6.18/2.41	YES
6.18/2.41	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.18/2.41	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.18/2.41	
6.18/2.41	
6.18/2.41	Termination of the given C Problem could be proven:
6.18/2.41	
6.18/2.41	(0) C Problem
6.18/2.41	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.18/2.41	(2) IntTRS
6.18/2.41	(3) TerminationGraphProcessor [SOUND, 44 ms]
6.18/2.41	(4) IntTRS
6.18/2.41	(5) IntTRSCompressionProof [EQUIVALENT, 37 ms]
6.18/2.41	(6) IntTRS
6.18/2.41	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.18/2.41	(8) IntTRS
6.18/2.41	(9) TerminationGraphProcessor [EQUIVALENT, 2 ms]
6.18/2.41	(10) IntTRS
6.18/2.41	(11) TerminationGraphProcessor [EQUIVALENT, 3 ms]
6.18/2.41	(12) YES
6.18/2.41	
6.18/2.41	
6.18/2.41	----------------------------------------
6.18/2.41	
6.18/2.41	(0)
6.18/2.41	Obligation:
6.18/2.41	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.18/2.41	----------------------------------------
6.18/2.41	
6.18/2.41	(1) CToIRSProof (EQUIVALENT)
6.18/2.41	Parsed C Integer Program as IRS.
6.18/2.41	----------------------------------------
6.18/2.41	
6.18/2.41	(2)
6.18/2.41	Obligation:
6.18/2.41	Rules:
6.18/2.41	f1(x, y, oldy) -> f2(x_1, y, oldy) :|: TRUE
6.18/2.41	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
6.18/2.41	f4(x5, x6, x7) -> f5(x6, x6, x7) :|: TRUE
6.18/2.41	f5(x8, x9, x10) -> f6(x8, x9, x9) :|: TRUE
6.18/2.41	f6(x11, x12, x13) -> f7(x11, x14, x13) :|: TRUE
6.18/2.41	f3(x15, x16, x17) -> f4(x15, x16, x17) :|: x15 > 0 && x16 <= 0 - x17
6.18/2.41	f7(x18, x19, x20) -> f3(x18, x19, x20) :|: TRUE
6.18/2.41	f3(x21, x22, x23) -> f8(x21, x22, x23) :|: x21 <= 0
6.18/2.41	f3(x24, x25, x26) -> f8(x24, x25, x26) :|: x25 > 0 - x26
6.18/2.41	Start term: f1(x, y, oldy)
6.18/2.41	
6.18/2.41	----------------------------------------
6.18/2.41	
6.18/2.41	(3) TerminationGraphProcessor (SOUND)
6.18/2.41	Constructed the termination graph and obtained one non-trivial SCC.
6.18/2.41	
6.18/2.41	----------------------------------------
6.18/2.41	
6.18/2.41	(4)
6.18/2.41	Obligation:
6.18/2.41	Rules:
6.18/2.41	f3(x15, x16, x17) -> f4(x15, x16, x17) :|: x15 > 0 && x16 <= 0 - x17
6.18/2.41	f7(x18, x19, x20) -> f3(x18, x19, x20) :|: TRUE
6.18/2.41	f6(x11, x12, x13) -> f7(x11, x14, x13) :|: TRUE
6.18/2.41	f5(x8, x9, x10) -> f6(x8, x9, x9) :|: TRUE
6.18/2.41	f4(x5, x6, x7) -> f5(x6, x6, x7) :|: TRUE
6.18/2.41	
6.18/2.41	----------------------------------------
6.18/2.41	
6.18/2.41	(5) IntTRSCompressionProof (EQUIVALENT)
6.18/2.41	Compressed rules.
6.18/2.41	----------------------------------------
6.18/2.41	
6.18/2.41	(6)
6.18/2.41	Obligation:
6.18/2.41	Rules:
6.18/2.41	f5(x8:0, x9:0, x10:0) -> f5(x14:0, x14:0, x9:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0
6.18/2.41	
6.18/2.41	----------------------------------------
6.18/2.42	
6.18/2.42	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.18/2.42	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.18/2.42	
6.18/2.42	   f5(x1, x2, x3) -> f5(x1, x2)
6.18/2.42	
6.18/2.42	----------------------------------------
6.18/2.42	
6.18/2.42	(8)
6.18/2.42	Obligation:
6.18/2.42	Rules:
6.18/2.42	f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0
6.18/2.42	
6.18/2.42	----------------------------------------
6.18/2.42	
6.18/2.42	(9) TerminationGraphProcessor (EQUIVALENT)
6.18/2.42	Constructed the termination graph and obtained one non-trivial SCC.
6.18/2.42	
6.18/2.42	f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0
6.18/2.42	has been transformed into
6.18/2.42	f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0.
6.18/2.42	
6.18/2.42	
6.18/2.42	f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0 and 
6.18/2.42	f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0
6.18/2.42	have been merged into the new rule
6.18/2.42	f5(x15, x16) -> f5(x17, x17) :|: x15 > 0 && x18 <= 0 - x16 && (x18 > 0 && x17 <= 0 - x18)
6.18/2.42	
6.18/2.42	
6.18/2.42	----------------------------------------
6.18/2.42	
6.18/2.42	(10)
6.18/2.42	Obligation:
6.18/2.42	Rules:
6.18/2.42	f5(x19, x20) -> f5(x21, x21) :|: TRUE && x19 >= 1 && x22 + x20 <= 0 && x22 >= 1 && x21 + x22 <= 0
6.18/2.42	
6.18/2.42	----------------------------------------
6.18/2.42	
6.18/2.42	(11) TerminationGraphProcessor (EQUIVALENT)
6.18/2.42	Constructed the termination graph and obtained no non-trivial SCC(s).
6.18/2.42	
6.18/2.42	----------------------------------------
6.18/2.42	
6.18/2.42	(12)
6.18/2.42	YES
6.18/2.44	EOF