7.77/2.80	YES
7.77/2.83	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
7.77/2.83	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.77/2.83	
7.77/2.83	
7.77/2.83	Termination of the given C Problem could be proven:
7.77/2.83	
7.77/2.83	(0) C Problem
7.77/2.83	(1) CToIRSProof [EQUIVALENT, 0 ms]
7.77/2.83	(2) IntTRS
7.77/2.83	(3) TerminationGraphProcessor [SOUND, 53 ms]
7.77/2.83	(4) IntTRS
7.77/2.83	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.77/2.83	(6) IntTRS
7.77/2.83	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
7.77/2.83	(8) IntTRS
7.77/2.83	(9) RankingReductionPairProof [EQUIVALENT, 11 ms]
7.77/2.83	(10) YES
7.77/2.83	
7.77/2.83	
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(0)
7.77/2.83	Obligation:
7.77/2.83	c file /export/starexec/sandbox/benchmark/theBenchmark.c
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(1) CToIRSProof (EQUIVALENT)
7.77/2.83	Parsed C Integer Program as IRS.
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(2)
7.77/2.83	Obligation:
7.77/2.83	Rules:
7.77/2.83	f1(x, y, z) -> f2(x_1, y, z) :|: TRUE
7.77/2.83	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
7.77/2.83	f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
7.77/2.83	f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = x9 + 1
7.77/2.83	f6(x12, x13, x14) -> f7(x12, x14, x14) :|: TRUE
7.77/2.83	f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 < x16
7.77/2.83	f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
7.77/2.83	f4(x21, x22, x23) -> f8(x21, x22, x23) :|: x21 >= x22
7.77/2.83	Start term: f1(x, y, z)
7.77/2.83	
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(3) TerminationGraphProcessor (SOUND)
7.77/2.83	Constructed the termination graph and obtained one non-trivial SCC.
7.77/2.83	
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(4)
7.77/2.83	Obligation:
7.77/2.83	Rules:
7.77/2.83	f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 < x16
7.77/2.83	f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
7.77/2.83	f6(x12, x13, x14) -> f7(x12, x14, x14) :|: TRUE
7.77/2.83	f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = x9 + 1
7.77/2.83	
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(5) IntTRSCompressionProof (EQUIVALENT)
7.77/2.83	Compressed rules.
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(6)
7.77/2.83	Obligation:
7.77/2.83	Rules:
7.77/2.83	f6(x12:0, x13:0, x14:0) -> f6(x12:0 + 1, x14:0, x14:0) :|: x14:0 > x12:0
7.77/2.83	
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
7.77/2.83	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
7.77/2.83	
7.77/2.83	   f6(x1, x2, x3) -> f6(x1, x3)
7.77/2.83	
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(8)
7.77/2.83	Obligation:
7.77/2.83	Rules:
7.77/2.83	f6(x12:0, x14:0) -> f6(x12:0 + 1, x14:0) :|: x14:0 > x12:0
7.77/2.83	
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(9) RankingReductionPairProof (EQUIVALENT)
7.77/2.83	Interpretation:
7.77/2.83	[ f6 ] = f6_2 + -1*f6_1
7.77/2.83	
7.77/2.83	The following rules are decreasing:
7.77/2.83	f6(x12:0, x14:0) -> f6(x12:0 + 1, x14:0) :|: x14:0 > x12:0
7.77/2.83	
7.77/2.83	The following rules are bounded:
7.77/2.83	f6(x12:0, x14:0) -> f6(x12:0 + 1, x14:0) :|: x14:0 > x12:0
7.77/2.83	
7.77/2.83	
7.77/2.83	----------------------------------------
7.77/2.83	
7.77/2.83	(10)
7.77/2.83	YES
8.13/2.86	EOF