8.67/3.13	YES
8.67/3.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
8.67/3.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.67/3.15	
8.67/3.15	
8.67/3.15	Termination of the given C Problem could be proven:
8.67/3.15	
8.67/3.15	(0) C Problem
8.67/3.15	(1) CToIRSProof [EQUIVALENT, 0 ms]
8.67/3.15	(2) IntTRS
8.67/3.15	(3) TerminationGraphProcessor [SOUND, 36 ms]
8.67/3.15	(4) IntTRS
8.67/3.15	(5) IntTRSCompressionProof [EQUIVALENT, 23 ms]
8.67/3.15	(6) IntTRS
8.67/3.15	(7) CaseAnalysis [EQUIVALENT, 15 ms]
8.67/3.15	(8) AND
8.67/3.15	    (9) IntTRS
8.67/3.15	        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
8.67/3.15	        (11) IntTRS
8.67/3.15	        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
8.67/3.15	        (13) YES
8.67/3.15	    (14) IntTRS
8.67/3.15	        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
8.67/3.15	        (16) IntTRS
8.67/3.15	        (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
8.67/3.15	        (18) YES
8.67/3.15	
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(0)
8.67/3.15	Obligation:
8.67/3.15	c file /export/starexec/sandbox/benchmark/theBenchmark.c
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(1) CToIRSProof (EQUIVALENT)
8.67/3.15	Parsed C Integer Program as IRS.
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(2)
8.67/3.15	Obligation:
8.67/3.15	Rules:
8.67/3.15	f1(x, y) -> f2(x_1, y) :|: TRUE
8.67/3.15	f2(x1, x2) -> f3(x1, x3) :|: TRUE
8.67/3.15	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 2 * x5
8.67/3.15	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 1
8.67/3.15	f3(x8, x9) -> f4(x8, x9) :|: x8 > 0
8.67/3.15	f6(x10, x11) -> f3(x10, x11) :|: TRUE
8.67/3.15	f3(x12, x13) -> f7(x12, x13) :|: x12 <= 0
8.67/3.15	Start term: f1(x, y)
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(3) TerminationGraphProcessor (SOUND)
8.67/3.15	Constructed the termination graph and obtained one non-trivial SCC.
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(4)
8.67/3.15	Obligation:
8.67/3.15	Rules:
8.67/3.15	f3(x8, x9) -> f4(x8, x9) :|: x8 > 0
8.67/3.15	f6(x10, x11) -> f3(x10, x11) :|: TRUE
8.67/3.15	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 1
8.67/3.15	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 2 * x5
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(5) IntTRSCompressionProof (EQUIVALENT)
8.67/3.15	Compressed rules.
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(6)
8.67/3.15	Obligation:
8.67/3.15	Rules:
8.67/3.15	f5(x14:0, x15:0) -> f5(x14:0 - 2 * (x15:0 + 1), x15:0 + 1) :|: x14:0 > 0
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(7) CaseAnalysis (EQUIVALENT)
8.67/3.15	Found the following inductive condition: 
8.67/3.15	f5(x0, x1): 1 + 2*x1>=0
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(8)
8.67/3.15	Complex Obligation (AND)
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(9)
8.67/3.15	Obligation:
8.67/3.15	Rules:
8.67/3.15	f5(x14:0, x15:0) -> f5(x14:0 - 2 * (x15:0 + 1), x15:0 + 1) :|: x14:0 > 0 && 2 * x15:0 + 1 >= 0
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(10) IntTRSCompressionProof (EQUIVALENT)
8.67/3.15	Compressed rules.
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(11)
8.67/3.15	Obligation:
8.67/3.15	Rules:
8.67/3.15	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 - 2 * (x15:0:0 + 1), x15:0:0 + 1) :|: x14:0:0 > 0 && 2 * x15:0:0 >= -1
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(12) PolynomialOrderProcessor (EQUIVALENT)
8.67/3.15	Found the following polynomial interpretation:
8.67/3.15	[f5(x, x1)] = x + x1
8.67/3.15	
8.67/3.15	The following rules are decreasing:
8.67/3.15	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 - 2 * (x15:0:0 + 1), x15:0:0 + 1) :|: x14:0:0 > 0 && 2 * x15:0:0 >= -1
8.67/3.15	The following rules are bounded:
8.67/3.15	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 - 2 * (x15:0:0 + 1), x15:0:0 + 1) :|: x14:0:0 > 0 && 2 * x15:0:0 >= -1
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(13)
8.67/3.15	YES
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(14)
8.67/3.15	Obligation:
8.67/3.15	Rules:
8.67/3.15	f5(x14:0, x15:0) -> f5(x14:0 - 2 * (x15:0 + 1), x15:0 + 1) :|: x14:0 > 0 && 2 * x15:0 + 1 < 0
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(15) IntTRSCompressionProof (EQUIVALENT)
8.67/3.15	Compressed rules.
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(16)
8.67/3.15	Obligation:
8.67/3.15	Rules:
8.67/3.15	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 - 2 * (x15:0:0 + 1), x15:0:0 + 1) :|: x14:0:0 > 0 && 2 * x15:0:0 < -1
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(17) PolynomialOrderProcessor (EQUIVALENT)
8.67/3.15	Found the following polynomial interpretation:
8.67/3.15	[f5(x, x1)] = -x1
8.67/3.15	
8.67/3.15	The following rules are decreasing:
8.67/3.15	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 - 2 * (x15:0:0 + 1), x15:0:0 + 1) :|: x14:0:0 > 0 && 2 * x15:0:0 < -1
8.67/3.15	The following rules are bounded:
8.67/3.15	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 - 2 * (x15:0:0 + 1), x15:0:0 + 1) :|: x14:0:0 > 0 && 2 * x15:0:0 < -1
8.67/3.15	
8.67/3.15	----------------------------------------
8.67/3.15	
8.67/3.15	(18)
8.67/3.15	YES
8.90/3.23	EOF