/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 660 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 230 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 177 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 89 ms]
(16) IntTRS
(17) RankingReductionPairProof [EQUIVALENT, 0 ms]
(18) IntTRS
(19) RankingReductionPairProof [EQUIVALENT, 8 ms]
(20) YES


----------------------------------------

(0)
Obligation:
need to prove termination of the following program:
class BubbleSort {
    public static void main(String[] args) {
	sort(new int[100]);
    }

    public static void sort(int[] x) {
	int n = x.length;
	for (int pass=1; pass < n; pass++)  // count how many times
	    // This next loop becomes shorter and shorter
	    for (int i=0; i < n - pass; i++)
		if (x[i] > x[i+1]) {
		    // exchange elements
		    int temp = x[i]; x[i] = x[i+1];  x[i+1] = temp;
		}
    }
}



----------------------------------------

(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
class BubbleSort {
    public static void main(String[] args) {
	sort(new int[100]);
    }

    public static void sort(int[] x) {
	int n = x.length;
	for (int pass=1; pass < n; pass++)  // count how many times
	    // This next loop becomes shorter and shorter
	    for (int i=0; i < n - pass; i++)
		if (x[i] > x[i+1]) {
		    // exchange elements
		    int temp = x[i]; x[i] = x[i+1];  x[i+1] = temp;
		}
    }
}



----------------------------------------

(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
----------------------------------------

