4.76/2.06	YES
4.76/2.08	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.76/2.08	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.76/2.08	
4.76/2.08	
4.76/2.08	Termination of the given C Problem could be proven:
4.76/2.08	
4.76/2.08	(0) C Problem
4.76/2.08	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.76/2.08	(2) IntTRS
4.76/2.08	(3) TerminationGraphProcessor [SOUND, 41 ms]
4.76/2.08	(4) IntTRS
4.76/2.08	(5) IntTRSCompressionProof [EQUIVALENT, 5 ms]
4.76/2.08	(6) IntTRS
4.76/2.08	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.76/2.08	(8) IntTRS
4.76/2.08	(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
4.76/2.08	(10) YES
4.76/2.08	
4.76/2.08	
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(0)
4.76/2.08	Obligation:
4.76/2.08	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(1) CToIRSProof (EQUIVALENT)
4.76/2.08	Parsed C Integer Program as IRS.
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(2)
4.76/2.08	Obligation:
4.76/2.08	Rules:
4.76/2.08	f1(c, x, y, z) -> f2(c, x_1, y, z) :|: TRUE
4.76/2.08	f2(x1, x2, x3, x4) -> f3(x1, x2, x5, x4) :|: TRUE
4.76/2.08	f3(x6, x7, x8, x9) -> f4(x6, x7, x8, x10) :|: TRUE
4.76/2.08	f4(x11, x12, x13, x14) -> f5(0, x12, x13, x14) :|: TRUE
4.76/2.08	f6(x15, x16, x17, x18) -> f7(x15, x16, arith, x18) :|: TRUE && arith = x17 + 1
4.76/2.08	f7(x39, x40, x41, x42) -> f8(x39, x40, x41, x43) :|: TRUE && x43 = x42 + 1
4.76/2.08	f8(x44, x45, x46, x47) -> f9(x48, x45, x46, x47) :|: TRUE && x48 = x44 + 1
4.76/2.08	f5(x27, x28, x29, x30) -> f6(x27, x28, x29, x30) :|: x28 > x29 + x30
4.76/2.08	f9(x31, x32, x33, x34) -> f5(x31, x32, x33, x34) :|: TRUE
4.76/2.08	f5(x35, x36, x37, x38) -> f10(x35, x36, x37, x38) :|: x36 <= x37 + x38
4.76/2.08	Start term: f1(c, x, y, z)
4.76/2.08	
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(3) TerminationGraphProcessor (SOUND)
4.76/2.08	Constructed the termination graph and obtained one non-trivial SCC.
4.76/2.08	
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(4)
4.76/2.08	Obligation:
4.76/2.08	Rules:
4.76/2.08	f5(x27, x28, x29, x30) -> f6(x27, x28, x29, x30) :|: x28 > x29 + x30
4.76/2.08	f9(x31, x32, x33, x34) -> f5(x31, x32, x33, x34) :|: TRUE
4.76/2.08	f8(x44, x45, x46, x47) -> f9(x48, x45, x46, x47) :|: TRUE && x48 = x44 + 1
4.76/2.08	f7(x39, x40, x41, x42) -> f8(x39, x40, x41, x43) :|: TRUE && x43 = x42 + 1
4.76/2.08	f6(x15, x16, x17, x18) -> f7(x15, x16, arith, x18) :|: TRUE && arith = x17 + 1
4.76/2.08	
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(5) IntTRSCompressionProof (EQUIVALENT)
4.76/2.08	Compressed rules.
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(6)
4.76/2.08	Obligation:
4.76/2.08	Rules:
4.76/2.08	f7(x39:0, x40:0, x41:0, x42:0) -> f7(x39:0 + 1, x40:0, x41:0 + 1, x42:0 + 1) :|: x41:0 + (x42:0 + 1) < x40:0
4.76/2.08	
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.76/2.08	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.76/2.08	
4.76/2.08	   f7(x1, x2, x3, x4) -> f7(x2, x3, x4)
4.76/2.08	
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(8)
4.76/2.08	Obligation:
4.76/2.08	Rules:
4.76/2.08	f7(x40:0, x41:0, x42:0) -> f7(x40:0, x41:0 + 1, x42:0 + 1) :|: x41:0 + (x42:0 + 1) < x40:0
4.76/2.08	
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(9) PolynomialOrderProcessor (EQUIVALENT)
4.76/2.08	Found the following polynomial interpretation:
4.76/2.08	[f7(x, x1, x2)] = -1 + x - x1 - x2
4.76/2.08	
4.76/2.08	The following rules are decreasing:
4.76/2.08	f7(x40:0, x41:0, x42:0) -> f7(x40:0, x41:0 + 1, x42:0 + 1) :|: x41:0 + (x42:0 + 1) < x40:0
4.76/2.08	The following rules are bounded:
4.76/2.08	f7(x40:0, x41:0, x42:0) -> f7(x40:0, x41:0 + 1, x42:0 + 1) :|: x41:0 + (x42:0 + 1) < x40:0
4.76/2.08	
4.76/2.08	----------------------------------------
4.76/2.08	
4.76/2.08	(10)
4.76/2.08	YES
5.13/2.13	EOF