4.96/2.03	YES
4.96/2.04	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.96/2.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.96/2.04	
4.96/2.04	
4.96/2.04	Termination of the given C Problem could be proven:
4.96/2.04	
4.96/2.04	(0) C Problem
4.96/2.04	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.96/2.04	(2) IntTRS
4.96/2.04	(3) TerminationGraphProcessor [SOUND, 52 ms]
4.96/2.04	(4) AND
4.96/2.04	    (5) IntTRS
4.96/2.04	        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.96/2.04	        (7) IntTRS
4.96/2.04	        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.96/2.04	        (9) IntTRS
4.96/2.04	        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.96/2.04	        (11) YES
4.96/2.04	    (12) IntTRS
4.96/2.04	        (13) IntTRSCompressionProof [EQUIVALENT, 4 ms]
4.96/2.04	        (14) IntTRS
4.96/2.04	        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.96/2.04	        (16) IntTRS
4.96/2.04	        (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.96/2.04	        (18) YES
4.96/2.04	
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(0)
4.96/2.04	Obligation:
4.96/2.04	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(1) CToIRSProof (EQUIVALENT)
4.96/2.04	Parsed C Integer Program as IRS.
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(2)
4.96/2.04	Obligation:
4.96/2.04	Rules:
4.96/2.04	f1(i, j) -> f2(0, j) :|: TRUE
4.96/2.04	f2(x, x1) -> f3(x, 5) :|: TRUE
4.96/2.04	f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1
4.96/2.04	f3(x4, x5) -> f4(x4, x5) :|: x4 < 100
4.96/2.04	f5(x6, x7) -> f3(x6, x7) :|: TRUE
4.96/2.04	f3(x8, x9) -> f6(x8, x9) :|: x8 >= 100
4.96/2.04	f7(x18, x19) -> f8(x18, x20) :|: TRUE && x20 = x19 + 3
4.96/2.04	f6(x12, x13) -> f7(x12, x13) :|: x13 < 21
4.96/2.04	f8(x14, x15) -> f6(x14, x15) :|: TRUE
4.96/2.04	f6(x16, x17) -> f9(x16, x17) :|: x17 >= 21
4.96/2.04	Start term: f1(i, j)
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(3) TerminationGraphProcessor (SOUND)
4.96/2.04	Constructed the termination graph and obtained 2 non-trivial SCCs.
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(4)
4.96/2.04	Complex Obligation (AND)
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(5)
4.96/2.04	Obligation:
4.96/2.04	Rules:
4.96/2.04	f3(x4, x5) -> f4(x4, x5) :|: x4 < 100
4.96/2.04	f5(x6, x7) -> f3(x6, x7) :|: TRUE
4.96/2.04	f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(6) IntTRSCompressionProof (EQUIVALENT)
4.96/2.04	Compressed rules.
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(7)
4.96/2.04	Obligation:
4.96/2.04	Rules:
4.96/2.04	f5(x6:0, x7:0) -> f5(x6:0 + 1, x7:0) :|: x6:0 < 100
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(8) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.96/2.04	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.96/2.04	
4.96/2.04	   f5(x1, x2) -> f5(x1)
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(9)
4.96/2.04	Obligation:
4.96/2.04	Rules:
4.96/2.04	f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 100
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(10) PolynomialOrderProcessor (EQUIVALENT)
4.96/2.04	Found the following polynomial interpretation:
4.96/2.04	[f5(x)] = 99 - x
4.96/2.04	
4.96/2.04	The following rules are decreasing:
4.96/2.04	f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 100
4.96/2.04	The following rules are bounded:
4.96/2.04	f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 100
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(11)
4.96/2.04	YES
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(12)
4.96/2.04	Obligation:
4.96/2.04	Rules:
4.96/2.04	f6(x12, x13) -> f7(x12, x13) :|: x13 < 21
4.96/2.04	f8(x14, x15) -> f6(x14, x15) :|: TRUE
4.96/2.04	f7(x18, x19) -> f8(x18, x20) :|: TRUE && x20 = x19 + 3
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(13) IntTRSCompressionProof (EQUIVALENT)
4.96/2.04	Compressed rules.
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(14)
4.96/2.04	Obligation:
4.96/2.04	Rules:
4.96/2.04	f8(x14:0, x15:0) -> f8(x14:0, x15:0 + 3) :|: x15:0 < 21
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(15) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.96/2.04	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.96/2.04	
4.96/2.04	   f8(x1, x2) -> f8(x2)
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(16)
4.96/2.04	Obligation:
4.96/2.04	Rules:
4.96/2.04	f8(x15:0) -> f8(x15:0 + 3) :|: x15:0 < 21
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(17) PolynomialOrderProcessor (EQUIVALENT)
4.96/2.04	Found the following polynomial interpretation:
4.96/2.04	[f8(x)] = 20 - x
4.96/2.04	
4.96/2.04	The following rules are decreasing:
4.96/2.04	f8(x15:0) -> f8(x15:0 + 3) :|: x15:0 < 21
4.96/2.04	The following rules are bounded:
4.96/2.04	f8(x15:0) -> f8(x15:0 + 3) :|: x15:0 < 21
4.96/2.04	
4.96/2.04	----------------------------------------
4.96/2.04	
4.96/2.04	(18)
4.96/2.04	YES
4.96/2.08	EOF