(4)
Obligation:
Termination Graph based on JBC Program:
BubbleSort.main([Ljava/lang/String;)V: Graph of 169 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: BubbleSort.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 58 IRulesP rules:
f1806_0_sort_Load(EOS(STATIC_1806), java.lang.Object(ARRAY(matching1)), matching2, i106, i106) -> f1807_0_sort_GE(EOS(STATIC_1807), java.lang.Object(ARRAY(100)), 100, i106, i106, 100) :|: TRUE && matching1 = 100 && matching2 = 100
f1807_0_sort_GE(EOS(STATIC_1807), java.lang.Object(ARRAY(matching1)), matching2, i108, i108, matching3) -> f1808_0_sort_GE(EOS(STATIC_1808), java.lang.Object(ARRAY(100)), 100, i108, i108, 100) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f1808_0_sort_GE(EOS(STATIC_1808), java.lang.Object(ARRAY(matching1)), matching2, i108, i108, matching3) -> f1810_0_sort_ConstantStackPush(EOS(STATIC_1810), java.lang.Object(ARRAY(100)), 100, i108) :|: i108 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
f1810_0_sort_ConstantStackPush(EOS(STATIC_1810), java.lang.Object(ARRAY(matching1)), matching2, i108) -> f1818_0_sort_Store(EOS(STATIC_1818), java.lang.Object(ARRAY(100)), 100, i108, 0) :|: TRUE && matching1 = 100 && matching2 = 100
f1818_0_sort_Store(EOS(STATIC_1818), java.lang.Object(ARRAY(matching1)), matching2, i108, matching3) -> f1822_0_sort_Load(EOS(STATIC_1822), java.lang.Object(ARRAY(100)), 100, i108, 0) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 0
f1822_0_sort_Load(EOS(STATIC_1822), java.lang.Object(ARRAY(matching1)), matching2, i108, matching3) -> f1864_0_sort_Load(EOS(STATIC_1864), java.lang.Object(ARRAY(100)), 100, i108, 0) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 0
f1864_0_sort_Load(EOS(STATIC_1864), java.lang.Object(ARRAY(matching1)), matching2, i108, i113) -> f1957_0_sort_Load(EOS(STATIC_1957), java.lang.Object(ARRAY(100)), 100, i108, i113) :|: TRUE && matching1 = 100 && matching2 = 100
f1957_0_sort_Load(EOS(STATIC_1957), java.lang.Object(ARRAY(matching1)), matching2, i108, i122) -> f2015_0_sort_Load(EOS(STATIC_2015), java.lang.Object(ARRAY(100)), 100, i108, i122) :|: TRUE && matching1 = 100 && matching2 = 100
f2015_0_sort_Load(EOS(STATIC_2015), java.lang.Object(ARRAY(matching1)), matching2, i108, i131) -> f2016_0_sort_Load(EOS(STATIC_2016), java.lang.Object(ARRAY(100)), 100, i108, i131, i131) :|: TRUE && matching1 = 100 && matching2 = 100
f2016_0_sort_Load(EOS(STATIC_2016), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131) -> f2017_0_sort_Load(EOS(STATIC_2017), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, 100) :|: TRUE && matching1 = 100 && matching2 = 100
f2017_0_sort_Load(EOS(STATIC_2017), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, matching3) -> f2018_0_sort_IntArithmetic(EOS(STATIC_2018), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, 100, i108) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2018_0_sort_IntArithmetic(EOS(STATIC_2018), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, matching3, i108) -> f2019_0_sort_GE(EOS(STATIC_2019), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, 100 - i108) :|: i108 > 0 && matching1 = 100 && matching2 = 100 && matching3 = 100
f2019_0_sort_GE(EOS(STATIC_2019), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, i133) -> f2020_0_sort_GE(EOS(STATIC_2020), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, i133) :|: i131 >= i133 && matching1 = 100 && matching2 = 100
f2019_0_sort_GE(EOS(STATIC_2019), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, i133) -> f2021_0_sort_GE(EOS(STATIC_2021), java.lang.Object(ARRAY(100)), 100, i108, i131, i131, i133) :|: i131 < i133 && matching1 = 100 && matching2 = 100
f2020_0_sort_GE(EOS(STATIC_2020), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, i133) -> f2025_0_sort_Inc(EOS(STATIC_2025), java.lang.Object(ARRAY(100)), 100, i108) :|: i131 >= i133 && matching1 = 100 && matching2 = 100
f2025_0_sort_Inc(EOS(STATIC_2025), java.lang.Object(ARRAY(matching1)), matching2, i108) -> f2031_0_sort_JMP(EOS(STATIC_2031), java.lang.Object(ARRAY(100)), 100, i108 + 1) :|: TRUE && matching1 = 100 && matching2 = 100
f2031_0_sort_JMP(EOS(STATIC_2031), java.lang.Object(ARRAY(matching1)), matching2, i134) -> f2044_0_sort_Load(EOS(STATIC_2044), java.lang.Object(ARRAY(100)), 100, i134) :|: TRUE && matching1 = 100 && matching2 = 100
f2044_0_sort_Load(EOS(STATIC_2044), java.lang.Object(ARRAY(matching1)), matching2, i134) -> f1805_0_sort_Load(EOS(STATIC_1805), java.lang.Object(ARRAY(100)), 100, i134) :|: TRUE && matching1 = 100 && matching2 = 100
f1805_0_sort_Load(EOS(STATIC_1805), java.lang.Object(ARRAY(matching1)), matching2, i106) -> f1806_0_sort_Load(EOS(STATIC_1806), java.lang.Object(ARRAY(100)), 100, i106, i106) :|: TRUE && matching1 = 100 && matching2 = 100
f2021_0_sort_GE(EOS(STATIC_2021), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, i131, i133) -> f2030_0_sort_Load(EOS(STATIC_2030), java.lang.Object(ARRAY(100)), 100, i108, i131) :|: i131 < i133 && matching1 = 100 && matching2 = 100
