4.75/1.93	YES
4.75/1.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.75/1.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.75/1.94	
4.75/1.94	
4.75/1.94	Termination of the given C Problem could be proven:
4.75/1.94	
4.75/1.94	(0) C Problem
4.75/1.94	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.75/1.94	(2) IntTRS
4.75/1.94	(3) TerminationGraphProcessor [SOUND, 47 ms]
4.75/1.94	(4) IntTRS
4.75/1.94	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.75/1.94	(6) IntTRS
4.75/1.94	(7) RankingReductionPairProof [EQUIVALENT, 0 ms]
4.75/1.94	(8) YES
4.75/1.94	
4.75/1.94	
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(0)
4.75/1.94	Obligation:
4.75/1.94	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(1) CToIRSProof (EQUIVALENT)
4.75/1.94	Parsed C Integer Program as IRS.
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(2)
4.75/1.94	Obligation:
4.75/1.94	Rules:
4.75/1.94	f1(x, y, z) -> f2(x_1, y, z) :|: TRUE
4.75/1.94	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
4.75/1.94	f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
4.75/1.94	f5(x9, x10, x11) -> f6(x9, x10, arith) :|: TRUE && arith = x11 + x10
4.75/1.94	f4(x12, x13, x14) -> f5(x12, x13, x14) :|: x13 > 0 && x12 >= x14
4.75/1.94	f6(x15, x16, x17) -> f4(x15, x16, x17) :|: TRUE
4.75/1.94	f4(x18, x19, x20) -> f7(x18, x19, x20) :|: x19 <= 0
4.75/1.94	f4(x21, x22, x23) -> f7(x21, x22, x23) :|: x21 < x23
4.75/1.94	Start term: f1(x, y, z)
4.75/1.94	
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(3) TerminationGraphProcessor (SOUND)
4.75/1.94	Constructed the termination graph and obtained one non-trivial SCC.
4.75/1.94	
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(4)
4.75/1.94	Obligation:
4.75/1.94	Rules:
4.75/1.94	f4(x12, x13, x14) -> f5(x12, x13, x14) :|: x13 > 0 && x12 >= x14
4.75/1.94	f6(x15, x16, x17) -> f4(x15, x16, x17) :|: TRUE
4.75/1.94	f5(x9, x10, x11) -> f6(x9, x10, arith) :|: TRUE && arith = x11 + x10
4.75/1.94	
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(5) IntTRSCompressionProof (EQUIVALENT)
4.75/1.94	Compressed rules.
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(6)
4.75/1.94	Obligation:
4.75/1.94	Rules:
4.75/1.94	f6(x15:0, x16:0, x17:0) -> f6(x15:0, x16:0, x17:0 + x16:0) :|: x16:0 > 0 && x17:0 <= x15:0
4.75/1.94	
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(7) RankingReductionPairProof (EQUIVALENT)
4.75/1.94	Interpretation:
4.75/1.94	[ f6 ] = -1*f6_3 + f6_1
4.75/1.94	
4.75/1.94	The following rules are decreasing:
4.75/1.94	f6(x15:0, x16:0, x17:0) -> f6(x15:0, x16:0, x17:0 + x16:0) :|: x16:0 > 0 && x17:0 <= x15:0
4.75/1.94	
4.75/1.94	The following rules are bounded:
4.75/1.94	f6(x15:0, x16:0, x17:0) -> f6(x15:0, x16:0, x17:0 + x16:0) :|: x16:0 > 0 && x17:0 <= x15:0
4.75/1.94	
4.75/1.94	
4.75/1.94	----------------------------------------
4.75/1.94	
4.75/1.94	(8)
4.75/1.94	YES
4.75/1.96	EOF