9.82/3.27	YES
10.05/3.31	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
10.05/3.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.05/3.31	
10.05/3.31	
10.05/3.31	Termination of the given C Problem could be proven:
10.05/3.31	
10.05/3.31	(0) C Problem
10.05/3.31	(1) CToIRSProof [EQUIVALENT, 0 ms]
10.05/3.31	(2) IntTRS
10.05/3.31	(3) TerminationGraphProcessor [SOUND, 45 ms]
10.05/3.31	(4) IntTRS
10.05/3.31	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
10.05/3.31	(6) IntTRS
10.05/3.31	(7) CaseAnalysis [EQUIVALENT, 15 ms]
10.05/3.31	(8) AND
10.05/3.31	    (9) IntTRS
10.05/3.31	        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
10.05/3.31	        (11) IntTRS
10.05/3.31	        (12) RankingReductionPairProof [EQUIVALENT, 4 ms]
10.05/3.31	        (13) YES
10.05/3.31	    (14) IntTRS
10.05/3.31	        (15) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
10.05/3.31	        (16) YES
10.05/3.31	
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(0)
10.05/3.31	Obligation:
10.05/3.31	c file /export/starexec/sandbox/benchmark/theBenchmark.c
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(1) CToIRSProof (EQUIVALENT)
10.05/3.31	Parsed C Integer Program as IRS.
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(2)
10.05/3.31	Obligation:
10.05/3.31	Rules:
10.05/3.31	f1(q, y) -> f2(x_1, y) :|: TRUE
10.05/3.31	f2(x, x1) -> f3(x, x2) :|: TRUE
10.05/3.31	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - x4
10.05/3.31	f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = x14 + 1
10.05/3.31	f3(x7, x8) -> f4(x7, x8) :|: x7 > 0
10.05/3.31	f6(x9, x10) -> f3(x9, x10) :|: TRUE
10.05/3.31	f3(x11, x12) -> f7(x11, x12) :|: x11 <= 0
10.05/3.31	Start term: f1(q, y)
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(3) TerminationGraphProcessor (SOUND)
10.05/3.31	Constructed the termination graph and obtained one non-trivial SCC.
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(4)
10.05/3.31	Obligation:
10.05/3.31	Rules:
10.05/3.31	f3(x7, x8) -> f4(x7, x8) :|: x7 > 0
10.05/3.31	f6(x9, x10) -> f3(x9, x10) :|: TRUE
10.05/3.31	f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = x14 + 1
10.05/3.31	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - x4
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(5) IntTRSCompressionProof (EQUIVALENT)
10.05/3.31	Compressed rules.
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(6)
10.05/3.31	Obligation:
10.05/3.31	Rules:
10.05/3.31	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(7) CaseAnalysis (EQUIVALENT)
10.05/3.31	Found the following inductive condition: 
10.05/3.31	f5(x0, x1): x1>=0
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(8)
10.05/3.31	Complex Obligation (AND)
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(9)
10.05/3.31	Obligation:
10.05/3.31	Rules:
10.05/3.31	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 >= 0
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(10) IntTRSCompressionProof (EQUIVALENT)
10.05/3.31	Compressed rules.
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(11)
10.05/3.31	Obligation:
10.05/3.31	Rules:
10.05/3.31	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
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(12) RankingReductionPairProof (EQUIVALENT)
10.05/3.31	Interpretation:
10.05/3.31	[ f5 ] = f5_1
10.05/3.31	
10.05/3.31	The following rules are decreasing:
10.05/3.31	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
10.05/3.31	
10.05/3.31	The following rules are bounded:
10.05/3.31	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
10.05/3.31	
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(13)
10.05/3.31	YES
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(14)
10.05/3.31	Obligation:
10.05/3.31	Rules:
10.05/3.31	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(15) PolynomialOrderProcessor (EQUIVALENT)
10.05/3.31	Found the following polynomial interpretation:
10.05/3.31	[f5(x, x1)] = -x1
10.05/3.31	
10.05/3.31	The following rules are decreasing:
10.05/3.31	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0
10.05/3.31	The following rules are bounded:
10.05/3.31	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0
10.05/3.31	
10.05/3.31	----------------------------------------
10.05/3.31	
10.05/3.31	(16)
10.05/3.31	YES
10.24/3.36	EOF