f2030_0_sort_Load(EOS(STATIC_2030), java.lang.Object(ARRAY(matching1)), matching2, i108, i131) -> f2033_0_sort_Load(EOS(STATIC_2033), java.lang.Object(ARRAY(100)), 100, i108, i131, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
f2033_0_sort_Load(EOS(STATIC_2033), java.lang.Object(ARRAY(matching1)), matching2, i108, i131, java.lang.Object(ARRAY(matching3))) -> f2047_0_sort_ArrayAccess(EOS(STATIC_2047), java.lang.Object(ARRAY(100)), 100, i108, i131, java.lang.Object(ARRAY(100)), i131) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2047_0_sort_ArrayAccess(EOS(STATIC_2047), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i136) -> f2050_0_sort_ArrayAccess(EOS(STATIC_2050), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2050_0_sort_ArrayAccess(EOS(STATIC_2050), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i136) -> f2053_0_sort_Load(EOS(STATIC_2053), java.lang.Object(ARRAY(100)), 100, i108, i136, i138) :|: i136 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
f2053_0_sort_Load(EOS(STATIC_2053), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138) -> f2055_0_sort_Load(EOS(STATIC_2055), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
f2055_0_sort_Load(EOS(STATIC_2055), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3))) -> f2058_0_sort_ConstantStackPush(EOS(STATIC_2058), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2058_0_sort_ConstantStackPush(EOS(STATIC_2058), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3)), i136) -> f2064_0_sort_IntArithmetic(EOS(STATIC_2064), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100)), i136, 1) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2064_0_sort_IntArithmetic(EOS(STATIC_2064), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3)), i136, matching4) -> f2068_0_sort_ArrayAccess(EOS(STATIC_2068), 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
f2068_0_sort_ArrayAccess(EOS(STATIC_2068), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3)), i140) -> f2070_0_sort_ArrayAccess(EOS(STATIC_2070), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, java.lang.Object(ARRAY(100)), i140) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2070_0_sort_ArrayAccess(EOS(STATIC_2070), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, java.lang.Object(ARRAY(matching3)), i140) -> f2073_0_sort_LE(EOS(STATIC_2073), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, i141) :|: i140 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
f2073_0_sort_LE(EOS(STATIC_2073), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, i141) -> f2084_0_sort_LE(EOS(STATIC_2084), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, i141) :|: i138 <= i141 && matching1 = 100 && matching2 = 100
f2073_0_sort_LE(EOS(STATIC_2073), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, i141) -> f2085_0_sort_LE(EOS(STATIC_2085), java.lang.Object(ARRAY(100)), 100, i108, i136, i138, i141) :|: i138 > i141 && matching1 = 100 && matching2 = 100
f2084_0_sort_LE(EOS(STATIC_2084), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, i141) -> f2088_0_sort_Inc(EOS(STATIC_2088), java.lang.Object(ARRAY(100)), 100, i108, i136) :|: i138 <= i141 && matching1 = 100 && matching2 = 100
f2088_0_sort_Inc(EOS(STATIC_2088), java.lang.Object(ARRAY(matching1)), matching2, i108, i136) -> f2092_0_sort_JMP(EOS(STATIC_2092), java.lang.Object(ARRAY(100)), 100, i108, i136 + 1) :|: TRUE && matching1 = 100 && matching2 = 100
f2092_0_sort_JMP(EOS(STATIC_2092), java.lang.Object(ARRAY(matching1)), matching2, i108, i142) -> f2096_0_sort_Load(EOS(STATIC_2096), java.lang.Object(ARRAY(100)), 100, i108, i142) :|: TRUE && matching1 = 100 && matching2 = 100
f2096_0_sort_Load(EOS(STATIC_2096), java.lang.Object(ARRAY(matching1)), matching2, i108, i142) -> f2015_0_sort_Load(EOS(STATIC_2015), java.lang.Object(ARRAY(100)), 100, i108, i142) :|: TRUE && matching1 = 100 && matching2 = 100
f2085_0_sort_LE(EOS(STATIC_2085), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i138, i141) -> f2089_0_sort_Load(EOS(STATIC_2089), java.lang.Object(ARRAY(100)), 100, i108, i136) :|: i138 > i141 && matching1 = 100 && matching2 = 100
f2089_0_sort_Load(EOS(STATIC_2089), java.lang.Object(ARRAY(matching1)), matching2, i108, i136) -> f2093_0_sort_Load(EOS(STATIC_2093), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
f2093_0_sort_Load(EOS(STATIC_2093), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3))) -> f2097_0_sort_ArrayAccess(EOS(STATIC_2097), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2097_0_sort_ArrayAccess(EOS(STATIC_2097), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i136) -> f2098_0_sort_Store(EOS(STATIC_2098), java.lang.Object(ARRAY(100)), 100, i108, i136, i144) :|: i136 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
f2098_0_sort_Store(EOS(STATIC_2098), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144) -> f2101_0_sort_Load(EOS(STATIC_2101), java.lang.Object(ARRAY(100)), 100, i108, i136, i144) :|: TRUE && matching1 = 100 && matching2 = 100
f2101_0_sort_Load(EOS(STATIC_2101), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144) -> f2104_0_sort_Load(EOS(STATIC_2104), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
