NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=arg1P0, -arg1P0 == 0, cost: 1 1: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1P1, (1-arg1P1+arg1 == 0 /\ -50+arg1 < 0 /\ -100+arg1 < 0), cost: 1 2: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1P2, (-1-arg1P2+arg1 == 0 /\ -49+arg1 > 0 /\ -100+arg1 < 0), cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=arg1P0, -arg1P0 == 0, cost: 1 New rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 Applied preprocessing Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1P1, (1-arg1P1+arg1 == 0 /\ -50+arg1 < 0 /\ -100+arg1 < 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 Applied preprocessing Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1P2, (-1-arg1P2+arg1 == 0 /\ -49+arg1 > 0 /\ -100+arg1 < 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 Simplified rules Start location: __init 4: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 5: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 6: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied acceleration Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=n+arg1, (n >= 0 /\ 51-n-arg1 > 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_cPPOAl.txt Applied instantiation Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=n+arg1, (n >= 0 /\ 51-n-arg1 > 0), cost: n New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (1 > 0 /\ 50-arg1 >= 0), cost: 50-arg1 Applied acceleration Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1-n0, (-48+arg1-n0 > 0 /\ 100-arg1 > 0 /\ n0 >= 0), cost: n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_NNInAj.txt Applied instantiation Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=arg1-n0, (-48+arg1-n0 > 0 /\ 100-arg1 > 0 /\ n0 >= 0), cost: n0 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (1 > 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: -49+arg1 Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : -50+arg1 == 0, cost: 2 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : -50+arg1 == 0, cost: 2 New rule: f55_0_main_GE -> [3] : (n1 >= 0 /\ 50-arg1 >= 0 /\ -50+arg1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_fGldMB.txt Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 Second rule: f55_0_main_GE -> [3] : (n1 >= 0 /\ 50-arg1 >= 0 /\ -50+arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (n1 >= 0 /\ 50-arg1 > 0 /\ 49-arg1 >= 0 /\ -49+arg1 >= 0), cost: NONTERM Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : -49+arg1 == 0, cost: 2 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : -49+arg1 == 0, cost: 2 New rule: f55_0_main_GE -> [3] : (n2 >= 0 /\ 49-arg1 >= 0 /\ -49+arg1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_oAbBpN.txt Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 Second rule: f55_0_main_GE -> [3] : (n2 >= 0 /\ 49-arg1 >= 0 /\ -49+arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (n2 >= 0 /\ 50-arg1 >= 0 /\ -50+arg1 >= 0 /\ -49+arg1 > 0 /\ 100-arg1 > 0), cost: NONTERM Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (1 > 0 /\ 50-arg1 >= 0), cost: 50-arg1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (-51+arg1 <= 0 /\ -49+arg1 > 0), cost: 52-arg1 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (-51+arg1 <= 0 /\ -49+arg1 > 0), cost: 52-arg1 New rule: f55_0_main_GE -> [3] : (-1+n3 >= 0 /\ 51-arg1 >= 0 /\ -49+arg1 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_HAfjlF.txt Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (1 > 0 /\ 50-arg1 >= 0), cost: 50-arg1 Second rule: f55_0_main_GE -> [3] : (-1+n3 >= 0 /\ 51-arg1 >= 0 /\ -49+arg1 > 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (1 > 0 /\ 1 >= 0 /\ -1+n3 >= 0 /\ 50-arg1 >= 0), cost: NONTERM Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (1 > 0 /\ 50-arg1 >= 0), cost: 50-arg1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, -50+arg1 <= 0, cost: 51-arg1 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, -50+arg1 <= 0, cost: 51-arg1 New rule: f55_0_main_GE -> [3] : (50-arg1 >= 0 /\ -1+n4 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_JpIAEl.txt Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=-1+arg1, (-49+arg1 > 0 /\ 100-arg1 > 0), cost: 1 Second rule: f55_0_main_GE -> [3] : (50-arg1 >= 0 /\ -1+n4 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (-1+n4 >= 0 /\ 51-arg1 >= 0 /\ -49+arg1 > 0 /\ 100-arg1 > 0), cost: NONTERM Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (1 > 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: -49+arg1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (50-arg1 > 0 /\ -48+arg1 >= 0), cost: -47+arg1 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (50-arg1 > 0 /\ -48+arg1 >= 0), cost: -47+arg1 New rule: f55_0_main_GE -> [3] : (50-arg1 > 0 /\ -48+arg1 >= 0 /\ -1+n5 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_jdlPno.txt Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (1 > 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: -49+arg1 Second rule: f55_0_main_GE -> [3] : (50-arg1 > 0 /\ -48+arg1 >= 0 /\ -1+n5 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (1 > 0 /\ 1 >= 0 /\ -1+n5 >= 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: NONTERM Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (1 > 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: -49+arg1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (-49+arg1 >= 0 /\ 100-arg1 > 0), cost: -48+arg1 Applied nonterm Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (-49+arg1 >= 0 /\ 100-arg1 > 0), cost: -48+arg1 New rule: f55_0_main_GE -> [3] : (-1+n6 >= 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_ggDAbO.txt Applied chaining First rule: f55_0_main_GE -> f55_0_main_GE : arg1'=1+arg1, 50-arg1 > 0, cost: 1 Second rule: f55_0_main_GE -> [3] : (-1+n6 >= 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (50-arg1 > 0 /\ 99-arg1 > 0 /\ -48+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, (1 > 0 /\ 50-arg1 >= 0), cost: 50-arg1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, -50+arg1 <= 0, cost: 50-arg1 Applied simplification Original rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (1 > 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: -49+arg1 New rule: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (-49+arg1 >= 0 /\ 100-arg1 > 0), cost: -49+arg1 Applied simplification Original rule: f55_0_main_GE -> [3] : (n1 >= 0 /\ 50-arg1 >= 0 /\ -50+arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (n1 >= 0 /\ -50+arg1 <= 0 /\ -50+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (n1 >= 0 /\ 50-arg1 > 0 /\ 49-arg1 >= 0 /\ -49+arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (n1 >= 0 /\ -49+arg1 <= 0 /\ -49+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (n2 >= 0 /\ 49-arg1 >= 0 /\ -49+arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (n2 >= 0 /\ -49+arg1 <= 0 /\ -49+arg1 >= 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (n2 >= 0 /\ 50-arg1 >= 0 /\ -50+arg1 >= 0 /\ -49+arg1 > 0 /\ 100-arg1 > 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (n2 >= 0 /\ -50+arg1 <= 0 /\ -49+arg1 > 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (-1+n3 >= 0 /\ 51-arg1 >= 0 /\ -49+arg1 > 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (-51+arg1 <= 0 /\ -1+n3 >= 0 /\ -49+arg1 > 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (1 > 0 /\ 1 >= 0 /\ -1+n3 >= 0 /\ 50-arg1 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (-1+n3 >= 0 /\ -50+arg1 <= 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (50-arg1 >= 0 /\ -1+n4 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (-1+n4 >= 0 /\ -50+arg1 <= 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (-1+n4 >= 0 /\ 51-arg1 >= 0 /\ -49+arg1 > 0 /\ 100-arg1 > 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (-51+arg1 <= 0 /\ -1+n4 >= 0 /\ -49+arg1 > 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (1 > 0 /\ 1 >= 0 /\ -1+n5 >= 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (-1+n5 >= 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: NONTERM Applied simplification Original rule: f55_0_main_GE -> [3] : (50-arg1 > 0 /\ 99-arg1 > 0 /\ -48+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM New rule: f55_0_main_GE -> [3] : (50-arg1 > 0 /\ -48+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM Applied deletion Removed the following rules: 5 6 Accelerated simple loops Start location: __init 4: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 17: f55_0_main_GE -> [3] : (50-arg1 > 0 /\ -48+arg1 >= 0 /\ -1+n5 >= 0), cost: NONTERM 19: f55_0_main_GE -> [3] : (-1+n6 >= 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: NONTERM 21: f55_0_main_GE -> f55_0_main_GE : arg1'=50, -50+arg1 <= 0, cost: 50-arg1 22: f55_0_main_GE -> f55_0_main_GE : arg1'=49, (-49+arg1 >= 0 /\ 100-arg1 > 0), cost: -49+arg1 23: f55_0_main_GE -> [3] : (n1 >= 0 /\ -50+arg1 <= 0 /\ -50+arg1 >= 0), cost: NONTERM 24: f55_0_main_GE -> [3] : (n1 >= 0 /\ -49+arg1 <= 0 /\ -49+arg1 >= 0), cost: NONTERM 25: f55_0_main_GE -> [3] : (n2 >= 0 /\ -49+arg1 <= 0 /\ -49+arg1 >= 0), cost: NONTERM 26: f55_0_main_GE -> [3] : (n2 >= 0 /\ -50+arg1 <= 0 /\ -49+arg1 > 0), cost: NONTERM 27: f55_0_main_GE -> [3] : (-51+arg1 <= 0 /\ -1+n3 >= 0 /\ -49+arg1 > 0), cost: NONTERM 28: f55_0_main_GE -> [3] : (-1+n3 >= 0 /\ -50+arg1 <= 0), cost: NONTERM 29: f55_0_main_GE -> [3] : (-1+n4 >= 0 /\ -50+arg1 <= 0), cost: NONTERM 30: f55_0_main_GE -> [3] : (-51+arg1 <= 0 /\ -1+n4 >= 0 /\ -49+arg1 > 0), cost: NONTERM 31: f55_0_main_GE -> [3] : (-1+n5 >= 0 /\ -49+arg1 >= 0 /\ 100-arg1 > 0), cost: NONTERM 32: f55_0_main_GE -> [3] : (50-arg1 > 0 /\ -48+arg1 >= 0 /\ -1+n6 >= 0), cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f55_0_main_GE -> f55_0_main_GE : arg1'=50, -50+arg1 <= 0, cost: 50-arg1 New rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=50, -50 <= 0, cost: 51 Applied chaining First rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f55_0_main_GE -> [3] : (-1+n3 >= 0 /\ -50+arg1 <= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : -50 <= 0, cost: NONTERM Applied chaining First rule: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 Second rule: f55_0_main_GE -> [3] : (-1+n4 >= 0 /\ -50+arg1 <= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : -50 <= 0, cost: NONTERM Applied deletion Removed the following rules: 17 19 21 22 23 24 25 26 27 28 29 30 31 32 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=0, TRUE, cost: 1 33: f1_0_main_ConstantStackPush -> f55_0_main_GE : arg1'=50, -50 <= 0, cost: 51 34: f1_0_main_ConstantStackPush -> [3] : -50 <= 0, cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 34: f1_0_main_ConstantStackPush -> [3] : -50 <= 0, cost: NONTERM 3: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P3, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : -50 <= 0, cost: NONTERM New rule: __init -> [3] : -50 <= 0, cost: NONTERM Applied deletion Removed the following rules: 3 34 Eliminated locations on linear paths Start location: __init 35: __init -> [3] : -50 <= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 35 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -50 <= 0