/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 325 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 66 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 18 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (17) IRSwT (18) TempFilterProof [SOUND, 30 ms] (19) IntTRS (20) PolynomialOrderProcessor [EQUIVALENT, 7 ms] (21) YES (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT (25) TempFilterProof [SOUND, 15 ms] (26) IntTRS (27) PolynomialOrderProcessor [EQUIVALENT, 6 ms] (28) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: /** * Example taken from "A Term Rewriting Approach to the Automated Termination * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) * and converted to Java. */ public class PastaB12 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0 || y > 0) { if (x > 0) { x--; } else if (y > 0) { y--; } else { continue; } } } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: /** * Example taken from "A Term Rewriting Approach to the Automated Termination * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) * and converted to Java. */ public class PastaB12 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0 || y > 0) { if (x > 0) { x--; } else if (y > 0) { y--; } else { continue; } } } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: PastaB12.main([Ljava/lang/String;)V: Graph of 187 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: PastaB12.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 20 IRulesP rules: f573_0_main_GT(EOS(STATIC_573), matching1, i46, matching2) -> f584_0_main_GT(EOS(STATIC_584), 0, i46, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f573_0_main_GT(EOS(STATIC_573), i90, i46, i90) -> f585_0_main_GT(EOS(STATIC_585), i90, i46, i90) :|: TRUE f584_0_main_GT(EOS(STATIC_584), matching1, i46, matching2) -> f595_0_main_Load(EOS(STATIC_595), 0, i46) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f595_0_main_Load(EOS(STATIC_595), matching1, i46) -> f606_0_main_LE(EOS(STATIC_606), 0, i46, i46) :|: TRUE && matching1 = 0 f606_0_main_LE(EOS(STATIC_606), matching1, i94, i94) -> f620_0_main_LE(EOS(STATIC_620), 0, i94, i94) :|: TRUE && matching1 = 0 f620_0_main_LE(EOS(STATIC_620), matching1, i94, i94) -> f634_0_main_Load(EOS(STATIC_634), 0, i94) :|: i94 > 0 && matching1 = 0 f634_0_main_Load(EOS(STATIC_634), matching1, i94) -> f644_0_main_LE(EOS(STATIC_644), 0, i94, 0) :|: TRUE && matching1 = 0 f644_0_main_LE(EOS(STATIC_644), matching1, i94, matching2) -> f691_0_main_Load(EOS(STATIC_691), 0, i94) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f691_0_main_Load(EOS(STATIC_691), matching1, i94) -> f696_0_main_LE(EOS(STATIC_696), 0, i94, i94) :|: TRUE && matching1 = 0 f696_0_main_LE(EOS(STATIC_696), matching1, i94, i94) -> f701_0_main_Inc(EOS(STATIC_701), 0, i94) :|: i94 > 0 && matching1 = 0 f701_0_main_Inc(EOS(STATIC_701), matching1, i94) -> f703_0_main_JMP(EOS(STATIC_703), 0, i94 + -1) :|: TRUE && matching1 = 0 f703_0_main_JMP(EOS(STATIC_703), matching1, i106) -> f1497_0_main_Load(EOS(STATIC_1497), 0, i106) :|: TRUE && matching1 = 0 f1497_0_main_Load(EOS(STATIC_1497), matching1, i106) -> f551_0_main_Load(EOS(STATIC_551), 0, i106) :|: TRUE && matching1 = 0 f551_0_main_Load(EOS(STATIC_551), i80, i46) -> f573_0_main_GT(EOS(STATIC_573), i80, i46, i80) :|: TRUE f585_0_main_GT(EOS(STATIC_585), i90, i46, i90) -> f596_0_main_Load(EOS(STATIC_596), i90, i46) :|: i90 > 0 f596_0_main_Load(EOS(STATIC_596), i90, i46) -> f608_0_main_LE(EOS(STATIC_608), i90, i46, i90) :|: TRUE f608_0_main_LE(EOS(STATIC_608), i90, i46, i90) -> f622_0_main_Inc(EOS(STATIC_622), i90, i46) :|: i90 > 0 f622_0_main_Inc(EOS(STATIC_622), i90, i46) -> f636_0_main_JMP(EOS(STATIC_636), i90 + -1, i46) :|: TRUE