5.53/2.32	YES
5.53/2.33	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
5.53/2.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.53/2.33	
5.53/2.33	
5.53/2.33	Termination of the given C Problem could be proven:
5.53/2.33	
5.53/2.33	(0) C Problem
5.53/2.33	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.53/2.33	(2) IntTRS
5.53/2.33	(3) TerminationGraphProcessor [SOUND, 45 ms]
5.53/2.33	(4) IntTRS
5.53/2.33	(5) IntTRSCompressionProof [EQUIVALENT, 32 ms]
5.53/2.33	(6) IntTRS
5.53/2.33	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
5.53/2.33	(8) IntTRS
5.53/2.33	(9) RankingReductionPairProof [EQUIVALENT, 18 ms]
5.53/2.33	(10) YES
5.53/2.33	
5.53/2.33	
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(0)
5.53/2.33	Obligation:
5.53/2.33	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(1) CToIRSProof (EQUIVALENT)
5.53/2.33	Parsed C Integer Program as IRS.
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(2)
5.53/2.33	Obligation:
5.53/2.33	Rules:
5.53/2.33	f1(x, y, z, oldx) -> f2(x_1, y, z, oldx) :|: TRUE
5.53/2.33	f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
5.53/2.33	f3(x6, x7, x8, x9) -> f4(x6, x7, x10, x9) :|: TRUE
5.53/2.33	f5(x11, x12, x13, x14) -> f6(x11, x12, x13, x11) :|: TRUE
5.53/2.33	f6(x15, x16, x17, x18) -> f7(x19, x16, x17, x18) :|: TRUE
5.53/2.33	f7(x20, x21, x22, x23) -> f8(x20, x22, x22, x23) :|: TRUE
5.53/2.33	f4(x24, x25, x26, x27) -> f5(x24, x25, x26, x27) :|: x24 > 0 && x24 < x25 && x24 > 2 * x27
5.53/2.33	f8(x28, x29, x30, x31) -> f4(x28, x29, x30, x31) :|: TRUE
5.53/2.33	f4(x32, x33, x34, x35) -> f9(x32, x33, x34, x35) :|: x32 <= 2 * x35
5.53/2.33	f4(x36, x37, x38, x39) -> f9(x36, x37, x38, x39) :|: x36 <= 0
5.53/2.33	f4(x40, x41, x42, x43) -> f9(x40, x41, x42, x43) :|: x40 >= x41
5.53/2.33	Start term: f1(x, y, z, oldx)
5.53/2.33	
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(3) TerminationGraphProcessor (SOUND)
5.53/2.33	Constructed the termination graph and obtained one non-trivial SCC.
5.53/2.33	
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(4)
5.53/2.33	Obligation:
5.53/2.33	Rules:
5.53/2.33	f4(x24, x25, x26, x27) -> f5(x24, x25, x26, x27) :|: x24 > 0 && x24 < x25 && x24 > 2 * x27
5.53/2.33	f8(x28, x29, x30, x31) -> f4(x28, x29, x30, x31) :|: TRUE
5.53/2.33	f7(x20, x21, x22, x23) -> f8(x20, x22, x22, x23) :|: TRUE
5.53/2.33	f6(x15, x16, x17, x18) -> f7(x19, x16, x17, x18) :|: TRUE
5.53/2.33	f5(x11, x12, x13, x14) -> f6(x11, x12, x13, x11) :|: TRUE
5.53/2.33	
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(5) IntTRSCompressionProof (EQUIVALENT)
5.53/2.33	Compressed rules.
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(6)
5.53/2.33	Obligation:
5.53/2.33	Rules:
5.53/2.33	f6(x15:0, x16:0, x17:0, x18:0) -> f6(x19:0, x17:0, x17:0, x19:0) :|: x19:0 > 0 && x19:0 < x17:0 && x19:0 > 2 * x18:0
5.53/2.33	
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
5.53/2.33	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
5.53/2.33	
5.53/2.33	   f6(x1, x2, x3, x4) -> f6(x3, x4)
5.53/2.33	
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(8)
5.53/2.33	Obligation:
5.53/2.33	Rules:
5.53/2.33	f6(x17:0, x18:0) -> f6(x17:0, x19:0) :|: x19:0 > 0 && x19:0 < x17:0 && x19:0 > 2 * x18:0
5.53/2.33	
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(9) RankingReductionPairProof (EQUIVALENT)
5.53/2.33	Interpretation:
5.53/2.33	[ f6 ] = 1/2*f6_1 + -1*f6_2
5.53/2.33	
5.53/2.33	The following rules are decreasing:
5.53/2.33	f6(x17:0, x18:0) -> f6(x17:0, x19:0) :|: x19:0 > 0 && x19:0 < x17:0 && x19:0 > 2 * x18:0
5.53/2.33	
5.53/2.33	The following rules are bounded:
5.53/2.33	f6(x17:0, x18:0) -> f6(x17:0, x19:0) :|: x19:0 > 0 && x19:0 < x17:0 && x19:0 > 2 * x18:0
5.53/2.33	
5.53/2.33	
5.53/2.33	----------------------------------------
5.53/2.33	
5.53/2.33	(10)
5.53/2.33	YES
5.91/2.36	EOF