/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 418 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 140 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 54 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 51 ms] (16) IntTRS (17) RankingReductionPairProof [EQUIVALENT, 27 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class Avg { public static void main(String[] args) { int x, y; x = args[0].length(); y = args[1].length(); average(x,y); } public static int average(int x, int y) { if (x > 0) { return average(x-1, y+1); } else if (y > 2) { return 1 + average(x+1, y-2); } else { return 1; } } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class Avg { public static void main(String[] args) { int x, y; x = args[0].length(); y = args[1].length(); average(x,y); } public static int average(int x, int y) { if (x > 0) { return average(x-1, y+1); } else if (y > 2) { return 1 + average(x+1, y-2); } else { return 1; } } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: Avg.main([Ljava/lang/String;)V: Graph of 136 nodes with 0 SCCs. Avg.average(II)I: Graph of 56 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: Avg.average(II)I SCC calls the following helper methods: Avg.average(II)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 30 IRulesP rules: f216_0_average_LE(EOS(STATIC_216), matching1, i30, matching2, i30, matching3) -> f219_0_average_LE(EOS(STATIC_219), 0, i30, 0, i30, 0) :|: TRUE && matching1 = 0 && matching2 = 0 && matching3 = 0 f216_0_average_LE(EOS(STATIC_216), i34, i30, i34, i30, i34) -> f220_0_average_LE(EOS(STATIC_220), i34, i30, i34, i30, i34) :|: TRUE f219_0_average_LE(EOS(STATIC_219), matching1, i30, matching2, i30, matching3) -> f223_0_average_Load(EOS(STATIC_223), 0, i30, 0, i30) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 && matching3 = 0 f223_0_average_Load(EOS(STATIC_223), matching1, i30, matching2, i30) -> f227_0_average_ConstantStackPush(EOS(STATIC_227), 0, i30, 0, i30, i30) :|: TRUE && matching1 = 0 && matching2 = 0 f227_0_average_ConstantStackPush(EOS(STATIC_227), matching1, i30, matching2, i30, i30) -> f231_0_average_LE(EOS(STATIC_231), 0, i30, 0, i30, i30, 2) :|: TRUE && matching1 = 0 && matching2 = 0 f231_0_average_LE(EOS(STATIC_231), matching1, i37, matching2, i37, i37, matching3) -> f238_0_average_LE(EOS(STATIC_238), 0, i37, 0, i37, i37, 2) :|: TRUE && matching1 = 0 && matching2 = 0 && matching3 = 2 f238_0_average_LE(EOS(STATIC_238), matching1, i37, matching2, i37, i37, matching3) -> f248_0_average_ConstantStackPush(EOS(STATIC_248), 0, i37, 0, i37) :|: i37 > 2 && matching1 = 0 && matching2 = 0 && matching3 = 2 f248_0_average_ConstantStackPush(EOS(STATIC_248), matching1, i37, matching2, i37) -> f260_0_average_Load(EOS(STATIC_260), 0, i37, 0, i37, 1) :|: TRUE && matching1 = 0 && matching2 = 0 f260_0_average_Load(EOS(STATIC_260), matching1, i37, matching2, i37, matching3) -> f270_0_average_ConstantStackPush(EOS(STATIC_270), 0, i37, i37, 1, 0) :|: TRUE && matching1 = 0 && matching2 = 0 && matching3 = 1 f270_0_average_ConstantStackPush(EOS(STATIC_270), matching1, i37, i37, matching2, matching3) -> f305_0_average_IntArithmetic(EOS(STATIC_305), 0, i37, i37, 1, 0, 1) :|: TRUE && matching1 = 0 && matching2 = 1 && matching3 = 0 f305_0_average_IntArithmetic(EOS(STATIC_305), matching1, i37, i37, matching2, matching3, matching4) -> f309_0_average_Load(EOS(STATIC_309), 0, i37, i37, 1, 1) :|: TRUE && matching1 = 0 && matching2 = 1 && matching3 = 0 && matching4 = 1 f309_0_average_Load(EOS(STATIC_309), matching1, i37, i37, matching2, matching3) -> f312_0_average_ConstantStackPush(EOS(STATIC_312), 0, i37, 1, 1, i37) :|: TRUE && matching1 = 0 && matching2 = 1 && matching3 = 1 f312_0_average_ConstantStackPush(EOS(STATIC_312), matching1, i37, matching2, matching3, i37) -> f315_0_average_IntArithmetic(EOS(STATIC_315), 0, i37, 1, 1, i37, 2) :|: TRUE && matching1 = 0 && matching2 = 1 && matching3 = 1 f315_0_average_IntArithmetic(EOS(STATIC_315), matching1, i37, matching2, matching3, i37, matching4) -> f317_0_average_InvokeMethod(EOS(STATIC_317), 0, i37, 1, 1, i37 - 2) :|: i37 > 0 && matching1 = 0 && matching2 = 1 && matching3 = 1 && matching4 = 2 f317_0_average_InvokeMethod(EOS(STATIC_317), matching1, i37, matching2, matching3, i51) -> f359_0_average_Load(EOS(STATIC_359), 1, i51, 1, i51) :|: i37 > 1 && i51 >= 1 && i51 < i37 && matching1 = 0 && matching2 = 1 && matching3 = 1 f317_0_average_InvokeMethod(EOS(STATIC_317), matching1, i37, matching2, matching3, i51) -> f359_1_average_Load(EOS(STATIC_359), 0, i37, 1, 1, i51) :|: i37 > 1 && i51 >= 1 && i51 < i37 && matching1 = 0 && matching2 = 1 && matching3 = 1 f359_0_average_Load(EOS(STATIC_359), matching1, i51, matching2, i51) -> f679_0_average_Load(EOS(STATIC_679), 1, i51, 1, i51) :|: TRUE && matching1 = 1 && matching2 = 1 f679_0_average_Load(EOS(STATIC_679), matching1, i51, matching2, i51) -> f210_0_average_Load(EOS(STATIC_210), 1, i51, 1, i51) :|: TRUE && matching1 = 1 && matching2 = 1 f210_0_average_Load(EOS(STATIC_210), i12, i30, i12, i30) -> f216_0_average_LE(EOS(STATIC_216), i12, i30, i12, i30, i12) :|: TRUE f220_0_average_LE(EOS(STATIC_220), i34, i30, i34, i30, i34) -> f224_0_average_Load(EOS(STATIC_224), i34, i30, i34, i30) :|: i34 > 0 f224_0_average_Load(EOS(STATIC_224), i34, i30, i34, i30) -> f228_0_average_ConstantStackPush(EOS(STATIC_228), i34, i30, i30, i34) :|: TRUE f228_0_average_ConstantStackPush(EOS(STATIC_228), i34, i30, i30, i34) -> f232_0_average_IntArithmetic(EOS(STATIC_232), i34, i30, i30, i34, 1) :|: TRUE