NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f51_0_main_GE : arg2'=arg2P0, arg1'=arg1P0, (-arg1P0 == 0 /\ 100-arg2P0 == 0), cost: 1 1: f51_0_main_GE -> f51_0_main_GE : arg2'=arg2P1, arg1'=arg1P1, (arg2-arg1 > 0 /\ 1+arg1-arg1P1 == 0 /\ 1+arg2-arg2P1 == 0), cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f51_0_main_GE : arg2'=arg2P0, arg1'=arg1P0, (-arg1P0 == 0 /\ 100-arg2P0 == 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f51_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 Applied preprocessing Original rule: f51_0_main_GE -> f51_0_main_GE : arg2'=arg2P1, arg1'=arg1P1, (arg2-arg1 > 0 /\ 1+arg1-arg1P1 == 0 /\ 1+arg2-arg2P1 == 0), cost: 1 New rule: f51_0_main_GE -> f51_0_main_GE : arg2'=1+arg2, arg1'=1+arg1, arg2-arg1 > 0, cost: 1 Simplified rules Start location: __init 3: f1_0_main_ConstantStackPush -> f51_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 4: f51_0_main_GE -> f51_0_main_GE : arg2'=1+arg2, arg1'=1+arg1, arg2-arg1 > 0, cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, TRUE, cost: 1 Applied nonterm Original rule: f51_0_main_GE -> f51_0_main_GE : arg2'=1+arg2, arg1'=1+arg1, arg2-arg1 > 0, cost: 1 New rule: f51_0_main_GE -> [3] : (arg2-arg1 > 0 /\ n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_nFaClc.txt Applied deletion Removed the following rules: 4 Accelerated simple loops Start location: __init 3: f1_0_main_ConstantStackPush -> f51_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 5: f51_0_main_GE -> [3] : (arg2-arg1 > 0 /\ n >= 0), cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f51_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 Second rule: f51_0_main_GE -> [3] : (arg2-arg1 > 0 /\ n >= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : 100 > 0, cost: NONTERM Applied deletion Removed the following rules: 5 Chained accelerated rules with incoming rules Start location: __init 3: f1_0_main_ConstantStackPush -> f51_0_main_GE : arg2'=100, arg1'=0, TRUE, cost: 1 6: f1_0_main_ConstantStackPush -> [3] : 100 > 0, cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 6: f1_0_main_ConstantStackPush -> [3] : 100 > 0, cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : 100 > 0, cost: NONTERM New rule: __init -> [3] : 100 > 0, cost: NONTERM Applied deletion Removed the following rules: 2 6 Eliminated locations on linear paths Start location: __init 7: __init -> [3] : 100 > 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 7 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: 100 > 0