4.51/1.97	YES
4.73/1.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.73/1.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.73/1.98	
4.73/1.98	
4.73/1.98	Termination of the given C Problem could be proven:
4.73/1.98	
4.73/1.98	(0) C Problem
4.73/1.98	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.73/1.98	(2) IntTRS
4.73/1.98	(3) TerminationGraphProcessor [SOUND, 53 ms]
4.73/1.98	(4) IntTRS
4.73/1.98	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
4.73/1.98	(6) IntTRS
4.73/1.98	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.73/1.98	(8) IntTRS
4.73/1.98	(9) RankingReductionPairProof [EQUIVALENT, 11 ms]
4.73/1.98	(10) YES
4.73/1.98	
4.73/1.98	
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(0)
4.73/1.98	Obligation:
4.73/1.98	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(1) CToIRSProof (EQUIVALENT)
4.73/1.98	Parsed C Integer Program as IRS.
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(2)
4.73/1.98	Obligation:
4.73/1.98	Rules:
4.73/1.98	f1(x, y, r) -> f2(x_1, y, r) :|: TRUE
4.73/1.98	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
4.73/1.98	f3(x5, x6, x7) -> f4(x5, x6, 1) :|: TRUE
4.73/1.98	f5(x8, x9, x10) -> f6(x8, x9, arith) :|: TRUE && arith = x10 * x8
4.73/1.98	f6(x23, x24, x25) -> f7(x23, x26, x25) :|: TRUE && x26 = x24 - 1
4.73/1.98	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > 0
4.73/1.98	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.73/1.98	f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x21 <= 0
4.73/1.98	Start term: f1(x, y, r)
4.73/1.98	
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(3) TerminationGraphProcessor (SOUND)
4.73/1.98	Constructed the termination graph and obtained one non-trivial SCC.
4.73/1.98	
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(4)
4.73/1.98	Obligation:
4.73/1.98	Rules:
4.73/1.98	f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > 0
4.73/1.98	f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
4.73/1.98	f6(x23, x24, x25) -> f7(x23, x26, x25) :|: TRUE && x26 = x24 - 1
4.73/1.98	f5(x8, x9, x10) -> f6(x8, x9, arith) :|: TRUE && arith = x10 * x8
4.73/1.98	
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(5) IntTRSCompressionProof (EQUIVALENT)
4.73/1.98	Compressed rules.
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(6)
4.73/1.98	Obligation:
4.73/1.98	Rules:
4.73/1.98	f6(x23:0, x24:0, x25:0) -> f6(x23:0, x24:0 - 1, x25:0 * x23:0) :|: x24:0 > 1
4.73/1.98	
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.73/1.98	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.73/1.98	
4.73/1.98	   f6(x1, x2, x3) -> f6(x2)
4.73/1.98	
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(8)
4.73/1.98	Obligation:
4.73/1.98	Rules:
4.73/1.98	f6(x24:0) -> f6(x24:0 - 1) :|: x24:0 > 1
4.73/1.98	
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(9) RankingReductionPairProof (EQUIVALENT)
4.73/1.98	Interpretation:
4.73/1.98	[ f6 ] = f6_1
4.73/1.98	
4.73/1.98	The following rules are decreasing:
4.73/1.98	f6(x24:0) -> f6(x24:0 - 1) :|: x24:0 > 1
4.73/1.98	
4.73/1.98	The following rules are bounded:
4.73/1.98	f6(x24:0) -> f6(x24:0 - 1) :|: x24:0 > 1
4.73/1.98	
4.73/1.98	
4.73/1.98	----------------------------------------
4.73/1.98	
4.73/1.98	(10)
4.73/1.98	YES
4.73/2.02	EOF