6.74/2.55	YES
6.74/2.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.74/2.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.74/2.56	
6.74/2.56	
6.74/2.56	Termination of the given C Problem could be proven:
6.74/2.56	
6.74/2.56	(0) C Problem
6.74/2.56	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.74/2.56	(2) IntTRS
6.74/2.56	(3) TerminationGraphProcessor [SOUND, 69 ms]
6.74/2.56	(4) IntTRS
6.74/2.56	(5) IntTRSCompressionProof [EQUIVALENT, 10 ms]
6.74/2.56	(6) IntTRS
6.74/2.56	(7) RankingReductionPairProof [EQUIVALENT, 8 ms]
6.74/2.56	(8) IntTRS
6.74/2.56	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
6.74/2.56	(10) YES
6.74/2.56	
6.74/2.56	
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(0)
6.74/2.56	Obligation:
6.74/2.56	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(1) CToIRSProof (EQUIVALENT)
6.74/2.56	Parsed C Integer Program as IRS.
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(2)
6.74/2.56	Obligation:
6.74/2.56	Rules:
6.74/2.56	f1(x, y) -> f2(x_1, y) :|: TRUE
6.74/2.56	f2(x1, x2) -> f3(x1, x3) :|: TRUE
6.74/2.56	f4(x4, x5) -> f5(x4, 1) :|: TRUE
6.74/2.56	f6(x6, x7) -> f7(x6, arith) :|: TRUE && arith = 2 * x7
6.74/2.56	f5(x8, x9) -> f6(x8, x9) :|: x8 > x9 && x9 > 0
6.74/2.56	f7(x10, x11) -> f5(x10, x11) :|: TRUE
6.74/2.56	f5(x12, x13) -> f8(x12, x13) :|: x12 <= x13
6.74/2.56	f5(x22, x23) -> f8(x22, x23) :|: x23 <= 0
6.74/2.56	f8(x24, x25) -> f9(x26, x25) :|: TRUE && x26 = x24 - 1
6.74/2.56	f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0 && x17 > 0
6.74/2.56	f9(x18, x19) -> f3(x18, x19) :|: TRUE
6.74/2.56	f3(x20, x21) -> f10(x20, x21) :|: x20 < 0
6.74/2.56	f3(x27, x28) -> f10(x27, x28) :|: x28 <= 0
6.74/2.56	Start term: f1(x, y)
6.74/2.56	
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(3) TerminationGraphProcessor (SOUND)
6.74/2.56	Constructed the termination graph and obtained one non-trivial SCC.
6.74/2.56	
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(4)
6.74/2.56	Obligation:
6.74/2.56	Rules:
6.74/2.56	f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0 && x17 > 0
6.74/2.56	f9(x18, x19) -> f3(x18, x19) :|: TRUE
6.74/2.56	f8(x24, x25) -> f9(x26, x25) :|: TRUE && x26 = x24 - 1
6.74/2.56	f5(x12, x13) -> f8(x12, x13) :|: x12 <= x13
6.74/2.56	f4(x4, x5) -> f5(x4, 1) :|: TRUE
6.74/2.56	f7(x10, x11) -> f5(x10, x11) :|: TRUE
6.74/2.56	f6(x6, x7) -> f7(x6, arith) :|: TRUE && arith = 2 * x7
6.74/2.56	f5(x8, x9) -> f6(x8, x9) :|: x8 > x9 && x9 > 0
6.74/2.56	f5(x22, x23) -> f8(x22, x23) :|: x23 <= 0
6.74/2.56	
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(5) IntTRSCompressionProof (EQUIVALENT)
6.74/2.56	Compressed rules.
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(6)
6.74/2.56	Obligation:
6.74/2.56	Rules:
6.74/2.56	f5(x8:0, x9:0) -> f5(x8:0, 2 * x9:0) :|: x9:0 < x8:0 && x9:0 > 0
6.74/2.56	f5(x12:0, x13:0) -> f5(x12:0 - 1, 1) :|: x12:0 > 0 && x13:0 > 0 && x13:0 >= x12:0
6.74/2.56	f5(x22:0, x23:0) -> f5(x22:0 - 1, 1) :|: x22:0 > 0 && x23:0 > 0 && x23:0 < 1
6.74/2.56	
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(7) RankingReductionPairProof (EQUIVALENT)
6.74/2.56	Interpretation:
6.74/2.56	[ f5 ] = f5_1
6.74/2.56	
6.74/2.56	The following rules are decreasing:
6.74/2.56	f5(x12:0, x13:0) -> f5(x12:0 - 1, 1) :|: x12:0 > 0 && x13:0 > 0 && x13:0 >= x12:0
6.74/2.56	f5(x22:0, x23:0) -> f5(x22:0 - 1, 1) :|: x22:0 > 0 && x23:0 > 0 && x23:0 < 1
6.74/2.56	
6.74/2.56	The following rules are bounded:
6.74/2.56	f5(x8:0, x9:0) -> f5(x8:0, 2 * x9:0) :|: x9:0 < x8:0 && x9:0 > 0
6.74/2.56	f5(x12:0, x13:0) -> f5(x12:0 - 1, 1) :|: x12:0 > 0 && x13:0 > 0 && x13:0 >= x12:0
6.74/2.56	f5(x22:0, x23:0) -> f5(x22:0 - 1, 1) :|: x22:0 > 0 && x23:0 > 0 && x23:0 < 1
6.74/2.56	
6.74/2.56	
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(8)
6.74/2.56	Obligation:
6.74/2.56	Rules:
6.74/2.56	f5(x8:0, x9:0) -> f5(x8:0, 2 * x9:0) :|: x9:0 < x8:0 && x9:0 > 0
6.74/2.56	
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(9) PolynomialOrderProcessor (EQUIVALENT)
6.74/2.56	Found the following polynomial interpretation:
6.74/2.56	[f5(x, x1)] = -1 + x - x1
6.74/2.56	
6.74/2.56	The following rules are decreasing:
6.74/2.56	f5(x8:0, x9:0) -> f5(x8:0, 2 * x9:0) :|: x9:0 < x8:0 && x9:0 > 0
6.74/2.56	The following rules are bounded:
6.74/2.56	f5(x8:0, x9:0) -> f5(x8:0, 2 * x9:0) :|: x9:0 < x8:0 && x9:0 > 0
6.74/2.56	
6.74/2.56	----------------------------------------
6.74/2.56	
6.74/2.56	(10)
6.74/2.56	YES
7.10/2.60	EOF