10.56/3.79	YES
10.56/3.80	proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
10.56/3.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.56/3.80	
10.56/3.80	
10.56/3.80	termination of the given Bare JBC problem could be proven:
10.56/3.80	
10.56/3.80	(0) Bare JBC problem
10.56/3.80	(1) BareJBCToJBCProof [EQUIVALENT, 94 ms]
10.56/3.80	(2) JBC problem
10.56/3.80	(3) JBCToGraph [EQUIVALENT, 637 ms]
10.56/3.80	(4) JBCTerminationGraph
10.56/3.80	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
10.56/3.80	(6) JBCTerminationSCC
10.56/3.80	(7) SCCToIRSProof [SOUND, 43 ms]
10.56/3.80	(8) IRSwT
10.56/3.80	(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
10.56/3.80	(10) IRSwT
10.56/3.80	(11) IRSwTTerminationDigraphProof [EQUIVALENT, 136 ms]
10.56/3.80	(12) IRSwT
10.56/3.80	(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
10.56/3.80	(14) IRSwT
10.56/3.80	(15) TempFilterProof [SOUND, 78 ms]
10.56/3.80	(16) IntTRS
10.56/3.80	(17) RankingReductionPairProof [EQUIVALENT, 25 ms]
10.56/3.80	(18) IntTRS
10.56/3.80	(19) RankingReductionPairProof [EQUIVALENT, 0 ms]
10.56/3.80	(20) YES
10.56/3.80	
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(0)
10.56/3.80	Obligation:
10.56/3.80	need to prove termination of the following program:
10.56/3.80	class BubbleSort {
10.56/3.80	    public static void main(String[] args) {
10.56/3.80		sort(new int[100]);
10.56/3.80	    }
10.56/3.80	
10.56/3.80	    public static void sort(int[] x) {
10.56/3.80		int n = x.length;
10.56/3.80		for (int pass=1; pass < n; pass++)  // count how many times
10.56/3.80		    // This next loop becomes shorter and shorter
10.56/3.80		    for (int i=0; i < n - pass; i++)
10.56/3.80			if (x[i] > x[i+1]) {
10.56/3.80			    // exchange elements
10.56/3.80			    int temp = x[i]; x[i] = x[i+1];  x[i+1] = temp;
10.56/3.80			}
10.56/3.80	    }
10.56/3.80	}
10.56/3.80	
10.56/3.80	
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(1) BareJBCToJBCProof (EQUIVALENT)
10.56/3.80	initialized classpath
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(2)
10.56/3.80	Obligation:
10.56/3.80	need to prove termination of the following program:
10.56/3.80	class BubbleSort {
10.56/3.80	    public static void main(String[] args) {
10.56/3.80		sort(new int[100]);
10.56/3.80	    }
10.56/3.80	
10.56/3.80	    public static void sort(int[] x) {
10.56/3.80		int n = x.length;
10.56/3.80		for (int pass=1; pass < n; pass++)  // count how many times
10.56/3.80		    // This next loop becomes shorter and shorter
10.56/3.80		    for (int i=0; i < n - pass; i++)
10.56/3.80			if (x[i] > x[i+1]) {
10.56/3.80			    // exchange elements
10.56/3.80			    int temp = x[i]; x[i] = x[i+1];  x[i+1] = temp;
10.56/3.80			}
10.56/3.80	    }
10.56/3.80	}
10.56/3.80	
10.56/3.80	
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(3) JBCToGraph (EQUIVALENT)
10.56/3.80	Constructed TerminationGraph.
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(4)
10.56/3.80	Obligation:
10.56/3.80	Termination Graph based on JBC Program:
10.56/3.80	BubbleSort.main([Ljava/lang/String;)V: Graph of 169 nodes with 1 SCC.
10.56/3.80	
10.56/3.80	
10.56/3.80	
10.56/3.80	
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(5) TerminationGraphToSCCProof (SOUND)
10.56/3.80	Splitted TerminationGraph to 1 SCCs.
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(6)
10.56/3.80	Obligation:
10.56/3.80	SCC of termination graph based on JBC Program.
