4.73/2.00	YES
4.73/2.02	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
4.73/2.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.73/2.02	
4.73/2.02	
4.73/2.02	Termination of the given C Problem could be proven:
4.73/2.02	
4.73/2.02	(0) C Problem
4.73/2.02	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.73/2.02	(2) IntTRS
4.73/2.02	(3) TerminationGraphProcessor [SOUND, 51 ms]
4.73/2.02	(4) IntTRS
4.73/2.02	(5) IntTRSCompressionProof [EQUIVALENT, 34 ms]
4.73/2.02	(6) IntTRS
4.73/2.02	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.73/2.02	(8) IntTRS
4.73/2.02	(9) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
4.73/2.02	(10) YES
4.73/2.02	
4.73/2.02	
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(0)
4.73/2.02	Obligation:
4.73/2.02	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(1) CToIRSProof (EQUIVALENT)
4.73/2.02	Parsed C Integer Program as IRS.
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(2)
4.73/2.02	Obligation:
4.73/2.02	Rules:
4.73/2.02	f1(x, tmp) -> f2(x_1, tmp) :|: TRUE
4.73/2.02	f2(x1, x2) -> f3(x1, x3) :|: TRUE
4.73/2.02	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1
4.73/2.02	f5(x6, x7) -> f6(x6, x8) :|: TRUE
4.73/2.02	f3(x9, x10) -> f4(x9, x10) :|: x9 > 0 && x9 = 2 * x10
4.73/2.02	f6(x11, x12) -> f3(x11, x12) :|: TRUE
4.73/2.02	f3(x13, x14) -> f7(x13, x14) :|: x13 <= 0
4.73/2.02	f3(x15, x16) -> f7(x15, x16) :|: x15 < 2 * x16
4.73/2.02	f3(x17, x18) -> f7(x17, x18) :|: x17 > 2 * x18
4.73/2.02	Start term: f1(x, tmp)
4.73/2.02	
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(3) TerminationGraphProcessor (SOUND)
4.73/2.02	Constructed the termination graph and obtained one non-trivial SCC.
4.73/2.02	
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(4)
4.73/2.02	Obligation:
4.73/2.02	Rules:
4.73/2.02	f3(x9, x10) -> f4(x9, x10) :|: x9 > 0 && x9 = 2 * x10
4.73/2.02	f6(x11, x12) -> f3(x11, x12) :|: TRUE
4.73/2.02	f5(x6, x7) -> f6(x6, x8) :|: TRUE
4.73/2.02	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1
4.73/2.02	
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(5) IntTRSCompressionProof (EQUIVALENT)
4.73/2.02	Compressed rules.
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(6)
4.73/2.02	Obligation:
4.73/2.02	Rules:
4.73/2.02	f5(times~cons_2~x8:0, x7:0) -> f5(2 * x8:0 - 1, x8:0) :|: 2 * x8:0 > 0 && times~cons_2~x8:0 = 2 * x8:0
4.73/2.02	
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.73/2.02	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.73/2.02	
4.73/2.02	   f5(x1, x2) -> f5(x1)
4.73/2.02	
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(8)
4.73/2.02	Obligation:
4.73/2.02	Rules:
4.73/2.02	f5(times~cons_2~x8:0) -> f5(2 * x8:0 - 1) :|: 2 * x8:0 > 0 && times~cons_2~x8:0 = 2 * x8:0
4.73/2.02	
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(9) PolynomialOrderProcessor (EQUIVALENT)
4.73/2.02	Found the following polynomial interpretation:
4.73/2.02	[f5(x)] = x
4.73/2.02	
4.73/2.02	The following rules are decreasing:
4.73/2.02	f5(times~cons_2~x8:0) -> f5(2 * x8:0 - 1) :|: 2 * x8:0 > 0 && times~cons_2~x8:0 = 2 * x8:0
4.73/2.02	The following rules are bounded:
4.73/2.02	f5(times~cons_2~x8:0) -> f5(2 * x8:0 - 1) :|: 2 * x8:0 > 0 && times~cons_2~x8:0 = 2 * x8:0
4.73/2.02	
4.73/2.02	----------------------------------------
4.73/2.02	
4.73/2.02	(10)
4.73/2.02	YES
5.03/2.05	EOF