/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 331 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 45 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 10 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 14 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) 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 PastaB14 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x == y && x > 0) { while (y > 0) { x--; y--; } } } } 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 PastaB14 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x == y && x > 0) { while (y > 0) { x--; y--; } } } } 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: PastaB14.main([Ljava/lang/String;)V: Graph of 190 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: PastaB14.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: f594_0_main_Load(EOS(STATIC_594), i116, i117, i116) -> f596_0_main_NE(EOS(STATIC_596), i116, i117, i116, i117) :|: TRUE f596_0_main_NE(EOS(STATIC_596), i117, i117, i117, i117) -> f605_0_main_NE(EOS(STATIC_605), i117, i117, i117, i117) :|: i116 = i117 f605_0_main_NE(EOS(STATIC_605), i117, i117, i117, i117) -> f617_0_main_Load(EOS(STATIC_617), i117, i117) :|: TRUE f617_0_main_Load(EOS(STATIC_617), i117, i117) -> f619_0_main_LE(EOS(STATIC_619), i117, i117, i117) :|: TRUE f619_0_main_LE(EOS(STATIC_619), i127, i127, i127) -> f621_0_main_LE(EOS(STATIC_621), i127, i127, i127) :|: TRUE f621_0_main_LE(EOS(STATIC_621), i127, i127, i127) -> f626_0_main_Load(EOS(STATIC_626), i127, i127) :|: i127 > 0 f626_0_main_Load(EOS(STATIC_626), i127, i127) -> f634_0_main_Load(EOS(STATIC_634), i127, i127) :|: TRUE f634_0_main_Load(EOS(STATIC_634), i131, i132) -> f708_0_main_Load(EOS(STATIC_708), i131, i132) :|: TRUE f708_0_main_Load(EOS(STATIC_708), i148, i149) -> f756_0_main_Load(EOS(STATIC_756), i148, i149) :|: TRUE f756_0_main_Load(EOS(STATIC_756), i169, i170) -> f760_0_main_LE(EOS(STATIC_760), i169, i170, i170) :|: TRUE f760_0_main_LE(EOS(STATIC_760), i169, matching1, matching2) -> f761_0_main_LE(EOS(STATIC_761), i169, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f760_0_main_LE(EOS(STATIC_760), i169, i177, i177) -> f762_0_main_LE(EOS(STATIC_762), i169, i177, i177) :|: TRUE f761_0_main_LE(EOS(STATIC_761), i169, matching1, matching2) -> f777_0_main_Load(EOS(STATIC_777), i169, 0) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f777_0_main_Load(EOS(STATIC_777), i169, matching1) -> f593_0_main_Load(EOS(STATIC_593), i169, 0) :|: TRUE && matching1 = 0 f593_0_main_Load(EOS(STATIC_593), i116, i117) -> f594_0_main_Load(EOS(STATIC_594), i116, i117, i116) :|: TRUE f762_0_main_LE(EOS(STATIC_762), i169, i177, i177) -> f781_0_main_Inc(EOS(STATIC_781), i169, i177) :|: i177 > 0 f781_0_main_Inc(EOS(STATIC_781), i169, i177) -> f783_0_main_Inc(EOS(STATIC_783), i169 + -1, i177) :|: TRUE f783_0_main_Inc(EOS(STATIC_783), i184, i177) -> f784_0_main_JMP(EOS(STATIC_784), i184, i177 + -1) :|: TRUE f784_0_main_JMP(EOS(STATIC_784), i184, i185) -> f794_0_main_Load(EOS(STATIC_794), i184, i185) :|: TRUE f794_0_main_Load(EOS(STATIC_794), i184, i185) -> f756_0_main_Load(EOS(STATIC_756), i184, i185) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f760_0_main_LE(EOS(STATIC_760), i169:0, i177:0, i177:0) -> f760_0_main_LE(EOS(STATIC_760), i169:0 - 1, i177:0 - 1, i177:0 - 1) :|: i177:0 > 0 Filtered constant ground arguments: f760_0_main_LE(x1, x2, x3, x4) -> f760_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f760_0_main_LE(x1, x2, x3) -> f760_0_main_LE(x1, x3) Filtered unneeded arguments: f760_0_main_LE(x1, x2) -> f760_0_main_LE(x2) Finished conversion. Obtained 1 rules.P rules: f760_0_main_LE(i177:0) -> f760_0_main_LE(i177:0 - 1) :|: i177:0 > 0 ---------------------------------------- (8) Obligation: Rules: f760_0_main_LE(i177:0) -> f760_0_main_LE(i177:0 - 1) :|: i177:0 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f760_0_main_LE(i177:0) -> f760_0_main_LE(arith) :|: i177:0 > 0 && arith = i177:0 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f760_0_main_LE(i177:0) -> f760_0_main_LE(arith) :|: i177:0 > 0 && arith = i177:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f760_0_main_LE(i177:0) -> f760_0_main_LE(arith) :|: i177:0 > 0 && arith = i177:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f760_0_main_LE(i177:0:0) -> f760_0_main_LE(i177:0:0 - 1) :|: i177:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f760_0_main_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f760_0_main_LE(i177:0:0) -> f760_0_main_LE(c) :|: c = i177:0:0 - 1 && i177:0:0 > 0 ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f760_0_main_LE(x)] = x The following rules are decreasing: f760_0_main_LE(i177:0:0) -> f760_0_main_LE(c) :|: c = i177:0:0 - 1 && i177:0:0 > 0 The following rules are bounded: f760_0_main_LE(i177:0:0) -> f760_0_main_LE(c) :|: c = i177:0:0 - 1 && i177:0:0 > 0 ---------------------------------------- (18) YES