10.56/3.80	SCC contains nodes from the following methods: BubbleSort.main([Ljava/lang/String;)V
10.56/3.80	SCC calls the following helper methods: 
10.56/3.80	Performed SCC analyses:
10.56/3.80	*Used field analysis yielded the following read fields:
10.56/3.80	
10.56/3.80	*Marker field analysis yielded the following relations that could be markers:
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(7) SCCToIRSProof (SOUND)
10.56/3.80	Transformed FIGraph SCCs to intTRSs. Log: 
10.56/3.80	Generated rules. Obtained 58 IRulesP rules:
10.56/3.80	f1716_0_sort_Load(EOS(STATIC_1716), java.lang.Object(ARRAY(matching1)), matching2, i106, i106) -> f1719_0_sort_GE(EOS(STATIC_1719), java.lang.Object(ARRAY(100)), 100, i106, i106, 100) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f1719_0_sort_GE(EOS(STATIC_1719), java.lang.Object(ARRAY(matching1)), matching2, i108, i108, matching3) -> f1727_0_sort_GE(EOS(STATIC_1727), java.lang.Object(ARRAY(100)), 100, i108, i108, 100) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f1727_0_sort_GE(EOS(STATIC_1727), java.lang.Object(ARRAY(matching1)), matching2, i108, i108, matching3) -> f1729_0_sort_ConstantStackPush(EOS(STATIC_1729), java.lang.Object(ARRAY(100)), 100, i108) :|: i108 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f1729_0_sort_ConstantStackPush(EOS(STATIC_1729), java.lang.Object(ARRAY(matching1)), matching2, i108) -> f1738_0_sort_Store(EOS(STATIC_1738), java.lang.Object(ARRAY(100)), 100, i108, 0) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f1738_0_sort_Store(EOS(STATIC_1738), java.lang.Object(ARRAY(matching1)), matching2, i108, matching3) -> f1740_0_sort_Load(EOS(STATIC_1740), java.lang.Object(ARRAY(100)), 100, i108, 0) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 0
10.56/3.80	f1740_0_sort_Load(EOS(STATIC_1740), java.lang.Object(ARRAY(matching1)), matching2, i108, matching3) -> f1817_0_sort_Load(EOS(STATIC_1817), java.lang.Object(ARRAY(100)), 100, i108, 0) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 0
10.56/3.80	f1817_0_sort_Load(EOS(STATIC_1817), java.lang.Object(ARRAY(matching1)), matching2, i108, i113) -> f1916_0_sort_Load(EOS(STATIC_1916), java.lang.Object(ARRAY(100)), 100, i108, i113) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f1916_0_sort_Load(EOS(STATIC_1916), java.lang.Object(ARRAY(matching1)), matching2, i108, i122) -> f2049_0_sort_Load(EOS(STATIC_2049), java.lang.Object(ARRAY(100)), 100, i108, i122) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2049_0_sort_Load(EOS(STATIC_2049), java.lang.Object(ARRAY(matching1)), matching2, i108, i131) -> f2050_0_sort_Load(EOS(STATIC_2050), java.lang.Object(ARRAY(100)), 100, i108, i131, i131) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2050_0_sort_Load(EOS(STATIC_2050), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131) -> f2051_0_sort_Load(EOS(STATIC_2051), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, 100) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2051_0_sort_Load(EOS(STATIC_2051), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, matching3) -> f2052_0_sort_IntArithmetic(EOS(STATIC_2052), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, 100, i108) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2052_0_sort_IntArithmetic(EOS(STATIC_2052), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, matching3, i108) -> f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, 100 - i108) :|: i108 > 0 && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, i133) -> f2054_0_sort_GE(EOS(STATIC_2054), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, i133) :|: i131 >= i133 && matching1 = 100 && matching2 = 100
10.56/3.80	f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, i133) -> f2055_0_sort_GE(EOS(STATIC_2055), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, i133) :|: i131 < i133 && matching1 = 100 && matching2 = 100
