE -> [3] : (0 >= 0 /\ 2-arg2+arg1 == 0 /\ -1+n3 >= 0), cost: NONTERM New rule: f162_0_main_GE -> [3] : (2-arg2+arg1 == 0 /\ -1+n3 >= 0), cost: NONTERM Applied deletion Removed the following rules: 5 6 Accelerated simple loops Start location: __init 4: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 8: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ 2-arg2+arg1 >= 0 /\ -1+n0 >= 0), cost: NONTERM 9: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ 2-arg2+arg1 >= 0 /\ -1+n2 >= 0), cost: NONTERM 11: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM 13: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, -2+arg2-arg1 >= 0, cost: -2+arg2-arg1 14: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ -1+n2 >= 0), cost: NONTERM 15: f162_0_main_GE -> [3] : (2-arg2+arg1 == 0 /\ -1+n3 >= 0), cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 Second rule: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ -1+n3 >= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM Applied chaining First rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 Second rule: f162_0_main_GE -> f162_0_main_GE : arg1'=-2+arg2, -2+arg2-arg1 >= 0, cost: -2+arg2-arg1 New rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=98, 98 >= 0, cost: 99 Applied chaining First rule: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 Second rule: f162_0_main_GE -> [3] : (-2+arg2-arg1 >= 0 /\ -1+n2 >= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM Applied deletion Removed the following rules: 8 9 11 13 14 15 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 16: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM 17: f1_0_main_ConstantStackPush -> f162_0_main_GE : arg2'=100, arg1'=98, 98 >= 0, cost: 99 3: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 16: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : 98 >= 0, cost: NONTERM New rule: __init -> [3] : 98 >= 0, cost: NONTERM Applied deletion Removed the following rules: 3 16 Eliminated locations on linear paths Start location: __init 18: __init -> [3] : 98 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 18 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: 98 >= 0