6.32/2.44	YES
6.32/2.46	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
6.32/2.46	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.32/2.46	
6.32/2.46	
6.32/2.46	Termination of the given C Problem could be proven:
6.32/2.46	
6.32/2.46	(0) C Problem
6.32/2.46	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.32/2.46	(2) IntTRS
6.32/2.46	(3) TerminationGraphProcessor [SOUND, 67 ms]
6.32/2.46	(4) IntTRS
6.32/2.46	(5) IntTRSCompressionProof [EQUIVALENT, 18 ms]
6.32/2.46	(6) IntTRS
6.32/2.46	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
6.32/2.46	(8) IntTRS
6.32/2.46	(9) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
6.32/2.46	(10) AND
6.32/2.46	    (11) IntTRS
6.32/2.46	        (12) TerminationGraphProcessor [EQUIVALENT, 0 ms]
6.32/2.46	        (13) YES
6.32/2.46	    (14) IntTRS
6.32/2.46	        (15) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
6.32/2.46	        (16) YES
6.32/2.46	
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(0)
6.32/2.46	Obligation:
6.32/2.46	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(1) CToIRSProof (EQUIVALENT)
6.32/2.46	Parsed C Integer Program as IRS.
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(2)
6.32/2.46	Obligation:
6.32/2.46	Rules:
6.32/2.46	f1(x, xtmp, res, restmp) -> f2(x_1, xtmp, res, restmp) :|: TRUE
6.32/2.46	f2(x1, x2, x3, x4) -> f3(x1, x2, 0, x4) :|: TRUE
6.32/2.46	f4(x5, x6, x7, x8) -> f5(x5, x5, x7, x8) :|: TRUE
6.32/2.46	f5(x9, x10, x11, x12) -> f6(x9, x10, x11, 0) :|: TRUE
6.32/2.46	f7(x13, x14, x15, x16) -> f8(x13, arith, x15, x16) :|: TRUE && arith = x14 - 2
6.32/2.46	f8(x53, x54, x55, x56) -> f9(x53, x54, x55, x57) :|: TRUE && x57 = x56 + 1
6.32/2.46	f6(x21, x22, x23, x24) -> f7(x21, x22, x23, x24) :|: x22 > 1
6.32/2.46	f9(x25, x26, x27, x28) -> f6(x25, x26, x27, x28) :|: TRUE
6.32/2.46	f6(x29, x30, x31, x32) -> f10(x29, x30, x31, x32) :|: x30 <= 1
6.32/2.46	f10(x33, x34, x35, x36) -> f11(x34, x34, x35, x36) :|: TRUE
6.32/2.46	f11(x58, x59, x60, x61) -> f12(x58, x59, x62, x61) :|: TRUE && x62 = x60 + 1
6.32/2.46	f3(x41, x42, x43, x44) -> f4(x41, x42, x43, x44) :|: x41 > 1
6.32/2.46	f12(x45, x46, x47, x48) -> f3(x45, x46, x47, x48) :|: TRUE
6.32/2.46	f3(x49, x50, x51, x52) -> f13(x49, x50, x51, x52) :|: x49 <= 1
6.32/2.46	Start term: f1(x, xtmp, res, restmp)
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(3) TerminationGraphProcessor (SOUND)
6.32/2.46	Constructed the termination graph and obtained one non-trivial SCC.
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(4)
6.32/2.46	Obligation:
6.32/2.46	Rules:
6.32/2.46	f3(x41, x42, x43, x44) -> f4(x41, x42, x43, x44) :|: x41 > 1
6.32/2.46	f12(x45, x46, x47, x48) -> f3(x45, x46, x47, x48) :|: TRUE
6.32/2.46	f11(x58, x59, x60, x61) -> f12(x58, x59, x62, x61) :|: TRUE && x62 = x60 + 1
6.32/2.46	f10(x33, x34, x35, x36) -> f11(x34, x34, x35, x36) :|: TRUE
6.32/2.46	f6(x29, x30, x31, x32) -> f10(x29, x30, x31, x32) :|: x30 <= 1
6.32/2.46	f5(x9, x10, x11, x12) -> f6(x9, x10, x11, 0) :|: TRUE
6.32/2.46	f4(x5, x6, x7, x8) -> f5(x5, x5, x7, x8) :|: TRUE
6.32/2.46	f9(x25, x26, x27, x28) -> f6(x25, x26, x27, x28) :|: TRUE
6.32/2.46	f8(x53, x54, x55, x56) -> f9(x53, x54, x55, x57) :|: TRUE && x57 = x56 + 1
6.32/2.46	f7(x13, x14, x15, x16) -> f8(x13, arith, x15, x16) :|: TRUE && arith = x14 - 2
6.32/2.46	f6(x21, x22, x23, x24) -> f7(x21, x22, x23, x24) :|: x22 > 1
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(5) IntTRSCompressionProof (EQUIVALENT)
6.32/2.46	Compressed rules.
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(6)
6.32/2.46	Obligation:
6.32/2.46	Rules:
6.32/2.46	f6(x21:0, x22:0, x23:0, x24:0) -> f6(x21:0, x22:0 - 2, x23:0, x24:0 + 1) :|: x22:0 > 1
6.32/2.46	f6(x29:0, x30:0, x31:0, x32:0) -> f6(x30:0, x30:0, x31:0 + 1, 0) :|: x30:0 < 2 && x30:0 > 1
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
6.32/2.46	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
6.32/2.46	
6.32/2.46	   f6(x1, x2, x3, x4) -> f6(x2)
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(8)
6.32/2.46	Obligation:
6.32/2.46	Rules:
6.32/2.46	f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1
6.32/2.46	f6(x30:0) -> f6(x30:0) :|: x30:0 < 2 && x30:0 > 1
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(9) PolynomialOrderProcessor (EQUIVALENT)
6.32/2.46	Found the following polynomial interpretation:
6.32/2.46	[f6(x)] = d - 2*x + 2*x^2
6.32/2.46	
6.32/2.46	The following rules are decreasing:
6.32/2.46	f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1
6.32/2.46	The following rules are bounded:
6.32/2.46	f6(x30:0) -> f6(x30:0) :|: x30:0 < 2 && x30:0 > 1
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(10)
6.32/2.46	Complex Obligation (AND)
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(11)
6.32/2.46	Obligation:
6.32/2.46	Rules:
6.32/2.46	f6(x30:0) -> f6(x30:0) :|: x30:0 < 2 && x30:0 > 1
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(12) TerminationGraphProcessor (EQUIVALENT)
6.32/2.46	Constructed the termination graph and obtained no non-trivial SCC(s).
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(13)
6.32/2.46	YES
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(14)
6.32/2.46	Obligation:
6.32/2.46	Rules:
6.32/2.46	f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(15) PolynomialOrderProcessor (EQUIVALENT)
6.32/2.46	Found the following polynomial interpretation:
6.32/2.46	[f6(x)] = -1 - x + x^2
6.32/2.46	
6.32/2.46	The following rules are decreasing:
6.32/2.46	f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1
6.32/2.46	The following rules are bounded:
6.32/2.46	f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1
6.32/2.46	
6.32/2.46	----------------------------------------
6.32/2.46	
6.32/2.46	(16)
6.32/2.46	YES
6.61/2.49	EOF