f2104_0_sort_Load(EOS(STATIC_2104), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3))) -> f2105_0_sort_Load(EOS(STATIC_2105), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2105_0_sort_Load(EOS(STATIC_2105), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136) -> f2108_0_sort_Load(EOS(STATIC_2108), 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
f2108_0_sort_Load(EOS(STATIC_2108), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4))) -> f2111_0_sort_ConstantStackPush(EOS(STATIC_2111), 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
f2111_0_sort_ConstantStackPush(EOS(STATIC_2111), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4)), i136) -> f2113_0_sort_IntArithmetic(EOS(STATIC_2113), 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
f2113_0_sort_IntArithmetic(EOS(STATIC_2113), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4)), i136, matching5) -> f2116_0_sort_ArrayAccess(EOS(STATIC_2116), 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
f2116_0_sort_ArrayAccess(EOS(STATIC_2116), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4)), i146) -> f2125_0_sort_ArrayAccess(EOS(STATIC_2125), 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
f2125_0_sort_ArrayAccess(EOS(STATIC_2125), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, java.lang.Object(ARRAY(matching4)), i146) -> f2128_0_sort_ArrayAccess(EOS(STATIC_2128), 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
f2128_0_sort_ArrayAccess(EOS(STATIC_2128), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, i147) -> f2139_0_sort_Load(EOS(STATIC_2139), java.lang.Object(ARRAY(100)), 100, i108, i136, i144) :|: i136 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
f2139_0_sort_Load(EOS(STATIC_2139), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144) -> f2146_0_sort_Load(EOS(STATIC_2146), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100))) :|: TRUE && matching1 = 100 && matching2 = 100
f2146_0_sort_Load(EOS(STATIC_2146), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3))) -> f2156_0_sort_ConstantStackPush(EOS(STATIC_2156), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2156_0_sort_ConstantStackPush(EOS(STATIC_2156), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136) -> f2166_0_sort_IntArithmetic(EOS(STATIC_2166), java.lang.Object(ARRAY(100)), 100, i108, i136, i144, java.lang.Object(ARRAY(100)), i136, 1) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2166_0_sort_IntArithmetic(EOS(STATIC_2166), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i136, matching4) -> f2178_0_sort_Load(EOS(STATIC_2178), 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
f2178_0_sort_Load(EOS(STATIC_2178), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, i144, java.lang.Object(ARRAY(matching3)), i148) -> f2189_0_sort_ArrayAccess(EOS(STATIC_2189), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100)), i148, i144) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2189_0_sort_ArrayAccess(EOS(STATIC_2189), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i149, i144) -> f2195_0_sort_ArrayAccess(EOS(STATIC_2195), java.lang.Object(ARRAY(100)), 100, i108, i136, java.lang.Object(ARRAY(100)), i149, i144) :|: TRUE && matching1 = 100 && matching2 = 100 && matching3 = 100
f2195_0_sort_ArrayAccess(EOS(STATIC_2195), java.lang.Object(ARRAY(matching1)), matching2, i108, i136, java.lang.Object(ARRAY(matching3)), i149, i144) -> f2206_0_sort_Inc(EOS(STATIC_2206), java.lang.Object(ARRAY(100)), 100, i108, i136) :|: i149 < 100 && matching1 = 100 && matching2 = 100 && matching3 = 100
f2206_0_sort_Inc(EOS(STATIC_2206), java.lang.Object(ARRAY(matching1)), matching2, i108, i136) -> f2088_0_sort_Inc(EOS(STATIC_2088), java.lang.Object(ARRAY(100)), 100, i108, i136) :|: TRUE && matching1 = 100 && matching2 = 100
Combined rules. Obtained 3 IRulesP rules:
f2019_0_sort_GE(EOS(STATIC_2019), java.lang.Object(ARRAY(100)), 100, i108:0, i131:0, i131:0, i133:0) -> f2019_0_sort_GE(EOS(STATIC_2019), 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
f2019_0_sort_GE(EOS(STATIC_2019), java.lang.Object(ARRAY(100)), 100, i108:0, i131:0, i131:0, i133:0) -> f2019_0_sort_GE(EOS(STATIC_2019), 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
f2019_0_sort_GE(EOS(STATIC_2019), java.lang.Object(ARRAY(100)), 100, i108:0, i131:0, i131:0, i133:0) -> f2019_0_sort_GE(EOS(STATIC_2019), 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
Filtered constant ground arguments:
   f2019_0_sort_GE(x1, x2, x3, x4, x5, x6, x7) -> f2019_0_sort_GE(x4, x5, x6, x7)
   EOS(x1) -> EOS
   java.lang.Object(x1) -> java.lang.Object
   ARRAY(x1) -> ARRAY
Filtered duplicate arguments:
   f2019_0_sort_GE(x1, x2, x3, x4) -> f2019_0_sort_GE(x1, x3, x4)
Finished conversion. Obtained 3 rules.P rules:
f2019_0_sort_GE(i108:0, i131:0, i133:0) -> f2019_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
f2019_0_sort_GE(i108:0, i131:0, i133:0) -> f2019_0_sort_GE(i108:0 + 1, 0, 100 - (i108:0 + 1)) :|: i133:0 <= i131:0 && i108:0 > -1 && i108:0 < 99
f2019_0_sort_GE(i108:0, i131:0, i133:0) -> f2019_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