f232_0_average_IntArithmetic(EOS(STATIC_232), i34, i30, i30, i34, matching1) -> f240_0_average_Load(EOS(STATIC_240), i34, i30, i30, i34 - 1) :|: i34 > 0 && matching1 = 1 f240_0_average_Load(EOS(STATIC_240), i34, i30, i30, i40) -> f250_0_average_ConstantStackPush(EOS(STATIC_250), i34, i30, i40, i30) :|: TRUE f250_0_average_ConstantStackPush(EOS(STATIC_250), i34, i30, i40, i30) -> f262_0_average_IntArithmetic(EOS(STATIC_262), i34, i30, i40, i30, 1) :|: TRUE f262_0_average_IntArithmetic(EOS(STATIC_262), i34, i30, i40, i30, matching1) -> f273_0_average_InvokeMethod(EOS(STATIC_273), i34, i30, i40, i30 + 1) :|: i30 >= 0 && matching1 = 1 f273_0_average_InvokeMethod(EOS(STATIC_273), i34, i30, i40, i42) -> f306_0_average_Load(EOS(STATIC_306), i40, i42, i40, i42) :|: i34 >= 1 && i42 >= 1 && i40 < i34 && i42 > i30 f273_0_average_InvokeMethod(EOS(STATIC_273), i34, i30, i40, i42) -> f306_1_average_Load(EOS(STATIC_306), i34, i30, i40, i42) :|: i34 >= 1 && i42 >= 1 && i40 < i34 && i42 > i30 f306_0_average_Load(EOS(STATIC_306), i40, i42, i40, i42) -> f310_0_average_Load(EOS(STATIC_310), i40, i42, i40, i42) :|: TRUE f310_0_average_Load(EOS(STATIC_310), i40, i42, i40, i42) -> f210_0_average_Load(EOS(STATIC_210), i40, i42, i40, i42) :|: TRUE Combined rules. Obtained 4 IRulesP rules: f216_0_average_LE(EOS(STATIC_216), 0, i30:0, 0, i30:0, 0) -> f216_0_average_LE(EOS(STATIC_216), 1, i30:0 - 2, 1, i30:0 - 2, 1) :|: i30:0 > 2 && i30:0 - 2 < i30:0 f216_0_average_LE(EOS(STATIC_216), i34:0, i30:0, i34:0, i30:0, i34:0) -> f216_0_average_LE(EOS(STATIC_216), i34:0 - 1, i30:0 + 1, i34:0 - 1, i30:0 + 1, i34:0 - 1) :|: i34:0 > 0 && i30:0 > -1 && i34:0 - 1 < i34:0 && i30:0 + 1 > i30:0 Removed following non-SCC rules: f216_0_average_LE(EOS(STATIC_216), 0, i30:0, 0, i30:0, 0) -> f359_1_average_Load(EOS(STATIC_359), 0, i30:0, 1, 1, i30:0 - 2) :|: i30:0 > 2 && i30:0 - 2 < i30:0 f216_0_average_LE(EOS(STATIC_216), i34:0, i30:0, i34:0, i30:0, i34:0) -> f306_1_average_Load(EOS(STATIC_306), i34:0, i30:0, i34:0 - 1, i30:0 + 1) :|: i34:0 > 0 && i30:0 > -1 && i34:0 - 1 < i34:0 && i30:0 + 1 > i30:0 Filtered constant ground arguments: f216_0_average_LE(x1, x2, x3, x4, x5, x6) -> f216_0_average_LE(x2, x3, x4, x5, x6) EOS(x1) -> EOS Filtered duplicate arguments: f216_0_average_LE(x1, x2, x3, x4, x5) -> f216_0_average_LE(x4, x5) Finished conversion. Obtained 2 rules.P rules: f216_0_average_LE(i30:0, cons_0) -> f216_0_average_LE(i30:0 - 2, 1) :|: i30:0 > 2 && i30:0 - 2 < i30:0 && cons_0 = 0 f216_0_average_LE(i30:0, i34:0) -> f216_0_average_LE(i30:0 + 1, i34:0 - 1) :|: i30:0 > -1 && i34:0 > 0 && i30:0 + 1 > i30:0 && i34:0 - 1 < i34:0 ---------------------------------------- (8) Obligation: Rules: f216_0_average_LE(i30:0, cons_0) -> f216_0_average_LE(i30:0 - 2, 1) :|: i30:0 > 2 && i30:0 - 2 < i30:0 && cons_0 = 0 