10.56/3.80	f2054_0_sort_GE(EOS(STATIC_2054), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, i133) -> f2056_0_sort_Inc(EOS(STATIC_2056), java.lang.Object(ARRAY(100)), 100, i108) :|: i131 >= i133 && matching1 = 100 && matching2 = 100
10.56/3.80	f2056_0_sort_Inc(EOS(STATIC_2056), java.lang.Object(ARRAY(matching1)), matching2, i108) -> f2058_0_sort_JMP(EOS(STATIC_2058), java.lang.Object(ARRAY(100)), 100, i108 + 1) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2058_0_sort_JMP(EOS(STATIC_2058), java.lang.Object(ARRAY(matching1)), matching2, i134) -> f2063_0_sort_Load(EOS(STATIC_2063), java.lang.Object(ARRAY(100)), 100, i134) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2063_0_sort_Load(EOS(STATIC_2063), java.lang.Object(ARRAY(matching1)), matching2, i134) -> f1715_0_sort_Load(EOS(STATIC_1715), java.lang.Object(ARRAY(100)), 100, i134) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f1715_0_sort_Load(EOS(STATIC_1715), java.lang.Object(ARRAY(matching1)), matching2, i106) -> f1716_0_sort_Load(EOS(STATIC_1716), java.lang.Object(ARRAY(100)), 100, i106, i106) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2055_0_sort_GE(EOS(STATIC_2055), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, i133) -> f2057_0_sort_Load(EOS(STATIC_2057), java.lang.Object(ARRAY(100)), 100, i108, i131) :|: i131 < i133 && matching1 = 100 && matching2 = 100
10.56/3.80	f2057_0_sort_Load(EOS(STATIC_2057), java.lang.Object(ARRAY(matching1)), matching2, i108, i131) -> f2059_0_sort_Load(EOS(STATIC_2059), java.lang.Object(ARRAY(100)), 100, i108, i131, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2059_0_sort_Load(EOS(STATIC_2059), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, java.lang.Object(ARRAY(matching3))) -> f2065_0_sort_ArrayAccess(EOS(STATIC_2065), java.lang.Object(ARRAY(100)), 100, i108, i131, java.lang.Object(ARRAY(100)), i131) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2065_0_sort_ArrayAccess(EOS(STATIC_2065), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i136) -> f2066_0_sort_ArrayAccess(EOS(STATIC_2066), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2066_0_sort_ArrayAccess(EOS(STATIC_2066), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i136) -> f2069_0_sort_Load(EOS(STATIC_2069), java.lang.Object(ARRAY(100)), 100, i108, i136, i138) :|: i136 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2069_0_sort_Load(EOS(STATIC_2069), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138) -> f2096_0_sort_Load(EOS(STATIC_2096), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2096_0_sort_Load(EOS(STATIC_2096), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3))) -> f2099_0_sort_ConstantStackPush(EOS(STATIC_2099), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2099_0_sort_ConstantStackPush(EOS(STATIC_2099), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3)), i136) -> f2105_0_sort_IntArithmetic(EOS(STATIC_2105), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100)), i136, 1) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2105_0_sort_IntArithmetic(EOS(STATIC_2105), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3)), i136, matching4) -> f2108_0_sort_ArrayAccess(EOS(STATIC_2108), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100)), i136 + 1) :|: i136 >= 0 && matching1 = 100 && matching2 = 100 && matching3 = 100 && matching4 = 1
