6.72/2.83	YES
6.72/2.83	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
6.72/2.83	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.72/2.83	
6.72/2.83	
6.72/2.83	Termination of the given C Problem could be proven:
6.72/2.83	
6.72/2.83	(0) C Problem
6.72/2.83	(1) CToLLVMProof [EQUIVALENT, 73 ms]
6.72/2.83	(2) LLVM problem
6.72/2.83	(3) LLVMToTerminationGraphProof [EQUIVALENT, 295 ms]
6.72/2.83	(4) LLVM Symbolic Execution Graph
6.72/2.83	(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
6.72/2.83	(6) LLVM Symbolic Execution SCC
6.72/2.83	(7) SCC2IRS [SOUND, 70 ms]
6.72/2.83	(8) IntTRS
6.72/2.83	(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.72/2.83	(10) IntTRS
6.72/2.83	(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
6.72/2.83	(12) YES
6.72/2.83	
6.72/2.83	
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(0)
6.72/2.83	Obligation:
6.72/2.83	c file /export/starexec/sandbox/benchmark/theBenchmark.c
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(1) CToLLVMProof (EQUIVALENT)
6.72/2.83	Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM.
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(2)
6.72/2.83	Obligation:
6.72/2.83	LLVM Problem
6.72/2.83	
6.72/2.83	Aliases:
6.72/2.83	
6.72/2.83	Data layout:
6.72/2.83	
6.72/2.83	"e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128-n8:16:32:64-S128"
6.72/2.83	
6.72/2.83	Machine:
6.72/2.83	
6.72/2.83	"x86_64-pc-linux-gnu"
6.72/2.83	
6.72/2.83	Type definitions:
6.72/2.83	
6.72/2.83	Global variables:
6.72/2.83	
6.72/2.83	Function declarations and definitions:
6.72/2.83	
6.72/2.83	*BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
6.72/2.83	*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
6.72/2.83		0:
6.72/2.83			%1 = alloca i32, align 4
6.72/2.83			%x = alloca i32, align 4
6.72/2.83			store 0, %1
6.72/2.83			%2 = call i32 @__VERIFIER_nondet_int()
6.72/2.83			store %2, %x
6.72/2.83			br %3
6.72/2.83		3:
6.72/2.83			%4 = load %x
6.72/2.83			%5 = icmp sgt %4 0
6.72/2.83			br %5, %6, %9
6.72/2.83		6:
6.72/2.83			%7 = load %x
6.72/2.83			%8 = sdiv %7 2
6.72/2.83			store %8, %x
6.72/2.83			br %3
6.72/2.83		9:
6.72/2.83			ret 0
6.72/2.83	
6.72/2.83	
6.72/2.83	Analyze Termination of all function calls matching the pattern:
6.72/2.83	main()
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(3) LLVMToTerminationGraphProof (EQUIVALENT)
6.72/2.83	Constructed symbolic execution graph for LLVM program and proved memory safety.
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(4)
6.72/2.83	Obligation:
6.72/2.83	SE Graph
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(5) SymbolicExecutionGraphToSCCProof (SOUND)
6.72/2.83	Splitted symbolic execution graph to 1 SCC.