----------------------------------------

(8)
Obligation:
Rules:
f2019_0_sort_GE(i108:0, i131:0, i133:0) -> f2019_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
f2019_0_sort_GE(x, x1, x2) -> f2019_0_sort_GE(x + 1, 0, 100 - (x + 1)) :|: x2 <= x1 && x > -1 && x < 99
f2019_0_sort_GE(x3, x4, x5) -> f2019_0_sort_GE(x3, x4 + 1, 100 - x3) :|: x4 < 100 && x5 > x4 && x4 > -1 && x4 < 99 && x3 > 0 && x6 >= x7

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(9) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(10)
Obligation:
Rules:
f2019_0_sort_GE(i108:0, i131:0, i133:0) -> f2019_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
f2019_0_sort_GE(x8, x9, x10) -> f2019_0_sort_GE(x11, 0, x12) :|: x10 <= x9 && x8 > -1 && x8 < 99 && x11 = x8 + 1 && x12 = 100 - (x8 + 1)
f2019_0_sort_GE(x13, x14, x15) -> f2019_0_sort_GE(x13, x16, x17) :|: x14 < 100 && x15 > x14 && x14 > -1 && x14 < 99 && x13 > 0 && x18 >= x19 && x16 = x14 + 1 && x17 = 100 - x13

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f2019_0_sort_GE(i108:0, i131:0, i133:0) -> f2019_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
(2) f2019_0_sort_GE(x8, x9, x10) -> f2019_0_sort_GE(x11, 0, x12) :|: x10 <= x9 && x8 > -1 && x8 < 99 && x11 = x8 + 1 && x12 = 100 - (x8 + 1)
(3) f2019_0_sort_GE(x13, x14, x15) -> f2019_0_sort_GE(x13, x16, x17) :|: x14 < 100 && x15 > x14 && x14 > -1 && x14 < 99 && x13 > 0 && x18 >= x19 && x16 = x14 + 1 && x17 = 100 - x13

Arcs:
(1) -> (1), (2), (3)
(2) -> (1), (3)
(3) -> (1), (2), (3)

This digraph is fully evaluated!
----------------------------------------

(12)
Obligation:

Termination digraph:
Nodes:
(1) f2019_0_sort_GE(i108:0, i131:0, i133:0) -> f2019_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
(2) f2019_0_sort_GE(x8, x9, x10) -> f2019_0_sort_GE(x11, 0, x12) :|: x10 <= x9 && x8 > -1 && x8 < 99 && x11 = x8 + 1 && x12 = 100 - (x8 + 1)
(3) f2019_0_sort_GE(x13, x14, x15) -> f2019_0_sort_GE(x13, x16, x17) :|: x14 < 100 && x15 > x14 && x14 > -1 && x14 < 99 && x13 > 0 && x18 >= x19 && x16 = x14 + 1 && x17 = 100 - x13

Arcs:
(1) -> (1), (2), (3)
(2) -> (1), (3)
(3) -> (1), (2), (3)

This digraph is fully evaluated!