10.56/3.80	f2108_0_sort_ArrayAccess(EOS(STATIC_2108), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3)), i140) -> f2109_0_sort_ArrayAccess(EOS(STATIC_2109), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100)), i140) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2109_0_sort_ArrayAccess(EOS(STATIC_2109), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3)), i140) -> f2116_0_sort_LE(EOS(STATIC_2116), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, i141) :|: i140 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2116_0_sort_LE(EOS(STATIC_2116), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, i141) -> f2131_0_sort_LE(EOS(STATIC_2131), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, i141) :|: i138 <= i141 && matching1 = 100 && matching2 = 100
10.56/3.80	f2116_0_sort_LE(EOS(STATIC_2116), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, i141) -> f2132_0_sort_LE(EOS(STATIC_2132), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, i141) :|: i138 > i141 && matching1 = 100 && matching2 = 100
10.56/3.80	f2131_0_sort_LE(EOS(STATIC_2131), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, i141) -> f2141_0_sort_Inc(EOS(STATIC_2141), java.lang.Object(ARRAY(100)), 100, i108, i136) :|: i138 <= i141 && matching1 = 100 && matching2 = 100
10.56/3.80	f2141_0_sort_Inc(EOS(STATIC_2141), java.lang.Object(ARRAY(matching1)), matching2, i108, i136) -> f2153_0_sort_JMP(EOS(STATIC_2153), java.lang.Object(ARRAY(100)), 100, i108, i136 + 1) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2153_0_sort_JMP(EOS(STATIC_2153), java.lang.Object(ARRAY(matching1)), matching2, i108, i142) -> f2178_0_sort_Load(EOS(STATIC_2178), java.lang.Object(ARRAY(100)), 100, i108, i142) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2178_0_sort_Load(EOS(STATIC_2178), java.lang.Object(ARRAY(matching1)), matching2, i108, i142) -> f2049_0_sort_Load(EOS(STATIC_2049), java.lang.Object(ARRAY(100)), 100, i108, i142) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2132_0_sort_LE(EOS(STATIC_2132), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, i141) -> f2143_0_sort_Load(EOS(STATIC_2143), java.lang.Object(ARRAY(100)), 100, i108, i136) :|: i138 > i141 && matching1 = 100 && matching2 = 100
10.56/3.80	f2143_0_sort_Load(EOS(STATIC_2143), java.lang.Object(ARRAY(matching1)), matching2, i108, i136) -> f2154_0_sort_Load(EOS(STATIC_2154), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2154_0_sort_Load(EOS(STATIC_2154), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3))) -> f2179_0_sort_ArrayAccess(EOS(STATIC_2179), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2179_0_sort_ArrayAccess(EOS(STATIC_2179), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i136) -> f2180_0_sort_Store(EOS(STATIC_2180), java.lang.Object(ARRAY(100)), 100, i108, i136, i144) :|: i136 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2180_0_sort_Store(EOS(STATIC_2180), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144) -> f2189_0_sort_Load(EOS(STATIC_2189), java.lang.Object(ARRAY(100)), 100, i108, i136, i144) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2189_0_sort_Load(EOS(STATIC_2189), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144) -> f2193_0_sort_Load(EOS(STATIC_2193), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2193_0_sort_Load(EOS(STATIC_2193), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3))) -> f2194_0_sort_Load(EOS(STATIC_2194), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2194_0_sort_Load(EOS(STATIC_2194), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136) -> f2205_0_sort_Load(EOS(STATIC_2205), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2205_0_sort_Load(EOS(STATIC_2205), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4))) -> f2209_0_sort_ConstantStackPush(EOS(STATIC_2209), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100 && matching4 = 100
10.56/3.80	f2209_0_sort_ConstantStackPush(EOS(STATIC_2209), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4)), i136) -> f2213_0_sort_IntArithmetic(EOS(STATIC_2213), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136, java.lang.Object(ARRAY(100)), i136, 1) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100 && matching4 = 100