f216_0_average_LE(x, x1) -> f216_0_average_LE(x + 1, x1 - 1) :|: x > -1 && x1 > 0 && x + 1 > x && x1 - 1 < x1 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f216_0_average_LE(i30:0, cons_0) -> f216_0_average_LE(arith, 1) :|: i30:0 > 2 && i30:0 - 2 < i30:0 && cons_0 = 0 && arith = i30:0 - 2 f216_0_average_LE(x2, x3) -> f216_0_average_LE(x4, x5) :|: x2 > -1 && x3 > 0 && x2 + 1 > x2 && x3 - 1 < x3 && x4 = x2 + 1 && x5 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f216_0_average_LE(i30:0, cons_0) -> f216_0_average_LE(arith, 1) :|: i30:0 > 2 && i30:0 - 2 < i30:0 && cons_0 = 0 && arith = i30:0 - 2 (2) f216_0_average_LE(x2, x3) -> f216_0_average_LE(x4, x5) :|: x2 > -1 && x3 > 0 && x2 + 1 > x2 && x3 - 1 < x3 && x4 = x2 + 1 && x5 = x3 - 1 Arcs: (1) -> (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f216_0_average_LE(i30:0, cons_0) -> f216_0_average_LE(arith, 1) :|: i30:0 > 2 && i30:0 - 2 < i30:0 && cons_0 = 0 && arith = i30:0 - 2 (2) f216_0_average_LE(x2, x3) -> f216_0_average_LE(x4, x5) :|: x2 > -1 && x3 > 0 && x2 + 1 > x2 && x3 - 1 < x3 && x4 = x2 + 1 && x5 = x3 - 1 Arcs: (1) -> (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f216_0_average_LE(i30:0:0, cons_0) -> f216_0_average_LE(i30:0:0 - 2, 1) :|: i30:0:0 > 2 && i30:0:0 - 2 < i30:0:0 && cons_0 = 0 f216_0_average_LE(x2:0, x3:0) -> f216_0_average_LE(x2:0 + 1, x3:0 - 1) :|: x2:0 + 1 > x2:0 && x3:0 - 1 < x3:0 && x3:0 > 0 && x2:0 > -1 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f216_0_average_LE(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f216_0_average_LE(i30:0:0, c) -> f216_0_average_LE(c1, c2) :|: c2 = 1 && (c1 = i30:0:0 - 2 && c = 0) && (i30:0:0 > 2 && i30:0:0 - 2 < i30:0:0 && cons_0 = 0) f216_0_average_LE(x2:0, x3:0) -> f216_0_average_LE(c3, c4) :|: c4 = x3:0 - 1 && c3 = x2:0 + 1 && (x2:0 + 1 > x2:0 && x3:0 - 1 < x3:0 && x3:0 > 0 && x2:0 > -1) ---------------------------------------- (17) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f216_0_average_LE ] = 3*f216_0_average_LE_2 + 2*f216_0_average_LE_1 The following rules are decreasing: f216_0_average_LE(i30:0:0, c) -> f216_0_average_LE(c1, c2) :|: c2 = 1 && (c1 = i30:0:0 - 2 && c = 0) && (i30:0:0 > 2 && i30:0:0 - 2 < i30:0:0 && cons_0 = 0) f216_0_average_LE(x2:0, x3:0) -> f216_0_average_LE(c3, c4) :|: c4 = x3:0 - 1 && c3 = x2:0 + 1 && (x2:0 + 1 > x2:0 && x3:0 - 1 < x3:0 && x3:0 > 0 && x2:0 > -1) The following rules are bounded: f216_0_average_LE(i30:0:0, c) -> f216_0_average_LE(c1, c2) :|: c2 = 1 && (c1 = i30:0:0 - 2 && c = 0) && (i30:0:0 > 2 && i30:0:0 - 2 < i30:0:0 && cons_0 = 0) f216_0_average_LE(x2:0, x3:0) -> f216_0_average_LE(c3, c4) :|: c4 = x3:0 - 1 && c3 = x2:0 + 1 && (x2:0 + 1 > x2:0 && x3:0 - 1 < x3:0 && x3:0 > 0 && x2:0 > -1) ---------------------------------------- (18) YES