f636_0_main_JMP(EOS(STATIC_636), i96, i46) -> f686_0_main_Load(EOS(STATIC_686), i96, i46) :|: TRUE f686_0_main_Load(EOS(STATIC_686), i96, i46) -> f551_0_main_Load(EOS(STATIC_551), i96, i46) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f573_0_main_GT(EOS(STATIC_573), 0, i46:0, 0) -> f573_0_main_GT(EOS(STATIC_573), 0, i46:0 - 1, 0) :|: i46:0 > 0 f573_0_main_GT(EOS(STATIC_573), i90:0, i46:0, i90:0) -> f573_0_main_GT(EOS(STATIC_573), i90:0 - 1, i46:0, i90:0 - 1) :|: i90:0 > 0 Filtered constant ground arguments: f573_0_main_GT(x1, x2, x3, x4) -> f573_0_main_GT(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f573_0_main_GT(x1, x2, x3) -> f573_0_main_GT(x2, x3) Finished conversion. Obtained 2 rules.P rules: f573_0_main_GT(i46:0, cons_0) -> f573_0_main_GT(i46:0 - 1, 0) :|: i46:0 > 0 && cons_0 = 0 f573_0_main_GT(i46:0, i90:0) -> f573_0_main_GT(i46:0, i90:0 - 1) :|: i90:0 > 0 ---------------------------------------- (8) Obligation: Rules: f573_0_main_GT(i46:0, cons_0) -> f573_0_main_GT(i46:0 - 1, 0) :|: i46:0 > 0 && cons_0 = 0 f573_0_main_GT(x, x1) -> f573_0_main_GT(x, x1 - 1) :|: x1 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f573_0_main_GT(i46:0, cons_0) -> f573_0_main_GT(arith, 0) :|: i46:0 > 0 && cons_0 = 0 && arith = i46:0 - 1 f573_0_main_GT(x2, x3) -> f573_0_main_GT(x2, x4) :|: x3 > 0 && x4 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f573_0_main_GT(i46:0, cons_0) -> f573_0_main_GT(arith, 0) :|: i46:0 > 0 && cons_0 = 0 && arith = i46:0 - 1 (2) f573_0_main_GT(x2, x3) -> f573_0_main_GT(x2, x4) :|: x3 > 0 && x4 = x3 - 1 Arcs: (1) -> (1) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f573_0_main_GT(x2, x3) -> f573_0_main_GT(x2, x4) :|: x3 > 0 && x4 = x3 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f573_0_main_GT(x2:0, x3:0) -> f573_0_main_GT(x2:0, x3:0 - 1) :|: x3:0 > 0 ---------------------------------------- (16) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f573_0_main_GT(x1, x2) -> f573_0_main_GT(x2) ---------------------------------------- (17) Obligation: Rules: f573_0_main_GT(x3:0) -> f573_0_main_GT(x3:0 - 1) :|: x3:0 > 0 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f573_0_main_GT(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (19) Obligation: Rules: f573_0_main_GT(x3:0) -> f573_0_main_GT(c) :|: c = x3:0 - 1 && x3:0 > 0 ---------------------------------------- (20) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f573_0_main_GT(x)] = x The following rules are decreasing: f573_0_main_GT(x3:0) -> f573_0_main_GT(c) :|: c = x3:0 - 1 && x3:0 > 0 The following rules are bounded: f573_0_main_GT(x3:0) -> f573_0_main_GT(c) :|: c = x3:0 - 1 && x3:0 > 0 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f573_0_main_GT(i46:0, cons_0) -> f573_0_main_GT(arith, 0) :|: i46:0 > 0 && cons_0 = 0 && arith = i46:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f573_0_main_GT(i46:0:0, cons_0) -> f573_0_main_GT(i46:0:0 - 1, 0) :|: i46:0:0 > 0 && cons_0 = 0 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f573_0_main_GT(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (26) Obligation: Rules: f573_0_main_GT(i46:0:0, c) -> f573_0_main_GT(c1, c2) :|: c2 = 0 && (c1 = i46:0:0 - 1 && c = 0) && (i46:0:0 > 0 && cons_0 = 0) ---------------------------------------- (27) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f573_0_main_GT(x, x1)] = x + c1*x1 The following rules are decreasing: f573_0_main_GT(i46:0:0, c) -> f573_0_main_GT(c1, c2) :|: c2 = 0 && (c1 = i46:0:0 - 1 && c = 0) && (i46:0:0 > 0 && cons_0 = 0) The following rules are bounded: f573_0_main_GT(i46:0:0, c) -> f573_0_main_GT(c1, c2) :|: c2 = 0 && (c1 = i46:0:0 - 1 && c = 0) && (i46:0:0 > 0 && cons_0 = 0) ---------------------------------------- (28) YES