10.56/3.80	f2213_0_sort_IntArithmetic(EOS(STATIC_2213), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4)), i136, matching5) -> f2221_0_sort_ArrayAccess(EOS(STATIC_2221), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136, java.lang.Object(ARRAY(100)), i136 + 1) :|: i136 >= 0 && matching1 = 100 && matching2 = 100 && matching3 = 100 && matching4 = 100 && matching5 = 1
10.56/3.80	f2221_0_sort_ArrayAccess(EOS(STATIC_2221), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4)), i146) -> f2233_0_sort_ArrayAccess(EOS(STATIC_2233), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136, java.lang.Object(ARRAY(100)), i146) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100 && matching4 = 100
10.56/3.80	f2233_0_sort_ArrayAccess(EOS(STATIC_2233), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4)), i146) -> f2239_0_sort_ArrayAccess(EOS(STATIC_2239), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136, i147) :|: i146 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100 && matching4 = 100
10.56/3.80	f2239_0_sort_ArrayAccess(EOS(STATIC_2239), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, i147) -> f2251_0_sort_Load(EOS(STATIC_2251), java.lang.Object(ARRAY(100)), 100, i108, i136, i144) :|: i136 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2251_0_sort_Load(EOS(STATIC_2251), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144) -> f2262_0_sort_Load(EOS(STATIC_2262), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	f2262_0_sort_Load(EOS(STATIC_2262), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3))) -> f2266_0_sort_ConstantStackPush(EOS(STATIC_2266), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2266_0_sort_ConstantStackPush(EOS(STATIC_2266), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136) -> f2270_0_sort_IntArithmetic(EOS(STATIC_2270), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136, 1) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2270_0_sort_IntArithmetic(EOS(STATIC_2270), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, matching4) -> f2273_0_sort_Load(EOS(STATIC_2273), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136 + 1) :|: i136 >= 0 && matching1 = 100 && matching2 = 100 && matching3 = 100 && matching4 = 1
10.56/3.80	f2273_0_sort_Load(EOS(STATIC_2273), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i148) -> f2277_0_sort_ArrayAccess(EOS(STATIC_2277), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100)), i148, i144) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2277_0_sort_ArrayAccess(EOS(STATIC_2277), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i149, i144) -> f2281_0_sort_ArrayAccess(EOS(STATIC_2281), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100)), i149, i144) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2281_0_sort_ArrayAccess(EOS(STATIC_2281), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i149, i144) -> f2285_0_sort_Inc(EOS(STATIC_2285), java.lang.Object(ARRAY(100)), 100, i108, i136) :|: i149 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
10.56/3.80	f2285_0_sort_Inc(EOS(STATIC_2285), java.lang.Object(ARRAY(matching1)), matching2, i108, i136) -> f2141_0_sort_Inc(EOS(STATIC_2141), java.lang.Object(ARRAY(100)), 100, i108, i136) :|: TRUE && matching1 = 100 && matching2 = 100
10.56/3.80	Combined rules. Obtained 3 IRulesP rules:
10.56/3.80	f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(100)), 100, i108:0, i131:0, i131:0, i133:0) -> f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(100)), 100, i108:0, i131:0 + 1, i131:0 + 1, 100 - i108:0) :|: i133:0 > i131:0 && i131:0 < 100 && i131:0 > -1 && i131:0 < 99 && i141:0 < i138:0 && i108:0 > 0
