5.87/2.47 NO 6.16/2.50 proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar 6.16/2.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.16/2.50 6.16/2.50 6.16/2.50 termination of the given Bare JBC problem could be disproven: 6.16/2.50 6.16/2.50 (0) Bare JBC problem 6.16/2.50 (1) BareJBCToJBCProof [EQUIVALENT, 93 ms] 6.16/2.50 (2) JBC problem 6.16/2.50 (3) JBCToGraph [EQUIVALENT, 309 ms] 6.16/2.50 (4) JBCTerminationGraph 6.16/2.50 (5) JBCNonTerm [COMPLETE, 203 ms] 6.16/2.50 (6) NO 6.16/2.50 6.16/2.50 6.16/2.50 ---------------------------------------- 6.16/2.50 6.16/2.50 (0) 6.16/2.50 Obligation: 6.16/2.50 need to prove termination of the following program: 6.16/2.50 package simple.gauss; 6.16/2.50 6.16/2.50 public class Gauss { 6.16/2.50 6.16/2.50 // does not terminate for negative numbers 6.16/2.50 6.16/2.50 public static int sum(int n) { 6.16/2.50 int sum = 0; 6.16/2.50 while (n != 0) { 6.16/2.50 sum += n; 6.16/2.50 n--; 6.16/2.50 } 6.16/2.50 return sum; 6.16/2.50 } 6.16/2.50 6.16/2.50 } 6.16/2.50 6.16/2.50 6.16/2.50 package simple.gauss; 6.16/2.50 6.16/2.50 public class Main { 6.16/2.50 6.16/2.50 /** 6.16/2.50 * @param args 6.16/2.50 */ 6.16/2.50 public static void main(String[] args) { 6.16/2.50 int value = args[1].length(); 6.16/2.50 if (args[0].length() % 2 == 0) { 6.16/2.50 value = -value; 6.16/2.50 } 6.16/2.50 Gauss.sum(value); 6.16/2.50 } 6.16/2.50 6.16/2.50 } 6.16/2.50 6.16/2.50 6.16/2.50 6.16/2.50 ---------------------------------------- 6.16/2.50 6.16/2.50 (1) BareJBCToJBCProof (EQUIVALENT) 6.16/2.50 initialized classpath 6.16/2.50 ---------------------------------------- 6.16/2.50 6.16/2.50 (2) 6.16/2.50 Obligation: 6.16/2.50 need to prove termination of the following program: 6.16/2.50 package simple.gauss; 6.16/2.50 6.16/2.50 public class Gauss { 6.16/2.50 6.16/2.50 // does not terminate for negative numbers 6.16/2.50 6.16/2.50 public static int sum(int n) { 6.16/2.50 int sum = 0; 6.16/2.50 while (n != 0) { 6.16/2.50 sum += n; 6.16/2.50 n--; 6.16/2.50 } 6.16/2.50 return sum; 6.16/2.50 } 6.16/2.50 6.16/2.50 } 6.16/2.50 6.16/2.50 6.16/2.50 package simple.gauss; 6.16/2.50 6.16/2.50 public class Main { 6.16/2.50 6.16/2.50 /** 6.16/2.50 * @param args 6.16/2.50 */ 6.16/2.50 public static void main(String[] args) { 6.16/2.50 int value = args[1].length(); 6.16/2.50 if (args[0].length() % 2 == 0) { 6.16/2.50 value = -value; 6.16/2.50 } 6.16/2.50 Gauss.sum(value); 6.16/2.50 } 6.16/2.50 6.16/2.50 } 6.16/2.50 6.16/2.50 6.16/2.50 6.16/2.50 ---------------------------------------- 6.16/2.50 6.16/2.50 (3) JBCToGraph (EQUIVALENT) 6.16/2.50 Constructed TerminationGraph. 