9.22/3.24	YES
9.22/3.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
9.22/3.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.22/3.26	
9.22/3.26	
9.22/3.26	Termination of the given C Problem could be proven:
9.22/3.26	
9.22/3.26	(0) C Problem
9.22/3.26	(1) CToIRSProof [EQUIVALENT, 0 ms]
9.22/3.26	(2) IntTRS
9.22/3.26	(3) TerminationGraphProcessor [SOUND, 52 ms]
9.22/3.26	(4) IntTRS
9.22/3.26	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
9.22/3.26	(6) IntTRS
9.22/3.26	(7) CaseAnalysis [EQUIVALENT, 16 ms]
9.22/3.26	(8) AND
9.22/3.26	    (9) IntTRS
9.22/3.26	        (10) IntTRSCompressionProof [EQUIVALENT, 1 ms]
9.22/3.26	        (11) IntTRS
9.22/3.26	        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
9.22/3.26	        (13) YES
9.22/3.26	    (14) IntTRS
9.22/3.26	        (15) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
9.22/3.26	        (16) YES
9.22/3.26	
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(0)
9.22/3.26	Obligation:
9.22/3.26	c file /export/starexec/sandbox/benchmark/theBenchmark.c
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(1) CToIRSProof (EQUIVALENT)
9.22/3.26	Parsed C Integer Program as IRS.
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(2)
9.22/3.26	Obligation:
9.22/3.26	Rules:
9.22/3.26	f1(x, y) -> f2(x_1, y) :|: TRUE
9.22/3.26	f2(x1, x2) -> f3(x1, 1) :|: TRUE
9.22/3.26	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - x4
9.22/3.26	f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = x14 + 1
9.22/3.26	f3(x7, x8) -> f4(x7, x8) :|: x7 > 0
9.22/3.26	f6(x9, x10) -> f3(x9, x10) :|: TRUE
9.22/3.26	f3(x11, x12) -> f7(x11, x12) :|: x11 <= 0
9.22/3.26	Start term: f1(x, y)
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(3) TerminationGraphProcessor (SOUND)
9.22/3.26	Constructed the termination graph and obtained one non-trivial SCC.
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(4)
9.22/3.26	Obligation:
9.22/3.26	Rules:
9.22/3.26	f3(x7, x8) -> f4(x7, x8) :|: x7 > 0
9.22/3.26	f6(x9, x10) -> f3(x9, x10) :|: TRUE
9.22/3.26	f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = x14 + 1
9.22/3.26	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - x4
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(5) IntTRSCompressionProof (EQUIVALENT)
9.22/3.26	Compressed rules.
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(6)
9.22/3.26	Obligation:
9.22/3.26	Rules:
9.22/3.26	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(7) CaseAnalysis (EQUIVALENT)
9.22/3.26	Found the following inductive condition: 
9.22/3.26	f5(x0, x1): x1>=0
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(8)
9.22/3.26	Complex Obligation (AND)
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(9)
9.22/3.26	Obligation:
9.22/3.26	Rules:
9.22/3.26	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 >= 0
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(10) IntTRSCompressionProof (EQUIVALENT)
9.22/3.26	Compressed rules.
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(11)
9.22/3.26	Obligation:
9.22/3.26	Rules:
9.22/3.26	f5(x13:0:0, x14:0:0) -> f5(x13:0:0 - (x14:0:0 + 1), x14:0:0 + 1) :|: x13:0:0 > 0 && x14:0:0 > -1
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(12) RankingReductionPairProof (EQUIVALENT)
9.22/3.26	Interpretation:
9.22/3.26	[ f5 ] = f5_1
9.22/3.26	
9.22/3.26	The following rules are decreasing:
9.22/3.26	f5(x13:0:0, x14:0:0) -> f5(x13:0:0 - (x14:0:0 + 1), x14:0:0 + 1) :|: x13:0:0 > 0 && x14:0:0 > -1
9.22/3.26	
9.22/3.26	The following rules are bounded:
9.22/3.26	f5(x13:0:0, x14:0:0) -> f5(x13:0:0 - (x14:0:0 + 1), x14:0:0 + 1) :|: x13:0:0 > 0 && x14:0:0 > -1
9.22/3.26	
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(13)
9.22/3.26	YES
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(14)
9.22/3.26	Obligation:
9.22/3.26	Rules:
9.22/3.26	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(15) PolynomialOrderProcessor (EQUIVALENT)
9.22/3.26	Found the following polynomial interpretation:
9.22/3.26	[f5(x, x1)] = -x1
9.22/3.26	
9.22/3.26	The following rules are decreasing:
9.22/3.26	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0
9.22/3.26	The following rules are bounded:
9.22/3.26	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0
9.22/3.26	
9.22/3.26	----------------------------------------
9.22/3.26	
9.22/3.26	(16)
9.22/3.26	YES
9.39/3.32	EOF