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(14)
Obligation:
Rules:
f2019_0_sort_GE(x13:0, x14:0, x15:0) -> f2019_0_sort_GE(x13:0, x14:0 + 1, 100 - x13:0) :|: x13:0 > 0 && x19:0 <= x18:0 && x14:0 < 99 && x14:0 > -1 && x15:0 > x14:0 && x14:0 < 100
f2019_0_sort_GE(x8:0, x9:0, x10:0) -> f2019_0_sort_GE(x8:0 + 1, 0, 100 - (x8:0 + 1)) :|: x9:0 >= x10:0 && x8:0 > -1 && x8:0 < 99
f2019_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2019_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

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f2019_0_sort_GE(INTEGER, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f2019_0_sort_GE(x13:0, x14:0, x15:0) -> f2019_0_sort_GE(x13:0, c, c1) :|: c1 = 100 - x13:0 && c = x14:0 + 1 && (x13:0 > 0 && x19:0 <= x18:0 && x14:0 < 99 && x14:0 > -1 && x15:0 > x14:0 && x14:0 < 100)
f2019_0_sort_GE(x8:0, x9:0, x10:0) -> f2019_0_sort_GE(c2, c3, c4) :|: c4 = 100 - (x8:0 + 1) && (c3 = 0 && c2 = x8:0 + 1) && (x9:0 >= x10:0 && x8:0 > -1 && x8:0 < 99)
f2019_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2019_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)

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(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f2019_0_sort_GE ] = -1*f2019_0_sort_GE_1

The following rules are decreasing:
f2019_0_sort_GE(x8:0, x9:0, x10:0) -> f2019_0_sort_GE(c2, c3, c4) :|: c4 = 100 - (x8:0 + 1) && (c3 = 0 && c2 = x8:0 + 1) && (x9:0 >= x10:0 && x8:0 > -1 && x8:0 < 99)

The following rules are bounded:
f2019_0_sort_GE(x8:0, x9:0, x10:0) -> f2019_0_sort_GE(c2, c3, c4) :|: c4 = 100 - (x8:0 + 1) && (c3 = 0 && c2 = x8:0 + 1) && (x9:0 >= x10:0 && x8:0 > -1 && x8:0 < 99)


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(18)
Obligation:
Rules:
f2019_0_sort_GE(x13:0, x14:0, x15:0) -> f2019_0_sort_GE(x13:0, c, c1) :|: c1 = 100 - x13:0 && c = x14:0 + 1 && (x13:0 > 0 && x19:0 <= x18:0 && x14:0 < 99 && x14:0 > -1 && x15:0 > x14:0 && x14:0 < 100)
f2019_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2019_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)

----------------------------------------

(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f2019_0_sort_GE ] = -1*f2019_0_sort_GE_2

The following rules are decreasing:
f2019_0_sort_GE(x13:0, x14:0, x15:0) -> f2019_0_sort_GE(x13:0, c, c1) :|: c1 = 100 - x13:0 && c = x14:0 + 1 && (x13:0 > 0 && x19:0 <= x18:0 && x14:0 < 99 && x14:0 > -1 && x15:0 > x14:0 && x14:0 < 100)
f2019_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2019_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)

The following rules are bounded:
f2019_0_sort_GE(x13:0, x14:0, x15:0) -> f2019_0_sort_GE(x13:0, c, c1) :|: c1 = 100 - x13:0 && c = x14:0 + 1 && (x13:0 > 0 && x19:0 <= x18:0 && x14:0 < 99 && x14:0 > -1 && x15:0 > x14:0 && x14:0 < 100)
f2019_0_sort_GE(i108:0:0, i131:0:0, i133:0:0) -> f2019_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)


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(20)
YES