/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 283 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 63 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 7 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 15 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class AG313 { public static void main(String[] args) { int x, y; x = args[0].length(); y = args[1].length() + 1; quot(x,y); } public static int quot(int x, int y) { int i = 0; if(x==0) return 0; while (x > 0 && y > 0) { i += 1; x = (x - 1)- (y - 1); } return i; } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class AG313 { public static void main(String[] args) { int x, y; x = args[0].length(); y = args[1].length() + 1; quot(x,y); } public static int quot(int x, int y) { int i = 0; if(x==0) return 0; while (x > 0 && y > 0) { i += 1; x = (x - 1)- (y - 1); } return i; } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: AG313.main([Ljava/lang/String;)V: Graph of 156 nodes with 1 SCC. ---------------------------------------- (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: AG313.main([Ljava/lang/String;)V SCC calls the following helper methods: 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 16 IRulesP rules: f1790_0_quot_LE(EOS(STATIC_1790), i421, i34, i421) -> f1795_0_quot_LE(EOS(STATIC_1795), i421, i34, i421) :|: TRUE f1795_0_quot_LE(EOS(STATIC_1795), i421, i34, i421) -> f1801_0_quot_Load(EOS(STATIC_1801), i421, i34) :|: i421 > 0 f1801_0_quot_Load(EOS(STATIC_1801), i421, i34) -> f1806_0_quot_LE(EOS(STATIC_1806), i421, i34, i34) :|: TRUE f1806_0_quot_LE(EOS(STATIC_1806), i421, i34, i34) -> f1833_0_quot_Inc(EOS(STATIC_1833), i421, i34) :|: i34 > 0 f1833_0_quot_Inc(EOS(STATIC_1833), i421, i34) -> f1838_0_quot_Load(EOS(STATIC_1838), i421, i34) :|: TRUE f1838_0_quot_Load(EOS(STATIC_1838), i421, i34) -> f1842_0_quot_ConstantStackPush(EOS(STATIC_1842), i34, i421) :|: TRUE f1842_0_quot_ConstantStackPush(EOS(STATIC_1842), i34, i421) -> f1846_0_quot_IntArithmetic(EOS(STATIC_1846), i34, i421, 1) :|: TRUE f1846_0_quot_IntArithmetic(EOS(STATIC_1846), i34, i421, matching1) -> f1849_0_quot_Load(EOS(STATIC_1849), i34, i421 - 1) :|: i421 > 0 && matching1 = 1 f1849_0_quot_Load(EOS(STATIC_1849), i34, i434) -> f1852_0_quot_ConstantStackPush(EOS(STATIC_1852), i34, i434, i34) :|: TRUE f1852_0_quot_ConstantStackPush(EOS(STATIC_1852), i34, i434, i34) -> f1855_0_quot_IntArithmetic(EOS(STATIC_1855), i34, i434, i34, 1) :|: TRUE f1855_0_quot_IntArithmetic(EOS(STATIC_1855), i34, i434, i34, matching1) -> f1858_0_quot_IntArithmetic(EOS(STATIC_1858), i34, i434, i34 - 1) :|: i34 > 0 && matching1 = 1 f1858_0_quot_IntArithmetic(EOS(STATIC_1858), i34, i434, i435) -> f1861_0_quot_Store(EOS(STATIC_1861), i34, i434 - i435) :|: i434 >= 0 && i435 >= 0 f1861_0_quot_Store(EOS(STATIC_1861), i34, i436) -> f1863_0_quot_JMP(EOS(STATIC_1863), i436, i34) :|: TRUE f1863_0_quot_JMP(EOS(STATIC_1863), i436, i34) -> f1925_0_quot_Load(EOS(STATIC_1925), i436, i34) :|: TRUE f1925_0_quot_Load(EOS(STATIC_1925), i436, i34) -> f1784_0_quot_Load(EOS(STATIC_1784), i436, i34) :|: TRUE f1784_0_quot_Load(EOS(STATIC_1784), i397, i34) -> f1790_0_quot_LE(EOS(STATIC_1790), i397, i34, i397) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f1790_0_quot_LE(EOS(STATIC_1790), i421:0, i34:0, i421:0) -> f1790_0_quot_LE(EOS(STATIC_1790), i421:0 - 1 - (i34:0 - 1), i34:0, i421:0 - 1 - (i34:0 - 1)) :|: i421:0 > 0 && i34:0 > 0 Filtered constant ground arguments: f1790_0_quot_LE(x1, x2, x3, x4) -> f1790_0_quot_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f1790_0_quot_LE(x1, x2, x3) -> f1790_0_quot_LE(x2, x3) Finished conversion. Obtained 1 rules.P rules: f1790_0_quot_LE(i34:0, i421:0) -> f1790_0_quot_LE(i34:0, i421:0 - 1 - (i34:0 - 1)) :|: i421:0 > 0 && i34:0 > 0 ---------------------------------------- (8) Obligation: Rules: f1790_0_quot_LE(i34:0, i421:0) -> f1790_0_quot_LE(i34:0, i421:0 - 1 - (i34:0 - 1)) :|: i421:0 > 0 && i34:0 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f1790_0_quot_LE(i34:0, i421:0) -> f1790_0_quot_LE(i34:0, arith) :|: i421:0 > 0 && i34:0 > 0 && arith = i421:0 - 1 - (i34:0 - 1) ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1790_0_quot_LE(i34:0, i421:0) -> f1790_0_quot_LE(i34:0, arith) :|: i421:0 > 0 && i34:0 > 0 && arith = i421:0 - 1 - (i34:0 - 1) Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f1790_0_quot_LE(i34:0, i421:0) -> f1790_0_quot_LE(i34:0, arith) :|: i421:0 > 0 && i34:0 > 0 && arith = i421:0 - 1 - (i34:0 - 1) Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f1790_0_quot_LE(i34:0:0, i421:0:0) -> f1790_0_quot_LE(i34:0:0, i421:0:0 - 1 - (i34:0:0 - 1)) :|: i421:0:0 > 0 && i34:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1790_0_quot_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f1790_0_quot_LE(i34:0:0, i421:0:0) -> f1790_0_quot_LE(i34:0:0, c) :|: c = i421:0:0 - 1 - (i34:0:0 - 1) && (i421:0:0 > 0 && i34:0:0 > 0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1790_0_quot_LE(x, x1)] = x1 The following rules are decreasing: f1790_0_quot_LE(i34:0:0, i421:0:0) -> f1790_0_quot_LE(i34:0:0, c) :|: c = i421:0:0 - 1 - (i34:0:0 - 1) && (i421:0:0 > 0 && i34:0:0 > 0) The following rules are bounded: f1790_0_quot_LE(i34:0:0, i421:0:0) -> f1790_0_quot_LE(i34:0:0, c) :|: c = i421:0:0 - 1 - (i34:0:0 - 1) && (i421:0:0 > 0 && i34:0:0 > 0) ---------------------------------------- (18) YES