/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 326 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 109 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 34 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 26 ms]
(16) IntTRS
(17) RankingReductionPairProof [EQUIVALENT, 0 ms]
(18) YES


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(0)
Obligation:
need to prove termination of the following program:
public class LeUserDefRec {
	public static void main(String[] args) {
		int x = args[0].length();
		int y = args[1].length();
		le(x, y);
	}

	public static boolean le(int x, int y) {
		if (x > 0 && y > 0) {
			return le(x-1, y-1);
		} else {
			return (x == 0);
		}
	}
}



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(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
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(2)
Obligation:
need to prove termination of the following program:
public class LeUserDefRec {
	public static void main(String[] args) {
		int x = args[0].length();
		int y = args[1].length();
		le(x, y);
	}

	public static boolean le(int x, int y) {
		if (x > 0 && y > 0) {
			return le(x-1, y-1);
		} else {
			return (x == 0);
		}
	}
}



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(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
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(4)
Obligation:
Termination Graph based on JBC Program:
LeUserDefRec.main([Ljava/lang/String;)V: Graph of 128 nodes with 0 SCCs.



LeUserDefRec.le(II)Z: Graph of 35 nodes with 0 SCCs.





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(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 1 SCCs.
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(6)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: LeUserDefRec.le(II)Z
SCC calls the following helper methods: LeUserDefRec.le(II)Z
Performed SCC analyses:
*Used field analysis yielded the following read fields:

*Marker field analysis yielded the following relations that could be markers:

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(7) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 16 IRulesP rules:
f319_0_le_LE(EOS(STATIC_319), i47, i30, i47, i30, i47) -> f335_0_le_LE(EOS(STATIC_335), i47, i30, i47, i30, i47) :|: TRUE
f335_0_le_LE(EOS(STATIC_335), i47, i30, i47, i30, i47) -> f346_0_le_Load(EOS(STATIC_346), i47, i30, i47, i30) :|: i47 > 0
f346_0_le_Load(EOS(STATIC_346), i47, i30, i47, i30) -> f358_0_le_LE(EOS(STATIC_358), i47, i30, i47, i30, i30) :|: TRUE
f358_0_le_LE(EOS(STATIC_358), i47, i50, i47, i50, i50) -> f369_0_le_LE(EOS(STATIC_369), i47, i50, i47, i50, i50) :|: TRUE
f369_0_le_LE(EOS(STATIC_369), i47, i50, i47, i50, i50) -> f384_0_le_Load(EOS(STATIC_384), i47, i50, i47, i50) :|: i50 > 0
f384_0_le_Load(EOS(STATIC_384), i47, i50, i47, i50) -> f394_0_le_ConstantStackPush(EOS(STATIC_394), i47, i50, i50, i47) :|: TRUE
f394_0_le_ConstantStackPush(EOS(STATIC_394), i47, i50, i50, i47) -> f399_0_le_IntArithmetic(EOS(STATIC_399), i47, i50, i50, i47, 1) :|: TRUE
f399_0_le_IntArithmetic(EOS(STATIC_399), i47, i50, i50, i47, matching1) -> f475_0_le_Load(EOS(STATIC_475), i47, i50, i50, i47 - 1) :|: i47 > 0 && matching1 = 1
f475_0_le_Load(EOS(STATIC_475), i47, i50, i50, i63) -> f482_0_le_ConstantStackPush(EOS(STATIC_482), i47, i50, i63, i50) :|: TRUE
f482_0_le_ConstantStackPush(EOS(STATIC_482), i47, i50, i63, i50) -> f495_0_le_IntArithmetic(EOS(STATIC_495), i47, i50, i63, i50, 1) :|: TRUE
f495_0_le_IntArithmetic(EOS(STATIC_495), i47, i50, i63, i50, matching1) -> f521_0_le_InvokeMethod(EOS(STATIC_521), i47, i50, i63, i50 - 1) :|: i50 > 0 && matching1 = 1
f521_0_le_InvokeMethod(EOS(STATIC_521), i47, i50, i63, i71) -> f527_0_le_Load(EOS(STATIC_527), i63, i71, i63, i71) :|: i47 >= 1 && i50 >= 1 && i63 < i47 && i71 < i50
f521_0_le_InvokeMethod(EOS(STATIC_521), i47, i50, i63, i71) -> f527_1_le_Load(EOS(STATIC_527), i47, i50, i63, i71) :|: i47 >= 1 && i50 >= 1 && i63 < i47 && i71 < i50
f527_0_le_Load(EOS(STATIC_527), i63, i71, i63, i71) -> f532_0_le_Load(EOS(STATIC_532), i63, i71, i63, i71) :|: TRUE
f532_0_le_Load(EOS(STATIC_532), i63, i71, i63, i71) -> f307_0_le_Load(EOS(STATIC_307), i63, i71, i63, i71) :|: TRUE
f307_0_le_Load(EOS(STATIC_307), i12, i30, i12, i30) -> f319_0_le_LE(EOS(STATIC_319), i12, i30, i12, i30, i12) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f319_0_le_LE(EOS(STATIC_319), i47:0, i30:0, i47:0, i30:0, i47:0) -> f319_0_le_LE(EOS(STATIC_319), i47:0 - 1, i30:0 - 1, i47:0 - 1, i30:0 - 1, i47:0 - 1) :|: i47:0 > 0 && i30:0 > 0 && i47:0 - 1 < i47:0 && i30:0 - 1 < i30:0
Removed following non-SCC rules:
f319_0_le_LE(EOS(STATIC_319), i47:0, i30:0, i47:0, i30:0, i47:0) -> f527_1_le_Load(EOS(STATIC_527), i47:0, i30:0, i47:0 - 1, i30:0 - 1) :|: i47:0 > 0 && i30:0 > 0 && i47:0 - 1 < i47:0 && i30:0 - 1 < i30:0
Filtered constant ground arguments:
   f319_0_le_LE(x1, x2, x3, x4, x5, x6) -> f319_0_le_LE(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f319_0_le_LE(x1, x2, x3, x4, x5) -> f319_0_le_LE(x4, x5)
Finished conversion. Obtained 1 rules.P rules:
f319_0_le_LE(i30:0, i47:0) -> f319_0_le_LE(i30:0 - 1, i47:0 - 1) :|: i30:0 > 0 && i47:0 > 0 && i30:0 - 1 < i30:0 && i47:0 - 1 < i47:0

