5.19/2.24	YES
5.19/2.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
5.19/2.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.19/2.26	
5.19/2.26	
5.19/2.26	Termination of the given C Problem could be proven:
5.19/2.26	
5.19/2.26	(0) C Problem
5.19/2.26	(1) CToIRSProof [EQUIVALENT, 0 ms]
5.19/2.26	(2) IntTRS
5.19/2.26	(3) TerminationGraphProcessor [SOUND, 49 ms]
5.19/2.26	(4) IntTRS
5.19/2.26	(5) IntTRSCompressionProof [EQUIVALENT, 16 ms]
5.19/2.26	(6) IntTRS
5.19/2.26	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
5.19/2.26	(8) IntTRS
5.19/2.26	(9) PolynomialOrderProcessor [EQUIVALENT, 12 ms]
5.19/2.26	(10) YES
5.19/2.26	
5.19/2.26	
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(0)
5.19/2.26	Obligation:
5.19/2.26	c file /export/starexec/sandbox/benchmark/theBenchmark.c
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(1) CToIRSProof (EQUIVALENT)
5.19/2.26	Parsed C Integer Program as IRS.
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(2)
5.19/2.26	Obligation:
5.19/2.26	Rules:
5.19/2.26	f1(i, j, k, ell) -> f2(x_1, j, k, ell) :|: TRUE
5.19/2.26	f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE
5.19/2.26	f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE
5.19/2.26	f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x10) :|: TRUE
5.19/2.26	f6(x14, x15, x16, x17) -> f7(x15, x15, x16, x17) :|: TRUE
5.19/2.26	f7(x18, x19, x20, x21) -> f8(x18, arith, x20, x21) :|: TRUE && arith = x21 + 1
5.19/2.26	f8(x38, x39, x40, x41) -> f9(x38, x39, x42, x41) :|: TRUE && x42 = x40 - 1
5.19/2.26	f4(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x26 <= 100 && x27 <= x28
5.19/2.26	f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
5.19/2.26	f4(x34, x35, x36, x37) -> f10(x34, x35, x36, x37) :|: x34 > 100
5.19/2.26	f4(x43, x44, x45, x46) -> f10(x43, x44, x45, x46) :|: x44 > x45
5.19/2.26	Start term: f1(i, j, k, ell)
5.19/2.26	
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(3) TerminationGraphProcessor (SOUND)
5.19/2.26	Constructed the termination graph and obtained one non-trivial SCC.
5.19/2.26	
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(4)
5.19/2.26	Obligation:
5.19/2.26	Rules:
5.19/2.26	f4(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x26 <= 100 && x27 <= x28
5.19/2.26	f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
5.19/2.26	f8(x38, x39, x40, x41) -> f9(x38, x39, x42, x41) :|: TRUE && x42 = x40 - 1
5.19/2.26	f7(x18, x19, x20, x21) -> f8(x18, arith, x20, x21) :|: TRUE && arith = x21 + 1
5.19/2.26	f6(x14, x15, x16, x17) -> f7(x15, x15, x16, x17) :|: TRUE
5.19/2.26	f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x10) :|: TRUE
5.19/2.26	
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(5) IntTRSCompressionProof (EQUIVALENT)
5.19/2.26	Compressed rules.
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(6)
5.19/2.26	Obligation:
5.19/2.26	Rules:
5.19/2.26	f6(x14:0, x15:0, x16:0, x17:0) -> f6(x15:0, x17:0 + 1, x16:0 - 1, x15:0) :|: x15:0 < 101 && x17:0 + 1 <= x16:0 - 1
5.19/2.26	
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
5.19/2.26	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
5.19/2.26	
5.19/2.26	   f6(x1, x2, x3, x4) -> f6(x2, x3, x4)
5.19/2.26	
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(8)
5.19/2.26	Obligation:
5.19/2.26	Rules:
5.19/2.26	f6(x15:0, x16:0, x17:0) -> f6(x17:0 + 1, x16:0 - 1, x15:0) :|: x15:0 < 101 && x17:0 + 1 <= x16:0 - 1
5.19/2.26	
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(9) PolynomialOrderProcessor (EQUIVALENT)
5.19/2.26	Found the following polynomial interpretation:
5.19/2.26	[f6(x, x1, x2)] = 98 - x + x1 - x2
5.19/2.26	
5.19/2.26	The following rules are decreasing:
5.19/2.26	f6(x15:0, x16:0, x17:0) -> f6(x17:0 + 1, x16:0 - 1, x15:0) :|: x15:0 < 101 && x17:0 + 1 <= x16:0 - 1
5.19/2.26	The following rules are bounded:
5.19/2.26	f6(x15:0, x16:0, x17:0) -> f6(x17:0 + 1, x16:0 - 1, x15:0) :|: x15:0 < 101 && x17:0 + 1 <= x16:0 - 1
5.19/2.26	
5.19/2.26	----------------------------------------
5.19/2.26	
5.19/2.26	(10)
5.19/2.26	YES
5.19/2.30	EOF