6.10/2.39	YES
6.10/2.41	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.10/2.41	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.10/2.41	
6.10/2.41	
6.10/2.41	Termination of the given C Problem could be proven:
6.10/2.41	
6.10/2.41	(0) C Problem
6.10/2.41	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.10/2.41	(2) IntTRS
6.10/2.41	(3) TerminationGraphProcessor [SOUND, 50 ms]
6.10/2.41	(4) IntTRS
6.10/2.41	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.10/2.41	(6) IntTRS
6.10/2.41	(7) TerminationGraphProcessor [EQUIVALENT, 2 ms]
6.10/2.41	(8) IntTRS
6.10/2.41	(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.10/2.41	(10) IntTRS
6.10/2.41	(11) PolynomialOrderProcessor [EQUIVALENT, 4 ms]
6.10/2.41	(12) YES
6.10/2.41	
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(0)
6.10/2.41	Obligation:
6.10/2.41	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(1) CToIRSProof (EQUIVALENT)
6.10/2.41	Parsed C Integer Program as IRS.
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(2)
6.10/2.41	Obligation:
6.10/2.41	Rules:
6.10/2.41	f1(q, z) -> f2(x_1, z) :|: TRUE
6.10/2.41	f2(x, x1) -> f3(x, x2) :|: TRUE
6.10/2.41	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 + x4 - 1
6.10/2.41	f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = 0 - x14
6.10/2.41	f3(x7, x8) -> f4(x7, x8) :|: x7 > 0
6.10/2.41	f6(x9, x10) -> f3(x9, x10) :|: TRUE
6.10/2.41	f3(x11, x12) -> f7(x11, x12) :|: x11 <= 0
6.10/2.41	Start term: f1(q, z)
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(3) TerminationGraphProcessor (SOUND)
6.10/2.41	Constructed the termination graph and obtained one non-trivial SCC.
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(4)
6.10/2.41	Obligation:
6.10/2.41	Rules:
6.10/2.41	f3(x7, x8) -> f4(x7, x8) :|: x7 > 0
6.10/2.41	f6(x9, x10) -> f3(x9, x10) :|: TRUE
6.10/2.41	f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = 0 - x14
6.10/2.41	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 + x4 - 1
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(5) IntTRSCompressionProof (EQUIVALENT)
6.10/2.41	Compressed rules.
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(6)
6.10/2.41	Obligation:
6.10/2.41	Rules:
6.10/2.41	f5(x13:0, x14:0) -> f5(x13:0 + (0 - x14:0) - 1, 0 - x14:0) :|: x13:0 > 0
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(7) TerminationGraphProcessor (EQUIVALENT)
6.10/2.41	Constructed the termination graph and obtained one non-trivial SCC.
6.10/2.41	
6.10/2.41	f5(x13:0, x14:0) -> f5(x13:0 + (0 - x14:0) - 1, 0 - x14:0) :|: x13:0 > 0
6.10/2.41	has been transformed into
6.10/2.41	f5(x13:0, x14:0) -> f5(x13:0 + (0 - x14:0) - 1, 0 - x14:0) :|: x13:0 > 0 && x4 > 0.
6.10/2.41	
6.10/2.41	
6.10/2.41	f5(x13:0, x14:0) -> f5(x13:0 + (0 - x14:0) - 1, 0 - x14:0) :|: x13:0 > 0 && x4 > 0 and 
6.10/2.41	f5(x13:0, x14:0) -> f5(x13:0 + (0 - x14:0) - 1, 0 - x14:0) :|: x13:0 > 0 && x4 > 0
6.10/2.41	have been merged into the new rule
6.10/2.41	f5(x12, x13) -> f5(x12 + (0 - x13) - 1 + (0 - (0 - x13)) - 1, 0 - (0 - x13)) :|: x12 > 0 && x14 > 0 && (x12 + (0 - x13) - 1 > 0 && x15 > 0)
6.10/2.41	
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(8)
6.10/2.41	Obligation:
6.10/2.41	Rules:
6.10/2.41	f5(x16, x17) -> f5(x16 + -2, x17) :|: TRUE && x16 >= 1 && x18 >= 1 && x16 + -1 * x17 >= 2 && x19 >= 1
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(9) IntTRSCompressionProof (EQUIVALENT)
6.10/2.41	Compressed rules.
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(10)
6.10/2.41	Obligation:
6.10/2.41	Rules:
6.10/2.41	f5(x16:0, x17:0) -> f5(x16:0 - 2, x17:0) :|: x16:0 + -1 * x17:0 >= 2 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(11) PolynomialOrderProcessor (EQUIVALENT)
6.10/2.41	Found the following polynomial interpretation:
6.10/2.41	[f5(x, x1)] = x
6.10/2.41	
6.10/2.41	The following rules are decreasing:
6.10/2.41	f5(x16:0, x17:0) -> f5(x16:0 - 2, x17:0) :|: x16:0 + -1 * x17:0 >= 2 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0
6.10/2.41	The following rules are bounded:
6.10/2.41	f5(x16:0, x17:0) -> f5(x16:0 - 2, x17:0) :|: x16:0 + -1 * x17:0 >= 2 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0
6.10/2.41	
6.10/2.41	----------------------------------------
6.10/2.41	
6.10/2.41	(12)
6.10/2.41	YES
6.50/2.45	EOF