10.56/3.80	f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(100)), 100, i108:0, i131:0, i131:0, i133:0) -> f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(100)), 100, i108:0, i131:0 + 1, i131:0 + 1, 100 - i108:0) :|: i133:0 > i131:0 && i131:0 < 100 && i131:0 > -1 && i131:0 < 99 && i141:0 >= i138:0 && i108:0 > 0
10.56/3.80	f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(100)), 100, i108:0, i131:0, i131:0, i133:0) -> f2053_0_sort_GE(EOS(STATIC_2053), java.lang.Object(ARRAY(100)), 100, i108:0 + 1, 0, 0, 100 - (i108:0 + 1)) :|: i108:0 < 99 && i133:0 <= i131:0 && i108:0 > -1
10.56/3.80	Filtered constant ground arguments:
10.56/3.80	   f2053_0_sort_GE(x1, x2, x3, x4, x5, x6, x7) -> f2053_0_sort_GE(x4, x5, x6, x7)
10.56/3.80	   EOS(x1) -> EOS
10.56/3.80	   java.lang.Object(x1) -> java.lang.Object
10.56/3.80	   ARRAY(x1) -> ARRAY
10.56/3.80	Filtered duplicate arguments:
10.56/3.80	   f2053_0_sort_GE(x1, x2, x3, x4) -> f2053_0_sort_GE(x1, x3, x4)
10.56/3.80	Finished conversion. Obtained 3 rules.P rules:
10.56/3.80	f2053_0_sort_GE(i108:0, i131:0, i133:0) -> f2053_0_sort_GE(i108:0, i131:0 + 1, 100 - i108:0) :|: i131:0 < 100 && i133:0 > i131:0 && i131:0 > -1 && i131:0 < 99 && i108:0 > 0 && i141:0 < i138:0
10.56/3.80	f2053_0_sort_GE(i108:0, i131:0, i133:0) -> f2053_0_sort_GE(i108:0, i131:0 + 1, 100 - i108:0) :|: i131:0 < 100 && i133:0 > i131:0 && i131:0 > -1 && i131:0 < 99 && i108:0 > 0 && i141:0 >= i138:0
10.56/3.80	f2053_0_sort_GE(i108:0, i131:0, i133:0) -> f2053_0_sort_GE(i108:0 + 1, 0, 100 - (i108:0 + 1)) :|: i133:0 <= i131:0 && i108:0 > -1 && i108:0 < 99
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(8)
10.56/3.80	Obligation:
10.56/3.80	Rules:
10.56/3.80	f2053_0_sort_GE(i108:0, i131:0, i133:0) -> f2053_0_sort_GE(i108:0, i131:0 + 1, 100 - i108:0) :|: i131:0 < 100 && i133:0 > i131:0 && i131:0 > -1 && i131:0 < 99 && i108:0 > 0 && i141:0 < i138:0
10.56/3.80	f2053_0_sort_GE(x, x1, x2) -> f2053_0_sort_GE(x, x1 + 1, 100 - x) :|: x1 < 100 && x2 > x1 && x1 > -1 && x1 < 99 && x > 0 && x3 >= x4
10.56/3.80	f2053_0_sort_GE(x5, x6, x7) -> f2053_0_sort_GE(x5 + 1, 0, 100 - (x5 + 1)) :|: x7 <= x6 && x5 > -1 && x5 < 99
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(9) IRSFormatTransformerProof (EQUIVALENT)
10.56/3.80	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(10)
10.56/3.80	Obligation:
10.56/3.80	Rules:
10.56/3.80	f2053_0_sort_GE(i108:0, i131:0, i133:0) -> f2053_0_sort_GE(i108:0, arith, arith1) :|: i131:0 < 100 && i133:0 > i131:0 && i131:0 > -1 && i131:0 < 99 && i108:0 > 0 && i141:0 < i138:0 && arith = i131:0 + 1 && arith1 = 100 - i108:0
10.56/3.80	f2053_0_sort_GE(x8, x9, x10) -> f2053_0_sort_GE(x8, x11, x12) :|: x9 < 100 && x10 > x9 && x9 > -1 && x9 < 99 && x8 > 0 && x13 >= x14 && x11 = x9 + 1 && x12 = 100 - x8
10.56/3.80	f2053_0_sort_GE(x15, x16, x17) -> f2053_0_sort_GE(x18, 0, x19) :|: x17 <= x16 && x15 > -1 && x15 < 99 && x18 = x15 + 1 && x19 = 100 - (x15 + 1)
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(11) IRSwTTerminationDigraphProof (EQUIVALENT)
10.56/3.80	Constructed termination digraph!
10.56/3.80	Nodes:
10.56/3.80	(1) f2053_0_sort_GE(i108:0, i131:0, i133:0) -> f2053_0_sort_GE(i108:0, arith, arith1) :|: i131:0 < 100 && i133:0 > i131:0 && i131:0 > -1 && i131:0 < 99 && i108:0 > 0 && i141:0 < i138:0 && arith = i131:0 + 1 && arith1 = 100 - i108:0
10.56/3.80	(2) f2053_0_sort_GE(x8, x9, x10) -> f2053_0_sort_GE(x8, x11, x12) :|: x9 < 100 && x10 > x9 && x9 > -1 && x9 < 99 && x8 > 0 && x13 >= x14 && x11 = x9 + 1 && x12 = 100 - x8
10.56/3.80	(3) f2053_0_sort_GE(x15, x16, x17) -> f2053_0_sort_GE(x18, 0, x19) :|: x17 <= x16 && x15 > -1 && x15 < 99 && x18 = x15 + 1 && x19 = 100 - (x15 + 1)
10.56/3.80	
10.56/3.80	Arcs:
10.56/3.80	(1) -> (1), (2), (3)
10.56/3.80	(2) -> (1), (2), (3)
10.56/3.80	(3) -> (1), (2)
10.56/3.80	
10.56/3.80	This digraph is fully evaluated!
