6.94/2.50	YES
6.94/2.51	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.94/2.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.94/2.51	
6.94/2.51	
6.94/2.51	Termination of the given C Problem could be proven:
6.94/2.51	
6.94/2.51	(0) C Problem
6.94/2.51	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.94/2.51	(2) IntTRS
6.94/2.51	(3) TerminationGraphProcessor [SOUND, 35 ms]
6.94/2.51	(4) IntTRS
6.94/2.51	(5) IntTRSCompressionProof [EQUIVALENT, 11 ms]
6.94/2.51	(6) IntTRS
6.94/2.51	(7) TerminationGraphProcessor [EQUIVALENT, 3 ms]
6.94/2.51	(8) IntTRS
6.94/2.51	(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.94/2.51	(10) IntTRS
6.94/2.51	(11) RankingReductionPairProof [EQUIVALENT, 6 ms]
6.94/2.51	(12) YES
6.94/2.51	
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(0)
6.94/2.51	Obligation:
6.94/2.51	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(1) CToIRSProof (EQUIVALENT)
6.94/2.51	Parsed C Integer Program as IRS.
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(2)
6.94/2.51	Obligation:
6.94/2.51	Rules:
6.94/2.51	f1(x, y) -> f2(x_1, y) :|: TRUE
6.94/2.51	f2(x1, x2) -> f3(x1, x3) :|: TRUE
6.94/2.51	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5 - 5
6.94/2.51	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = 0 - 2 * x15
6.94/2.51	f3(x8, x9) -> f4(x8, x9) :|: x8 > 0
6.94/2.51	f6(x10, x11) -> f3(x10, x11) :|: TRUE
6.94/2.51	f3(x12, x13) -> f7(x12, x13) :|: x12 <= 0
6.94/2.51	Start term: f1(x, y)
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(3) TerminationGraphProcessor (SOUND)
6.94/2.51	Constructed the termination graph and obtained one non-trivial SCC.
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(4)
6.94/2.51	Obligation:
6.94/2.51	Rules:
6.94/2.51	f3(x8, x9) -> f4(x8, x9) :|: x8 > 0
6.94/2.51	f6(x10, x11) -> f3(x10, x11) :|: TRUE
6.94/2.51	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = 0 - 2 * x15
6.94/2.51	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5 - 5
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(5) IntTRSCompressionProof (EQUIVALENT)
6.94/2.51	Compressed rules.
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(6)
6.94/2.51	Obligation:
6.94/2.51	Rules:
6.94/2.51	f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(7) TerminationGraphProcessor (EQUIVALENT)
6.94/2.51	Constructed the termination graph and obtained one non-trivial SCC.
6.94/2.51	
6.94/2.51	f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0
6.94/2.51	has been transformed into
6.94/2.51	f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0 && x4 > 0.
6.94/2.51	
6.94/2.51	
6.94/2.51	f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0 && x4 > 0 and 
6.94/2.51	f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0 && x4 > 0
6.94/2.51	have been merged into the new rule
6.94/2.51	f5(x12, x13) -> f5(x12 + (0 - 2 * x13) - 5 + (0 - 2 * (0 - 2 * x13)) - 5, 0 - 2 * (0 - 2 * x13)) :|: x12 > 0 && x14 > 0 && (x12 + (0 - 2 * x13) - 5 > 0 && x15 > 0)
6.94/2.51	
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(8)
6.94/2.51	Obligation:
6.94/2.51	Rules:
6.94/2.51	f5(x16, x17) -> f5(x16 + 2 * x17 + -10, 4 * x17) :|: TRUE && x16 >= 1 && x18 >= 1 && x16 + -2 * x17 >= 6 && x19 >= 1
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(9) IntTRSCompressionProof (EQUIVALENT)
6.94/2.51	Compressed rules.
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(10)
6.94/2.51	Obligation:
6.94/2.51	Rules:
6.94/2.51	f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0 - 10, 4 * x17:0) :|: x16:0 + -2 * x17:0 >= 6 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(11) RankingReductionPairProof (EQUIVALENT)
6.94/2.51	Interpretation:
6.94/2.51	[ f5 ] = 1/10*f5_1 + -1/15*f5_2
6.94/2.51	
6.94/2.51	The following rules are decreasing:
6.94/2.51	f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0 - 10, 4 * x17:0) :|: x16:0 + -2 * x17:0 >= 6 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0
6.94/2.51	
6.94/2.51	The following rules are bounded:
6.94/2.51	f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0 - 10, 4 * x17:0) :|: x16:0 + -2 * x17:0 >= 6 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0
6.94/2.51	
6.94/2.51	
6.94/2.51	----------------------------------------
6.94/2.51	
6.94/2.51	(12)
6.94/2.51	YES
7.07/2.63	EOF