/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.jar /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.jar # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 94 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 1488 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 143 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 46 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 17 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class Fibonacci { public static void main(String[] args) { fib(args.length); } public static int fib(int x) { if (x == 0) { return 0; } else if (x == 1) { return 1; } else { return fib(x-1) + fib(x-2); } } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class Fibonacci { public static void main(String[] args) { fib(args.length); } public static int fib(int x) { if (x == 0) { return 0; } else if (x == 1) { return 1; } else { return fib(x-1) + fib(x-2); } } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: Fibonacci.main([Ljava/lang/String;)V: Graph of 19 nodes with 0 SCCs. Fibonacci.fib(I)I: Graph of 42 nodes with 0 SCCs. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 1 SCCs. ---------------------------------------- (6) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: Fibonacci.fib(I)I SCC calls the following helper methods: Fibonacci.fib(I)I Performed SCC analyses: *Used field analysis yielded the following read fields: *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 29 IRulesP rules: f22_0_fib_NE(EOS(STATIC_22), i4, i4, i4) -> f23_0_fib_NE(EOS(STATIC_23), i4, i4, i4) :|: TRUE f23_0_fib_NE(EOS(STATIC_23), i4, i4, i4) -> f25_0_fib_Load(EOS(STATIC_25), i4, i4) :|: i4 > 0 f25_0_fib_Load(EOS(STATIC_25), i4, i4) -> f27_0_fib_ConstantStackPush(EOS(STATIC_27), i4, i4, i4) :|: TRUE f27_0_fib_ConstantStackPush(EOS(STATIC_27), i4, i4, i4) -> f29_0_fib_NE(EOS(STATIC_29), i4, i4, i4, 1) :|: TRUE f29_0_fib_NE(EOS(STATIC_29), i5, i5, i5, matching1) -> f34_0_fib_NE(EOS(STATIC_34), i5, i5, i5, 1) :|: TRUE && matching1 = 1 f34_0_fib_NE(EOS(STATIC_34), i5, i5, i5, matching1) -> f52_0_fib_Load(EOS(STATIC_52), i5, i5) :|: i5 > 1 && matching1 = 1 f52_0_fib_Load(EOS(STATIC_52), i5, i5) -> f55_0_fib_ConstantStackPush(EOS(STATIC_55), i5, i5, i5) :|: TRUE f55_0_fib_ConstantStackPush(EOS(STATIC_55), i5, i5, i5) -> f60_0_fib_IntArithmetic(EOS(STATIC_60), i5, i5, i5, 1) :|: TRUE f60_0_fib_IntArithmetic(EOS(STATIC_60), i5, i5, i5, matching1) -> f62_0_fib_InvokeMethod(EOS(STATIC_62), i5, i5, i5 - 1) :|: i5 > 0 && matching1 = 1 f62_0_fib_InvokeMethod(EOS(STATIC_62), i5, i5, i10) -> f65_0_fib_Load(EOS(STATIC_65), i10, i10) :|: i5 > 1 && i10 >= 1 && i10 < i5 f62_0_fib_InvokeMethod(EOS(STATIC_62), i5, i5, i10) -> f65_1_fib_Load(EOS(STATIC_65), i5, i5, i10) :|: i5 > 1 && i10 >= 1 && i10 < i5 f65_0_fib_Load(EOS(STATIC_65), i10, i10) -> f77_0_fib_Load(EOS(STATIC_77), i10, i10) :|: TRUE f77_0_fib_Load(EOS(STATIC_77), i10, i10) -> f21_0_fib_Load(EOS(STATIC_21), i10, i10) :|: TRUE f21_0_fib_Load(EOS(STATIC_21), i2, i2) -> f22_0_fib_NE(EOS(STATIC_22), i2, i2, i2) :|: TRUE f250_0_fib_Return(EOS(STATIC_250), i5, i5, matching1) -> f251_0_fib_Load(EOS(STATIC_251), i5, i5, 1) :|: TRUE && matching1 = 1 