9.08/3.16	YES
9.08/3.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
9.08/3.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.08/3.17	
9.08/3.17	
9.08/3.17	Termination of the given C Problem could be proven:
9.08/3.17	
9.08/3.17	(0) C Problem
9.08/3.17	(1) CToIRSProof [EQUIVALENT, 0 ms]
9.08/3.17	(2) IntTRS
9.08/3.17	(3) TerminationGraphProcessor [SOUND, 35 ms]
9.08/3.17	(4) IntTRS
9.08/3.17	(5) IntTRSCompressionProof [EQUIVALENT, 23 ms]
9.08/3.17	(6) IntTRS
9.08/3.17	(7) CaseAnalysis [EQUIVALENT, 14 ms]
9.08/3.17	(8) AND
9.08/3.17	    (9) IntTRS
9.08/3.17	        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
9.08/3.17	        (11) IntTRS
9.08/3.17	        (12) RankingReductionPairProof [EQUIVALENT, 5 ms]
9.08/3.17	        (13) YES
9.08/3.17	    (14) IntTRS
9.08/3.17	        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
9.08/3.17	        (16) IntTRS
9.08/3.17	        (17) RankingReductionPairProof [EQUIVALENT, 0 ms]
9.08/3.17	        (18) YES
9.08/3.17	
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(0)
9.08/3.17	Obligation:
9.08/3.17	c file /export/starexec/sandbox/benchmark/theBenchmark.c
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(1) CToIRSProof (EQUIVALENT)
9.08/3.17	Parsed C Integer Program as IRS.
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(2)
9.08/3.17	Obligation:
9.08/3.17	Rules:
9.08/3.17	f1(x, y) -> f2(x_1, y) :|: TRUE
9.08/3.17	f2(x1, x2) -> f3(x1, x3) :|: TRUE
9.08/3.17	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5
9.08/3.17	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 - 1
9.08/3.17	f3(x8, x9) -> f4(x8, x9) :|: x8 > 0
9.08/3.17	f6(x10, x11) -> f3(x10, x11) :|: TRUE
9.08/3.17	f3(x12, x13) -> f7(x12, x13) :|: x12 <= 0
9.08/3.17	Start term: f1(x, y)
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(3) TerminationGraphProcessor (SOUND)
9.08/3.17	Constructed the termination graph and obtained one non-trivial SCC.
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(4)
9.08/3.17	Obligation:
9.08/3.17	Rules:
9.08/3.17	f3(x8, x9) -> f4(x8, x9) :|: x8 > 0
9.08/3.17	f6(x10, x11) -> f3(x10, x11) :|: TRUE
9.08/3.17	f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 - 1
9.08/3.17	f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(5) IntTRSCompressionProof (EQUIVALENT)
9.08/3.17	Compressed rules.
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(6)
9.08/3.17	Obligation:
9.08/3.17	Rules:
9.08/3.17	f5(x14:0, x15:0) -> f5(x14:0 + (x15:0 - 1), x15:0 - 1) :|: x14:0 > 0
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(7) CaseAnalysis (EQUIVALENT)
9.08/3.17	Found the following inductive condition: 
9.08/3.17	f5(x0, x1): -x1>=0
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(8)
9.08/3.17	Complex Obligation (AND)
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(9)
9.08/3.17	Obligation:
9.08/3.17	Rules:
9.08/3.17	f5(x14:0, x15:0) -> f5(x14:0 + (x15:0 - 1), x15:0 - 1) :|: x14:0 > 0 && -1 * x15:0 >= 0
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(10) IntTRSCompressionProof (EQUIVALENT)
9.08/3.17	Compressed rules.
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(11)
9.08/3.17	Obligation:
9.08/3.17	Rules:
9.08/3.17	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 + (x15:0:0 - 1), x15:0:0 - 1) :|: x14:0:0 > 0 && 0 <= -1 * x15:0:0
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(12) RankingReductionPairProof (EQUIVALENT)
9.08/3.17	Interpretation:
9.08/3.17	[ f5 ] = f5_1
9.08/3.17	
9.08/3.17	The following rules are decreasing:
9.08/3.17	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 + (x15:0:0 - 1), x15:0:0 - 1) :|: x14:0:0 > 0 && 0 <= -1 * x15:0:0
9.08/3.17	
9.08/3.17	The following rules are bounded:
9.08/3.17	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 + (x15:0:0 - 1), x15:0:0 - 1) :|: x14:0:0 > 0 && 0 <= -1 * x15:0:0
9.08/3.17	
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(13)
9.08/3.17	YES
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(14)
9.08/3.17	Obligation:
9.08/3.17	Rules:
9.08/3.17	f5(x14:0, x15:0) -> f5(x14:0 + (x15:0 - 1), x15:0 - 1) :|: x14:0 > 0 && -1 * x15:0 < 0
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(15) IntTRSCompressionProof (EQUIVALENT)
9.08/3.17	Compressed rules.
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(16)
9.08/3.17	Obligation:
9.08/3.17	Rules:
9.08/3.17	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 + (x15:0:0 - 1), x15:0:0 - 1) :|: x14:0:0 > 0 && 0 > -1 * x15:0:0
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(17) RankingReductionPairProof (EQUIVALENT)
9.08/3.17	Interpretation:
9.08/3.17	[ f5 ] = f5_2
9.08/3.17	
9.08/3.17	The following rules are decreasing:
9.08/3.17	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 + (x15:0:0 - 1), x15:0:0 - 1) :|: x14:0:0 > 0 && 0 > -1 * x15:0:0
9.08/3.17	
9.08/3.17	The following rules are bounded:
9.08/3.17	f5(x14:0:0, x15:0:0) -> f5(x14:0:0 + (x15:0:0 - 1), x15:0:0 - 1) :|: x14:0:0 > 0 && 0 > -1 * x15:0:0
9.08/3.17	
9.08/3.17	
9.08/3.17	----------------------------------------
9.08/3.17	
9.08/3.17	(18)
9.08/3.17	YES
9.08/3.20	EOF