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(12)
10.56/3.80	Obligation:
10.56/3.80	
10.56/3.80	Termination digraph:
10.56/3.80	Nodes:
10.56/3.80	(1) f2053_0_sort_GE(i108:0, i131:0, i133:0) -> f2053_0_sort_GE(i108:0, arith, arith1) :|: i131:0 < 100 && i133:0 > i131:0 && i131:0 > -1 && i131:0 < 99 && i108:0 > 0 && i141:0 < i138:0 && arith = i131:0 + 1 && arith1 = 100 - i108:0
10.56/3.80	(2) f2053_0_sort_GE(x8, x9, x10) -> f2053_0_sort_GE(x8, x11, x12) :|: x9 < 100 && x10 > x9 && x9 > -1 && x9 < 99 && x8 > 0 && x13 >= x14 && x11 = x9 + 1 && x12 = 100 - x8
10.56/3.80	(3) f2053_0_sort_GE(x15, x16, x17) -> f2053_0_sort_GE(x18, 0, x19) :|: x17 <= x16 && x15 > -1 && x15 < 99 && x18 = x15 + 1 && x19 = 100 - (x15 + 1)
10.56/3.80	
10.56/3.80	Arcs:
10.56/3.80	(1) -> (1), (2), (3)
10.56/3.80	(2) -> (1), (2), (3)
10.56/3.80	(3) -> (1), (2)
10.56/3.80	
10.56/3.80	This digraph is fully evaluated!
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(13) IntTRSCompressionProof (EQUIVALENT)
10.56/3.80	Compressed rules.
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(14)
10.56/3.80	Obligation:
10.56/3.80	Rules:
10.56/3.80	f2053_0_sort_GE(x15:0, x16:0, x17:0) -> f2053_0_sort_GE(x15:0 + 1, 0, 100 - (x15:0 + 1)) :|: x17:0 <= x16:0 && x15:0 > -1 && x15:0 < 99
10.56/3.80	f2053_0_sort_GE(x8:0, x9:0, x10:0) -> f2053_0_sort_GE(x8:0, x9:0 + 1, 100 - x8:0) :|: x8:0 > 0 && x14:0 <= x13:0 && x9:0 < 99 && x9:0 > -1 && x9:0 < x10:0 && x9:0 < 100
10.56/3.80	f2053_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2053_0_sort_GE(i108:0:0, i131:0:0 + 1, 100 - i108:0:0) :|: i108:0:0 > 0 && i141:0:0 < i138:0:0 && i131:0:0 < 99 && i131:0:0 > -1 && i133:0:0 > i131:0:0 && i131:0:0 < 100
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(15) TempFilterProof (SOUND)
10.56/3.80	Used the following sort dictionary for filtering: 
10.56/3.80	f2053_0_sort_GE(INTEGER, VARIABLE, INTEGER)
10.56/3.80	Replaced non-predefined constructor symbols by 0.