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(8)
Obligation:
Rules:
f319_0_le_LE(i30:0, i47:0) -> f319_0_le_LE(i30:0 - 1, i47:0 - 1) :|: i30:0 > 0 && i47:0 > 0 && i30:0 - 1 < i30:0 && i47:0 - 1 < i47:0

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(9) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
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(10)
Obligation:
Rules:
f319_0_le_LE(i30:0, i47:0) -> f319_0_le_LE(arith, arith1) :|: i30:0 > 0 && i47:0 > 0 && i30:0 - 1 < i30:0 && i47:0 - 1 < i47:0 && arith = i30:0 - 1 && arith1 = i47:0 - 1

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f319_0_le_LE(i30:0, i47:0) -> f319_0_le_LE(arith, arith1) :|: i30:0 > 0 && i47:0 > 0 && i30:0 - 1 < i30:0 && i47:0 - 1 < i47:0 && arith = i30:0 - 1 && arith1 = i47:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!
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(12)
Obligation:

Termination digraph:
Nodes:
(1) f319_0_le_LE(i30:0, i47:0) -> f319_0_le_LE(arith, arith1) :|: i30:0 > 0 && i47:0 > 0 && i30:0 - 1 < i30:0 && i47:0 - 1 < i47:0 && arith = i30:0 - 1 && arith1 = i47:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f319_0_le_LE(i30:0:0, i47:0:0) -> f319_0_le_LE(i30:0:0 - 1, i47:0:0 - 1) :|: i30:0:0 - 1 < i30:0:0 && i47:0:0 - 1 < i47:0:0 && i47:0:0 > 0 && i30:0:0 > 0

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f319_0_le_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(16)
Obligation:
Rules:
f319_0_le_LE(i30:0:0, i47:0:0) -> f319_0_le_LE(c, c1) :|: c1 = i47:0:0 - 1 && c = i30:0:0 - 1 && (i30:0:0 - 1 < i30:0:0 && i47:0:0 - 1 < i47:0:0 && i47:0:0 > 0 && i30:0:0 > 0)

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(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f319_0_le_LE ] = f319_0_le_LE_1

The following rules are decreasing:
f319_0_le_LE(i30:0:0, i47:0:0) -> f319_0_le_LE(c, c1) :|: c1 = i47:0:0 - 1 && c = i30:0:0 - 1 && (i30:0:0 - 1 < i30:0:0 && i47:0:0 - 1 < i47:0:0 && i47:0:0 > 0 && i30:0:0 > 0)

The following rules are bounded:
f319_0_le_LE(i30:0:0, i47:0:0) -> f319_0_le_LE(c, c1) :|: c1 = i47:0:0 - 1 && c = i30:0:0 - 1 && (i30:0:0 - 1 < i30:0:0 && i47:0:0 - 1 < i47:0:0 && i47:0:0 > 0 && i30:0:0 > 0)


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(18)
YES