4.18/1.89	YES
4.18/1.91	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.18/1.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.18/1.91	
4.18/1.91	
4.18/1.91	Termination of the given C Problem could be proven:
4.18/1.91	
4.18/1.91	(0) C Problem
4.18/1.91	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.18/1.91	(2) IntTRS
4.18/1.91	(3) TerminationGraphProcessor [SOUND, 47 ms]
4.18/1.91	(4) IntTRS
4.18/1.91	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.18/1.91	(6) IntTRS
4.18/1.91	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.18/1.91	(8) IntTRS
4.18/1.91	(9) PolynomialOrderProcessor [EQUIVALENT, 7 ms]
4.18/1.91	(10) YES
4.18/1.91	
4.18/1.91	
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(0)
4.18/1.91	Obligation:
4.18/1.91	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(1) CToIRSProof (EQUIVALENT)
4.18/1.91	Parsed C Integer Program as IRS.
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(2)
4.18/1.91	Obligation:
4.18/1.91	Rules:
4.18/1.91	f1(i, sum, bound) -> f2(i, sum, x_1) :|: TRUE
4.18/1.91	f2(x, x1, x2) -> f3(0, x1, x2) :|: TRUE
4.18/1.91	f3(x3, x4, x5) -> f4(x3, 0, x5) :|: TRUE
4.18/1.91	f5(x6, x7, x8) -> f6(x6, arith, x8) :|: TRUE && arith = x7 + x6
4.18/1.91	f6(x21, x22, x23) -> f7(x24, x22, x23) :|: TRUE && x24 = x21 + 1
4.18/1.91	f4(x12, x13, x14) -> f5(x12, x13, x14) :|: x12 < x14
4.18/1.91	f7(x15, x16, x17) -> f4(x15, x16, x17) :|: TRUE
4.18/1.91	f4(x18, x19, x20) -> f8(x18, x19, x20) :|: x18 >= x20
4.18/1.91	Start term: f1(i, sum, bound)
4.18/1.91	
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(3) TerminationGraphProcessor (SOUND)
4.18/1.91	Constructed the termination graph and obtained one non-trivial SCC.
4.18/1.91	
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(4)
4.18/1.91	Obligation:
4.18/1.91	Rules:
4.18/1.91	f4(x12, x13, x14) -> f5(x12, x13, x14) :|: x12 < x14
4.18/1.91	f7(x15, x16, x17) -> f4(x15, x16, x17) :|: TRUE
4.18/1.91	f6(x21, x22, x23) -> f7(x24, x22, x23) :|: TRUE && x24 = x21 + 1
4.18/1.91	f5(x6, x7, x8) -> f6(x6, arith, x8) :|: TRUE && arith = x7 + x6
4.18/1.91	
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(5) IntTRSCompressionProof (EQUIVALENT)
4.18/1.91	Compressed rules.
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(6)
4.18/1.91	Obligation:
4.18/1.91	Rules:
4.18/1.91	f6(x21:0, x22:0, x23:0) -> f6(x21:0 + 1, x22:0 + (x21:0 + 1), x23:0) :|: x23:0 > x21:0 + 1
4.18/1.91	
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.18/1.91	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.18/1.91	
4.18/1.91	   f6(x1, x2, x3) -> f6(x1, x3)
4.18/1.91	
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(8)
4.18/1.91	Obligation:
4.18/1.91	Rules:
4.18/1.91	f6(x21:0, x23:0) -> f6(x21:0 + 1, x23:0) :|: x23:0 > x21:0 + 1
4.18/1.91	
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(9) PolynomialOrderProcessor (EQUIVALENT)
4.18/1.91	Found the following polynomial interpretation:
4.18/1.91	[f6(x, x1)] = -x + x1
4.18/1.91	
4.18/1.91	The following rules are decreasing:
4.18/1.91	f6(x21:0, x23:0) -> f6(x21:0 + 1, x23:0) :|: x23:0 > x21:0 + 1
4.18/1.91	The following rules are bounded:
4.18/1.91	f6(x21:0, x23:0) -> f6(x21:0 + 1, x23:0) :|: x23:0 > x21:0 + 1
4.18/1.91	
4.18/1.91	----------------------------------------
4.18/1.91	
4.18/1.91	(10)
4.18/1.91	YES
4.50/1.93	EOF