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(16)
10.56/3.80	Obligation:
10.56/3.80	Rules:
10.56/3.80	f2053_0_sort_GE(x15:0, x16:0, x17:0) -> f2053_0_sort_GE(c, c1, c2) :|: c2 = 100 - (x15:0 + 1) && (c1 = 0 && c = x15:0 + 1) && (x17:0 <= x16:0 && x15:0 > -1 && x15:0 < 99)
10.56/3.80	f2053_0_sort_GE(x8:0, x9:0, x10:0) -> f2053_0_sort_GE(x8:0, c3, c4) :|: c4 = 100 - x8:0 && c3 = x9:0 + 1 && (x8:0 > 0 && x14:0 <= x13:0 && x9:0 < 99 && x9:0 > -1 && x9:0 < x10:0 && x9:0 < 100)
10.56/3.80	f2053_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2053_0_sort_GE(i108:0:0, c5, c6) :|: c6 = 100 - i108:0:0 && c5 = i131:0:0 + 1 && (i108:0:0 > 0 && i141:0:0 < i138:0:0 && i131:0:0 < 99 && i131:0:0 > -1 && i133:0:0 > i131:0:0 && i131:0:0 < 100)
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(17) RankingReductionPairProof (EQUIVALENT)
10.56/3.80	Interpretation:
10.56/3.80	[ f2053_0_sort_GE ] = -1*f2053_0_sort_GE_1
10.56/3.80	
10.56/3.80	The following rules are decreasing:
10.56/3.80	f2053_0_sort_GE(x15:0, x16:0, x17:0) -> f2053_0_sort_GE(c, c1, c2) :|: c2 = 100 - (x15:0 + 1) && (c1 = 0 && c = x15:0 + 1) && (x17:0 <= x16:0 && x15:0 > -1 && x15:0 < 99)
10.56/3.80	
10.56/3.80	The following rules are bounded:
10.56/3.80	f2053_0_sort_GE(x15:0, x16:0, x17:0) -> f2053_0_sort_GE(c, c1, c2) :|: c2 = 100 - (x15:0 + 1) && (c1 = 0 && c = x15:0 + 1) && (x17:0 <= x16:0 && x15:0 > -1 && x15:0 < 99)
10.56/3.80	
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(18)
10.56/3.80	Obligation:
10.56/3.80	Rules:
10.56/3.80	f2053_0_sort_GE(x8:0, x9:0, x10:0) -> f2053_0_sort_GE(x8:0, c3, c4) :|: c4 = 100 - x8:0 && c3 = x9:0 + 1 && (x8:0 > 0 && x14:0 <= x13:0 && x9:0 < 99 && x9:0 > -1 && x9:0 < x10:0 && x9:0 < 100)
10.56/3.80	f2053_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2053_0_sort_GE(i108:0:0, c5, c6) :|: c6 = 100 - i108:0:0 && c5 = i131:0:0 + 1 && (i108:0:0 > 0 && i141:0:0 < i138:0:0 && i131:0:0 < 99 && i131:0:0 > -1 && i133:0:0 > i131:0:0 && i131:0:0 < 100)
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(19) RankingReductionPairProof (EQUIVALENT)
10.56/3.80	Interpretation:
10.56/3.80	[ f2053_0_sort_GE ] = -1*f2053_0_sort_GE_2
10.56/3.80	
10.56/3.80	The following rules are decreasing:
10.56/3.80	f2053_0_sort_GE(x8:0, x9:0, x10:0) -> f2053_0_sort_GE(x8:0, c3, c4) :|: c4 = 100 - x8:0 && c3 = x9:0 + 1 && (x8:0 > 0 && x14:0 <= x13:0 && x9:0 < 99 && x9:0 > -1 && x9:0 < x10:0 && x9:0 < 100)
10.56/3.80	f2053_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2053_0_sort_GE(i108:0:0, c5, c6) :|: c6 = 100 - i108:0:0 && c5 = i131:0:0 + 1 && (i108:0:0 > 0 && i141:0:0 < i138:0:0 && i131:0:0 < 99 && i131:0:0 > -1 && i133:0:0 > i131:0:0 && i131:0:0 < 100)
10.56/3.80	
10.56/3.80	The following rules are bounded:
10.56/3.80	f2053_0_sort_GE(x8:0, x9:0, x10:0) -> f2053_0_sort_GE(x8:0, c3, c4) :|: c4 = 100 - x8:0 && c3 = x9:0 + 1 && (x8:0 > 0 && x14:0 <= x13:0 && x9:0 < 99 && x9:0 > -1 && x9:0 < x10:0 && x9:0 < 100)
10.56/3.80	f2053_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2053_0_sort_GE(i108:0:0, c5, c6) :|: c6 = 100 - i108:0:0 && c5 = i131:0:0 + 1 && (i108:0:0 > 0 && i141:0:0 < i138:0:0 && i131:0:0 < 99 && i131:0:0 > -1 && i133:0:0 > i131:0:0 && i131:0:0 < 100)
10.56/3.80	
10.56/3.80	
10.56/3.80	----------------------------------------
10.56/3.80	
10.56/3.80	(20)
10.56/3.80	YES
11.11/4.06	EOF