5.59/2.28	YES
5.80/2.29	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
5.80/2.29	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.80/2.29	
5.80/2.29	
5.80/2.29	Termination of the given C Problem could be proven:
5.80/2.29	
5.80/2.29	(0) C Problem
5.80/2.29	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.80/2.29	(2) IntTRS
5.80/2.29	(3) TerminationGraphProcessor [SOUND, 62 ms]
5.80/2.29	(4) IntTRS
5.80/2.29	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
5.80/2.29	(6) IntTRS
5.80/2.29	(7) PolynomialOrderProcessor [EQUIVALENT, 7 ms]
5.80/2.29	(8) IntTRS
5.80/2.29	(9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
5.80/2.29	(10) IntTRS
5.80/2.29	(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
5.80/2.29	(12) YES
5.80/2.29	
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(0)
5.80/2.29	Obligation:
5.80/2.29	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(1) CToIRSProof (EQUIVALENT)
5.80/2.29	Parsed C Integer Program as IRS.
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(2)
5.80/2.29	Obligation:
5.80/2.29	Rules:
5.80/2.29	f1(i, j, n) -> f2(x_1, j, n) :|: TRUE
5.80/2.29	f2(x, x1, x2) -> f3(x, x3, x2) :|: TRUE
5.80/2.29	f3(x4, x5, x6) -> f4(x4, x5, x7) :|: TRUE
5.80/2.29	f5(x8, x9, x10) -> f6(x8, 0, x10) :|: TRUE
5.80/2.29	f7(x11, x12, x13) -> f8(x11, arith, x13) :|: TRUE && arith = x12 + 1
5.80/2.29	f6(x14, x15, x16) -> f7(x14, x15, x16) :|: x15 <= x14
5.80/2.29	f8(x17, x18, x19) -> f6(x17, x18, x19) :|: TRUE
5.80/2.29	f6(x20, x21, x22) -> f9(x20, x21, x22) :|: x21 > x20
5.80/2.29	f9(x35, x36, x37) -> f10(x38, x36, x37) :|: TRUE && x38 = x35 + 1
5.80/2.29	f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x26 < x28
5.80/2.29	f10(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
5.80/2.29	f4(x32, x33, x34) -> f11(x32, x33, x34) :|: x32 >= x34
5.80/2.29	Start term: f1(i, j, n)
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(3) TerminationGraphProcessor (SOUND)
5.80/2.29	Constructed the termination graph and obtained one non-trivial SCC.
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(4)
5.80/2.29	Obligation:
5.80/2.29	Rules:
5.80/2.29	f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x26 < x28
5.80/2.29	f10(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
5.80/2.29	f9(x35, x36, x37) -> f10(x38, x36, x37) :|: TRUE && x38 = x35 + 1
5.80/2.29	f6(x20, x21, x22) -> f9(x20, x21, x22) :|: x21 > x20
5.80/2.29	f5(x8, x9, x10) -> f6(x8, 0, x10) :|: TRUE
5.80/2.29	f8(x17, x18, x19) -> f6(x17, x18, x19) :|: TRUE
5.80/2.29	f7(x11, x12, x13) -> f8(x11, arith, x13) :|: TRUE && arith = x12 + 1
5.80/2.29	f6(x14, x15, x16) -> f7(x14, x15, x16) :|: x15 <= x14
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(5) IntTRSCompressionProof (EQUIVALENT)
5.80/2.29	Compressed rules.
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(6)
5.80/2.29	Obligation:
5.80/2.29	Rules:
5.80/2.29	f6(x20:0, x21:0, x22:0) -> f6(x20:0 + 1, 0, x22:0) :|: x21:0 > x20:0 && x22:0 > x20:0 + 1
5.80/2.29	f6(x14:0, x15:0, x16:0) -> f6(x14:0, x15:0 + 1, x16:0) :|: x15:0 <= x14:0
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(7) PolynomialOrderProcessor (EQUIVALENT)
5.80/2.29	Found the following polynomial interpretation:
5.80/2.29	[f6(x, x1, x2)] = -1 - x + x2
5.80/2.29	
5.80/2.29	The following rules are decreasing:
5.80/2.29	f6(x20:0, x21:0, x22:0) -> f6(x20:0 + 1, 0, x22:0) :|: x21:0 > x20:0 && x22:0 > x20:0 + 1
5.80/2.29	The following rules are bounded:
5.80/2.29	f6(x20:0, x21:0, x22:0) -> f6(x20:0 + 1, 0, x22:0) :|: x21:0 > x20:0 && x22:0 > x20:0 + 1
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(8)
5.80/2.29	Obligation:
5.80/2.29	Rules:
5.80/2.29	f6(x14:0, x15:0, x16:0) -> f6(x14:0, x15:0 + 1, x16:0) :|: x15:0 <= x14:0
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(9) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
5.80/2.29	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
5.80/2.29	
5.80/2.29	   f6(x1, x2, x3) -> f6(x1, x2)
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(10)
5.80/2.29	Obligation:
5.80/2.29	Rules:
5.80/2.29	f6(x14:0, x15:0) -> f6(x14:0, x15:0 + 1) :|: x15:0 <= x14:0
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(11) PolynomialOrderProcessor (EQUIVALENT)
5.80/2.29	Found the following polynomial interpretation:
5.80/2.29	[f6(x, x1)] = x - x1
5.80/2.29	
5.80/2.29	The following rules are decreasing:
5.80/2.29	f6(x14:0, x15:0) -> f6(x14:0, x15:0 + 1) :|: x15:0 <= x14:0
5.80/2.29	The following rules are bounded:
5.80/2.29	f6(x14:0, x15:0) -> f6(x14:0, x15:0 + 1) :|: x15:0 <= x14:0
5.80/2.29	
5.80/2.29	----------------------------------------
5.80/2.29	
5.80/2.29	(12)
5.80/2.29	YES
5.80/2.32	EOF