f251_0_fib_Load(EOS(STATIC_251), i5, i5, matching1) -> f670_0_fib_Load(EOS(STATIC_670), i5, i5, 1) :|: TRUE && matching1 = 1 f670_0_fib_Load(EOS(STATIC_670), i5, i5, i131) -> f2083_0_fib_Load(EOS(STATIC_2083), i5, i5, i131) :|: TRUE f2083_0_fib_Load(EOS(STATIC_2083), i5, i5, i403) -> f2113_0_fib_Load(EOS(STATIC_2113), i5, i5, i403) :|: TRUE f2113_0_fib_Load(EOS(STATIC_2113), i5, i5, i443) -> f2115_0_fib_ConstantStackPush(EOS(STATIC_2115), i5, i443, i5) :|: TRUE f2115_0_fib_ConstantStackPush(EOS(STATIC_2115), i5, i443, i5) -> f2117_0_fib_IntArithmetic(EOS(STATIC_2117), i5, i443, i5, 2) :|: TRUE f2117_0_fib_IntArithmetic(EOS(STATIC_2117), i5, i443, i5, matching1) -> f2118_0_fib_InvokeMethod(EOS(STATIC_2118), i5, i443, i5 - 2) :|: i5 > 0 && matching1 = 2 f2118_0_fib_InvokeMethod(EOS(STATIC_2118), i5, i443, i448) -> f2119_0_fib_Load(EOS(STATIC_2119), i448, i448) :|: i5 > 1 && i448 < i5 f2118_0_fib_InvokeMethod(EOS(STATIC_2118), i5, i443, i448) -> f2119_1_fib_Load(EOS(STATIC_2119), i5, i443, i448) :|: i5 > 1 && i448 < i5 f2119_0_fib_Load(EOS(STATIC_2119), i448, i448) -> f2120_0_fib_Load(EOS(STATIC_2120), i448, i448) :|: TRUE f2120_0_fib_Load(EOS(STATIC_2120), i448, i448) -> f21_0_fib_Load(EOS(STATIC_21), i448, i448) :|: TRUE f2139_0_fib_Return(EOS(STATIC_2139), i5, i5, i476) -> f2109_0_fib_Return(EOS(STATIC_2109), i5, i5, i476) :|: TRUE f2109_0_fib_Return(EOS(STATIC_2109), i5, i5, i443) -> f2113_0_fib_Load(EOS(STATIC_2113), i5, i5, i443) :|: TRUE f65_1_fib_Load(EOS(STATIC_65), i5, i5, matching1) -> f250_0_fib_Return(EOS(STATIC_250), i5, i5, 1) :|: TRUE && matching1 = 1 f65_1_fib_Load(EOS(STATIC_65), i5, i5, i10) -> f2139_0_fib_Return(EOS(STATIC_2139), i5, i5, i476) :|: TRUE Combined rules. Obtained 5 IRulesP rules: f22_0_fib_NE(EOS(STATIC_22), 2, 2, 2) -> f2118_0_fib_InvokeMethod(EOS(STATIC_2118), 2, 1, 0) :|: TRUE f22_0_fib_NE(EOS(STATIC_22), i4:0, i4:0, i4:0) -> f22_0_fib_NE(EOS(STATIC_22), i4:0 - 1, i4:0 - 1, i4:0 - 1) :|: i4:0 > 1 && i4:0 - 1 < i4:0 f22_0_fib_NE(EOS(STATIC_22), i4:0, i4:0, i4:0) -> f2118_0_fib_InvokeMethod(EOS(STATIC_2118), i4:0, i476:0, i4:0 - 2) :|: i4:0 > 1 && i4:0 - 1 < i4:0 f2118_0_fib_InvokeMethod(EOS(STATIC_2118), i5:0, i443:0, i448:0) -> f22_0_fib_NE(EOS(STATIC_22), i448:0, i448:0, i448:0) :|: i5:0 > 1 && i5:0 > i448:0 Removed following non-SCC rules: f2118_0_fib_InvokeMethod(EOS(STATIC_2118), i5:0, i443:0, i448:0) -> f2119_1_fib_Load(EOS(STATIC_2119), i5:0, i443:0, i448:0) :|: i5:0 > 1 && i5:0 > i448:0 Filtered constant ground arguments: f22_0_fib_NE(x1, x2, x3, x4) -> f22_0_fib_NE(x2, x3, x4) f2118_0_fib_InvokeMethod(x1, x2, x3, x4) -> f2118_0_fib_InvokeMethod(x2, x3, x4) Filtered duplicate arguments: f22_0_fib_NE(x1, x2, x3) -> f22_0_fib_NE(x3) Filtered unneeded arguments: f2118_0_fib_InvokeMethod(x1, x2, x3) -> f2118_0_fib_InvokeMethod(x1, x3) Finished conversion. Obtained 4 rules.P rules: f22_0_fib_NE(cons_2) -> f2118_0_fib_InvokeMethod(2, 0) :|: TRUE && cons_2 = 2 f22_0_fib_NE(i4:0) -> f22_0_fib_NE(i4:0 - 1) :|: i4:0 > 1 && i4:0 - 1 < i4:0 f22_0_fib_NE(i4:0) -> f2118_0_fib_InvokeMethod(i4:0, i4:0 - 2) :|: i4:0 > 1 && i4:0 - 1 < i4:0 f2118_0_fib_InvokeMethod(i5:0, i448:0) -> f22_0_fib_NE(i448:0) :|: i5:0 > 1 && i5:0 > i448:0 ---------------------------------------- (8) Obligation: Rules: f22_0_fib_NE(cons_2) -> f2118_0_fib_InvokeMethod(2, 0) :|: TRUE && cons_2 = 2 f22_0_fib_NE(i4:0) -> f22_0_fib_NE(i4:0 - 1) :|: i4:0 > 1 && i4:0 - 1 < i4:0 f22_0_fib_NE(x) -> f2118_0_fib_InvokeMethod(x, x - 2) :|: x > 1 && x - 1 < x f2118_0_fib_InvokeMethod(i5:0, i448:0) -> f22_0_fib_NE(i448:0) :|: i5:0 > 1 && i5:0 > i448:0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f22_0_fib_NE(cons_2) -> f2118_0_fib_InvokeMethod(2, 0) :|: TRUE && cons_2 = 2 f22_0_fib_NE(i4:0) -> f22_0_fib_NE(arith) :|: i4:0 > 1 && i4:0 - 1 < i4:0 && arith = i4:0 - 1 f22_0_fib_NE(x1) -> f2118_0_fib_InvokeMethod(x1, x2) :|: x1 > 1 && x1 - 1 < x1 && x2 = x1 - 2 f2118_0_fib_InvokeMethod(i5:0, i448:0) -> f22_0_fib_NE(i448:0) :|: i5:0 > 1 && i5:0 > i448:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f22_0_fib_NE(cons_2) -> f2118_0_fib_InvokeMethod(2, 0) :|: TRUE && cons_2 = 2 (2) f22_0_fib_NE(i4:0) -> f22_0_fib_NE(arith) :|: i4:0 > 1 && i4:0 - 1 < i4:0 && arith = i4:0 - 1 (3) f22_0_fib_NE(x1) -> f2118_0_fib_InvokeMethod(x1, x2) :|: x1 > 1 && x1 - 1 < x1 && x2 = x1 - 2 (4) f2118_0_fib_InvokeMethod(i5:0, i448:0) -> f22_0_fib_NE(i448:0) :|: i5:0 > 1 && i5:0 > i448:0 Arcs: (1) -> (4) (2) -> (1), (2), (3) (3) -> (4) (4) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f22_0_fib_NE(cons_2) -> f2118_0_fib_InvokeMethod(2, 0) :|: TRUE && cons_2 = 2 (2) f22_0_fib_NE(i4:0) -> f22_0_fib_NE(arith) :|: i4:0 > 1 && i4:0 - 1 < i4:0 && arith = i4:0 - 1 (3) f2118_0_fib_InvokeMethod(i5:0, i448:0) -> f22_0_fib_NE(i448:0) :|: i5:0 > 1 && i5:0 > i448:0 (4) f22_0_fib_NE(x1) -> f2118_0_fib_InvokeMethod(x1, x2) :|: x1 > 1 && x1 - 1 < x1 && x2 = x1 - 2 Arcs: (1) -> (3) (2) -> (1), (2), (4) (3) -> (1), (2), (4) (4) -> (3) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f22_0_fib_NE(cons_2) -> f22_0_fib_NE(0) :|: TRUE && cons_2 = 2 f22_0_fib_NE(i4:0:0) -> f22_0_fib_NE(i4:0:0 - 1) :|: i4:0:0 > 1 && i4:0:0 - 1 < i4:0:0 f22_0_fib_NE(x1:0) -> f22_0_fib_NE(x1:0 - 2) :|: x1:0 - 2 < x1:0 && x1:0 - 1 < x1:0 && x1:0 > 1 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f22_0_fib_NE(VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f22_0_fib_NE(c) -> f22_0_fib_NE(c1) :|: c1 = 0 && c = 2 && (TRUE && cons_2 = 2) f22_0_fib_NE(i4:0:0) -> f22_0_fib_NE(c2) :|: c2 = i4:0:0 - 1 && (i4:0:0 > 1 && i4:0:0 - 1 < i4:0:0) f22_0_fib_NE(x1:0) -> f22_0_fib_NE(c3) :|: c3 = x1:0 - 2 && (x1:0 - 2 < x1:0 && x1:0 - 1 < x1:0 && x1:0 > 1) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f22_0_fib_NE(x)] = x The following rules are decreasing: f22_0_fib_NE(c) -> f22_0_fib_NE(c1) :|: c1 = 0 && c = 2 && (TRUE && cons_2 = 2) f22_0_fib_NE(i4:0:0) -> f22_0_fib_NE(c2) :|: c2 = i4:0:0 - 1 && (i4:0:0 > 1 && i4:0:0 - 1 < i4:0:0) f22_0_fib_NE(x1:0) -> f22_0_fib_NE(c3) :|: c3 = x1:0 - 2 && (x1:0 - 2 < x1:0 && x1:0 - 1 < x1:0 && x1:0 > 1) The following rules are bounded: f22_0_fib_NE(c) -> f22_0_fib_NE(c1) :|: c1 = 0 && c = 2 && (TRUE && cons_2 = 2) f22_0_fib_NE(i4:0:0) -> f22_0_fib_NE(c2) :|: c2 = i4:0:0 - 1 && (i4:0:0 > 1 && i4:0:0 - 1 < i4:0:0) f22_0_fib_NE(x1:0) -> f22_0_fib_NE(c3) :|: c3 = x1:0 - 2 && (x1:0 - 2 < x1:0 && x1:0 - 1 < x1:0 && x1:0 > 1) ---------------------------------------- (18) YES