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(6)
6.72/2.83	Obligation:
6.72/2.83	SCC
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(7) SCC2IRS (SOUND)
6.72/2.83	Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
6.72/2.83	Generated rules. Obtained 9 rulesP rules:
6.72/2.83	f_75(v11, v12, v13, v16, 1, v14, v17, v18, 0, 3, 2, 4) -> f_76(v11, v12, v13, v16, 1, v14, v17, v18, 0, 3, 2, 4) :|: 0 < v16
6.72/2.83	f_76(v11, v12, v13, v16, 1, v14, v17, v18, 0, 3, 2, 4) -> f_78(v11, v12, v13, v16, 1, v14, v17, v18, 0, 3, 2, 4) :|: 0 = 0
6.72/2.83	f_78(v11, v12, v13, v16, 1, v14, v17, v18, 0, 3, 2, 4) -> f_80(v11, v12, v13, v16, 1, v14, v17, v18, 0, 3, 2, 4) :|: TRUE
6.72/2.83	f_80(v11, v12, v13, v16, 1, v14, v17, v18, 0, 3, 2, 4) -> f_82(v11, v12, v13, v16, 1, v17, v18, 0, 3, 4) :|: 0 = 0
6.72/2.83	f_82(v11, v12, v13, v16, 1, v17, v18, 0, 3, 4) -> f_83(v11, v12, v13, v16, 1, v20, v17, v18, 0, 3, 2, 4) :|: v20 = v16 / 2
6.72/2.83	f_83(v11, v12, v13, v16, 1, v20, v17, v18, 0, 3, 2, 4) -> f_84(v11, v12, v13, v16, 1, v20, v17, v18, 0, 3, 2, 4) :|: TRUE
6.72/2.83	f_84(v11, v12, v13, v16, 1, v20, v17, v18, 0, 3, 2, 4) -> f_85(v11, v12, v13, v16, 1, v20, v17, v18, 0, 3, 2, 4) :|: TRUE
6.72/2.83	f_85(v11, v12, v13, v16, 1, v20, v17, v18, 0, 3, 2, 4) -> f_74(v11, v12, v13, v16, 1, v20, v17, v18, 0, 3, 2, 4) :|: TRUE
6.72/2.83	f_74(v11, v12, v13, v14, 1, v16, v17, v18, 0, 3, 2, 4) -> f_75(v11, v12, v13, v16, 1, v14, v17, v18, 0, 3, 2, 4) :|: 0 = 0
6.72/2.83	Combined rules. Obtained 1 rulesP rules:
6.72/2.83	f_75(v11:0, v12:0, v13:0, v16:0, 1, v14:0, v17:0, v18:0, 0, 3, 2, 4) -> f_75(v11:0, v12:0, v13:0, v20:0, 1, v16:0, v17:0, v18:0, 0, 3, 2, 4) :|: v20:0 = v16:0 / 2 && v16:0 > 0
6.72/2.83	Filtered unneeded arguments:
6.72/2.83	   f_75(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f_75(x4)
6.72/2.83	Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
6.72/2.83	f_75(v16:0) -> f_75'(v16:0) :|: v16:0 > 0
6.72/2.83	f_75'(v16:0) -> f_75(div) :|: v16:0 > 0 && v16:0 - 2 * div < 2 && v16:0 - 2 * div >= 0
6.72/2.83	
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(8)
6.72/2.83	Obligation:
6.72/2.83	Rules:
6.72/2.83	f_75(v16:0) -> f_75'(v16:0) :|: v16:0 > 0
6.72/2.83	f_75'(x) -> f_75(x1) :|: x > 0 && x - 2 * x1 < 2 && x - 2 * x1 >= 0
6.72/2.83	
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(9) IntTRSCompressionProof (EQUIVALENT)
6.72/2.83	Compressed rules.
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(10)
6.72/2.83	Obligation:
6.72/2.83	Rules:
6.72/2.83	f_75(v16:0:0) -> f_75(x1:0) :|: v16:0:0 - 2 * x1:0 >= 0 && v16:0:0 - 2 * x1:0 < 2 && v16:0:0 > 0
6.72/2.83	
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(11) RankingReductionPairProof (EQUIVALENT)
6.72/2.83	Interpretation:
6.72/2.83	[ f_75 ] = 2*f_75_1
6.72/2.83	
6.72/2.83	The following rules are decreasing:
6.72/2.83	f_75(v16:0:0) -> f_75(x1:0) :|: v16:0:0 - 2 * x1:0 >= 0 && v16:0:0 - 2 * x1:0 < 2 && v16:0:0 > 0
6.72/2.83	
6.72/2.83	The following rules are bounded:
6.72/2.83	f_75(v16:0:0) -> f_75(x1:0) :|: v16:0:0 - 2 * x1:0 >= 0 && v16:0:0 - 2 * x1:0 < 2 && v16:0:0 > 0
6.72/2.83	
6.72/2.83	
6.72/2.83	----------------------------------------
6.72/2.83	
6.72/2.83	(12)
6.72/2.83	YES
6.72/2.86	EOF