5.08/2.12	YES
5.08/2.13	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
5.08/2.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.08/2.13	
5.08/2.13	
5.08/2.13	Termination of the given C Problem could be proven:
5.08/2.13	
5.08/2.13	(0) C Problem
5.08/2.13	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.08/2.13	(2) IntTRS
5.08/2.13	(3) TerminationGraphProcessor [SOUND, 29 ms]
5.08/2.13	(4) IntTRS
5.08/2.13	(5) IntTRSCompressionProof [EQUIVALENT, 34 ms]
5.08/2.13	(6) IntTRS
5.08/2.13	(7) TerminationGraphProcessor [EQUIVALENT, 0 ms]
5.08/2.13	(8) IntTRS
5.08/2.13	(9) TerminationGraphProcessor [EQUIVALENT, 4 ms]
5.08/2.13	(10) YES
5.08/2.13	
5.08/2.13	
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(0)
5.08/2.13	Obligation:
5.08/2.13	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(1) CToIRSProof (EQUIVALENT)
5.08/2.13	Parsed C Integer Program as IRS.
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(2)
5.08/2.13	Obligation:
5.08/2.13	Rules:
5.08/2.13	f1(x) -> f2(x_1) :|: TRUE
5.08/2.13	f3(x1) -> f4(arith) :|: TRUE && arith = 0 - 2 * x1 + 10
5.08/2.13	f2(x2) -> f3(x2) :|: x2 >= 0
5.08/2.13	f4(x3) -> f2(x3) :|: TRUE
5.08/2.13	f2(x4) -> f5(x4) :|: x4 < 0
5.08/2.13	Start term: f1(x)
5.08/2.13	
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(3) TerminationGraphProcessor (SOUND)
5.08/2.13	Constructed the termination graph and obtained one non-trivial SCC.
5.08/2.13	
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(4)
5.08/2.13	Obligation:
5.08/2.13	Rules:
5.08/2.13	f2(x2) -> f3(x2) :|: x2 >= 0
5.08/2.13	f4(x3) -> f2(x3) :|: TRUE
5.08/2.13	f3(x1) -> f4(arith) :|: TRUE && arith = 0 - 2 * x1 + 10
5.08/2.13	
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(5) IntTRSCompressionProof (EQUIVALENT)
5.08/2.13	Compressed rules.
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(6)
5.08/2.13	Obligation:
5.08/2.13	Rules:
5.08/2.13	f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 > -1
5.08/2.13	
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(7) TerminationGraphProcessor (EQUIVALENT)
5.08/2.13	Constructed the termination graph and obtained one non-trivial SCC.
5.08/2.13	
5.08/2.13	f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 > -1
5.08/2.13	has been transformed into
5.08/2.13	f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 = 0 - 2 * x2 + 10 && x3:0 > -1 && x2 > -1.
5.08/2.13	
5.08/2.13	
5.08/2.13	f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 = 0 - 2 * x2 + 10 && x3:0 > -1 && x2 > -1 and 
5.08/2.13	f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 = 0 - 2 * x2 + 10 && x3:0 > -1 && x2 > -1
5.08/2.13	have been merged into the new rule
5.08/2.13	f4(x7) -> f4(0 - 2 * (0 - 2 * x7 + 10) + 10) :|: x7 = 0 - 2 * x8 + 10 && x7 > -1 && x8 > -1 && (0 - 2 * x7 + 10 = 0 - 2 * x9 + 10 && 0 - 2 * x7 + 10 > -1 && x9 > -1)
5.08/2.13	
5.08/2.13	
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(8)
5.08/2.13	Obligation:
5.08/2.13	Rules:
5.08/2.13	f4(x10) -> f4(4 * x10 + -10) :|: TRUE && x10 + 2 * x11 = 10 && x10 >= 0 && x11 >= 0 && -1 * x10 + x12 = 0 && -1 * x10 >= -5 && x12 >= 0
5.08/2.13	
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(9) TerminationGraphProcessor (EQUIVALENT)
5.08/2.13	Constructed the termination graph and obtained no non-trivial SCC(s).
5.08/2.13	
5.08/2.13	----------------------------------------
5.08/2.13	
5.08/2.13	(10)
5.08/2.13	YES
5.08/2.17	EOF