6.16/2.50 ---------------------------------------- 6.16/2.50 6.16/2.50 (4) 6.16/2.50 Obligation: 6.16/2.50 Termination Graph based on JBC Program: 6.16/2.50 simple.gauss.Main.main([Ljava/lang/String;)V: Graph of 139 nodes with 2 SCCs. 6.16/2.50 6.16/2.50 6.16/2.50 6.16/2.50 6.16/2.50 6.16/2.50 ---------------------------------------- 6.16/2.50 6.16/2.50 (5) JBCNonTerm (COMPLETE) 6.16/2.50 Reached a loop using the following run: 6.16/2.50 6.16/2.50 0: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 1: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 2: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 3: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 4: 6.16/2.50 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 5: 6.16/2.50 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 6: 6.16/2.50 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 7: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 8: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 9: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 10: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 a27([java.lang.String...]): {o33, o15} -->{java.lang.Object...} 6.16/2.50 o15!: String(count=1, hash=#, offset=0, value=o16?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 o16:: [CHAR] -->{java.lang.Object...} 6.16/2.50 a27-><-o34 6.16/2.50 a27-><-o33 6.16/2.50 a27-><-o16 6.16/2.50 a27-><-o15 6.16/2.50 YES: (JL1) 6.16/2.50 11: 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 YES: (JL1) 6.16/2.50 12: 6.16/2.50 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 YES: (JL1) 6.16/2.50 13: 6.16/2.50 6.16/2.50 o33!: String(count=0, hash=#, offset=0, value=o34?) -->{java.lang.Object...} 6.16/2.50 o34:: [CHAR] -->{java.lang.Object...} 6.16/2.50 YES: (JL1) 6.16/2.50 14: 6.16/2.50 6.16/2.50 YES: (JL1) 6.16/2.50 15: 6.16/2.50 YES: (JL1) 6.16/2.50 16: 6.16/2.50 YES: (JL1) 6.16/2.50 17: 6.16/2.50 YES: (JL1) 6.16/2.50 18: 6.16/2.50 YES: (JL1) 6.16/2.50 19: 6.16/2.50 YES: (JL1) 6.16/2.50 20: 6.16/2.50 YES: (JL1) 6.16/2.50 21: 6.16/2.50 YES: (JL1) 6.16/2.50 22: 6.16/2.50 YES: (JL1) 6.16/2.50 23: 6.16/2.50 6.16/2.50 YES: (JL1) 6.16/2.50 24: 6.16/2.50 6.16/2.50 YES: (JL1) 6.16/2.50 25: 6.16/2.50 6.16/2.50 YES: (JL1) 6.16/2.50 Start state of loop: 6.16/2.50 6.16/2.50 6.16/2.50 [a16(lv_0_0)] 6.16/2.50 6.16/2.50 i352: (-inf,0](u2){-inf,+inf} 6.16/2.50 i354: (-inf,0](u2){-inf,+inf} 6.16/2.50 i6: [2,+inf){0,+inf} 6.16/2.50 a16([java.lang.String...]): length i6 -->{java.lang.Object...} 6.16/2.50 YES: (JL1) 6.16/2.50 6.16/2.50 6.16/2.50 In the loop head node, references [i352] were interesting. 6.16/2.50 6.16/2.50 All methods calls in the loop body are side-effect free, hence they can be ignored. 6.16/2.50 6.16/2.50 By SMT, we could prove 6.16/2.50 6.16/2.50 ((initial_i352 <= 0 and initial_i354 <= 0 and 2 <= initial_i6) and (((path1_i352 = path1_i382 and path1_i387 = (path1_i354 + path1_i382) and path1_i392 = (path1_i382 + -1) and path1_i392 = res_i352 and path1_i352 = initial_i352) and path1_i382 < 0) and ((res1_i352 = res1_i382 and res1_i387 = (res1_i354 + res1_i382) and res1_i392 = (res1_i382 + -1) and res_i352 = res1_i352) and !res1_i382 < 0))) 6.16/2.50 6.16/2.50 to be UNSAT. Consequently, the loop will not terminate. 6.16/2.50 ---------------------------------------- 6.16/2.50 6.16/2.50 (6) 6.16/2.50 NO 6.23/2.53 EOF