6.93/2.51	YES
6.93/2.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.93/2.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.93/2.52	
6.93/2.52	
6.93/2.52	Termination of the given C Problem could be proven:
6.93/2.52	
6.93/2.52	(0) C Problem
6.93/2.52	(1) CToIRSProof [EQUIVALENT, 0 ms]
6.93/2.52	(2) IntTRS
6.93/2.52	(3) TerminationGraphProcessor [SOUND, 50 ms]
6.93/2.52	(4) IntTRS
6.93/2.52	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.93/2.52	(6) IntTRS
6.93/2.52	(7) TerminationGraphProcessor [EQUIVALENT, 3 ms]
6.93/2.52	(8) IntTRS
6.93/2.52	(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.93/2.52	(10) IntTRS
6.93/2.52	(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
6.93/2.52	(12) YES
6.93/2.52	
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(0)
6.93/2.52	Obligation:
6.93/2.52	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(1) CToIRSProof (EQUIVALENT)
6.93/2.52	Parsed C Integer Program as IRS.
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(2)
6.93/2.52	Obligation:
6.93/2.52	Rules:
6.93/2.52	f1(x, y, z) -> f2(x_1, y, z) :|: TRUE
6.93/2.52	f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
6.93/2.52	f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
6.93/2.52	f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 2 * x9 + x10
6.93/2.52	f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = x25 + 1
6.93/2.52	f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 + x16 >= 0 && x15 <= x17
6.93/2.52	f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
6.93/2.52	f4(x21, x22, x23) -> f8(x21, x22, x23) :|: x21 + x22 < 0
6.93/2.52	f4(x28, x29, x30) -> f8(x28, x29, x30) :|: x28 > x30
6.93/2.52	Start term: f1(x, y, z)
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(3) TerminationGraphProcessor (SOUND)
6.93/2.52	Constructed the termination graph and obtained one non-trivial SCC.
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(4)
6.93/2.52	Obligation:
6.93/2.52	Rules:
6.93/2.52	f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 + x16 >= 0 && x15 <= x17
6.93/2.52	f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
6.93/2.52	f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = x25 + 1
6.93/2.52	f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 2 * x9 + x10
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(5) IntTRSCompressionProof (EQUIVALENT)
6.93/2.52	Compressed rules.
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(6)
6.93/2.52	Obligation:
6.93/2.52	Rules:
6.93/2.52	f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x24:0 + (x25:0 + 1) >= 0 && x26:0 >= x24:0
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(7) TerminationGraphProcessor (EQUIVALENT)
6.93/2.52	Constructed the termination graph and obtained one non-trivial SCC.
6.93/2.52	
6.93/2.52	f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x24:0 + (x25:0 + 1) >= 0 && x26:0 >= x24:0
6.93/2.52	has been transformed into
6.93/2.52	f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x26:0 = x8 && (x25:0 = x7 + 1 && (x24:0 = 2 * x6 + (x7 + 1) && (x24:0 + (x25:0 + 1) >= 0 && x26:0 >= x24:0))) && x6 + (x7 + 1) >= 0 && x8 >= x6.
6.93/2.52	
6.93/2.52	
6.93/2.52	f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x26:0 = x8 && (x25:0 = x7 + 1 && (x24:0 = 2 * x6 + (x7 + 1) && (x24:0 + (x25:0 + 1) >= 0 && x26:0 >= x24:0))) && x6 + (x7 + 1) >= 0 && x8 >= x6 and 
6.93/2.52	f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x26:0 = x8 && (x25:0 = x7 + 1 && (x24:0 = 2 * x6 + (x7 + 1) && (x24:0 + (x25:0 + 1) >= 0 && x26:0 >= x24:0))) && x6 + (x7 + 1) >= 0 && x8 >= x6
6.93/2.52	have been merged into the new rule
6.93/2.52	f6(x21, x22, x23) -> f6(2 * (2 * x21 + (x22 + 1)) + (x22 + 1 + 1), x22 + 1 + 1, x23) :|: x23 = x24 && (x22 = x25 + 1 && (x21 = 2 * x26 + (x25 + 1) && (x21 + (x22 + 1) >= 0 && x23 >= x21))) && x26 + (x25 + 1) >= 0 && x24 >= x26 && (x23 = x27 && (x22 + 1 = x28 + 1 && (2 * x21 + (x22 + 1) = 2 * x29 + (x28 + 1) && (2 * x21 + (x22 + 1) + (x22 + 1 + 1) >= 0 && x23 >= 2 * x21 + (x22 + 1)))) && x29 + (x28 + 1) >= 0 && x27 >= x29)
6.93/2.52	
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(8)
6.93/2.52	Obligation:
6.93/2.52	Rules:
6.93/2.52	f6(x30, x31, x32) -> f6(4 * x30 + 3 * x31 + 4, x31 + 2, x32) :|: TRUE && x32 + -1 * x33 = 0 && x31 + -1 * x34 = 1 && x30 + -2 * x35 + -1 * x34 = 1 && x30 + x31 >= -1 && x32 + -1 * x30 >= 0 && x35 + x34 >= -1 && x33 + -1 * x35 >= 0 && x32 + -1 * x36 = 0 && x31 + -1 * x37 = 0 && 2 * x30 + x31 + -2 * x38 + -1 * x37 = 0 && x32 + -2 * x30 + -1 * x31 >= 1 && x38 + x37 >= -1 && x36 + -1 * x38 >= 0
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(9) IntTRSCompressionProof (EQUIVALENT)
6.93/2.52	Compressed rules.
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(10)
6.93/2.52	Obligation:
6.93/2.52	Rules:
6.93/2.52	f6(x30:0, x31:0, x32:0) -> f6(4 * x30:0 + 3 * x31:0 + 4, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= -1 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 1 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= -1 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= -1 && x30:0 + -2 * x35:0 + -1 * x34:0 = 1 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(11) RankingReductionPairProof (EQUIVALENT)
6.93/2.52	Interpretation:
6.93/2.52	[ f6 ] = 1/4*f6_3 + -1/4*f6_1
6.93/2.52	
6.93/2.52	The following rules are decreasing:
6.93/2.52	f6(x30:0, x31:0, x32:0) -> f6(4 * x30:0 + 3 * x31:0 + 4, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= -1 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 1 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= -1 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= -1 && x30:0 + -2 * x35:0 + -1 * x34:0 = 1 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1
6.93/2.52	
6.93/2.52	The following rules are bounded:
6.93/2.52	f6(x30:0, x31:0, x32:0) -> f6(4 * x30:0 + 3 * x31:0 + 4, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= -1 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 1 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= -1 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= -1 && x30:0 + -2 * x35:0 + -1 * x34:0 = 1 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1
6.93/2.52	
6.93/2.52	
6.93/2.52	----------------------------------------
6.93/2.52	
6.93/2.52	(12)
6.93/2.52	YES
6.93/2.56	EOF