18.88/16.79	YES
18.98/16.82	proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
18.98/16.82	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
18.98/16.82	
18.98/16.82	
18.98/16.82	Termination of the given C Problem could be proven:
18.98/16.82	
18.98/16.82	(0) C Problem
18.98/16.82	(1) CToLLVMProof [EQUIVALENT, 184 ms]
18.98/16.82	(2) LLVM problem
18.98/16.82	(3) LLVMToTerminationGraphProof [EQUIVALENT, 2275 ms]
18.98/16.82	(4) LLVM Symbolic Execution Graph
18.98/16.82	(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
18.98/16.82	(6) LLVM Symbolic Execution SCC
18.98/16.82	(7) SCC2IRS [SOUND, 84 ms]
18.98/16.82	(8) IntTRS
18.98/16.82	(9) TerminationGraphProcessor [EQUIVALENT, 30 ms]
18.98/16.82	(10) IntTRS
18.98/16.82	(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
18.98/16.82	(12) IntTRS
18.98/16.82	(13) RankingReductionPairProof [EQUIVALENT, 9 ms]
18.98/16.82	(14) YES
18.98/16.82	
18.98/16.82	
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(0)
18.98/16.82	Obligation:
18.98/16.82	c file /export/starexec/sandbox2/benchmark/theBenchmark.c
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(1) CToLLVMProof (EQUIVALENT)
18.98/16.82	Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM.
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(2)
18.98/16.82	Obligation:
18.98/16.82	LLVM Problem
18.98/16.82	
18.98/16.82	Aliases:
18.98/16.82	
18.98/16.82	Data layout:
18.98/16.82	
18.98/16.82	"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"
18.98/16.82	
18.98/16.82	Machine:
18.98/16.82	
18.98/16.82	"x86_64-pc-linux-gnu"
18.98/16.82	
18.98/16.82	Type definitions:
18.98/16.82	
18.98/16.82	Global variables:
18.98/16.82	
18.98/16.82	Function declarations and definitions:
18.98/16.82	
18.98/16.82	*BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc
18.98/16.82	*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
18.98/16.82		0:
18.98/16.82			%1 = alloca i32, align 4
18.98/16.82			%x = alloca i32, align 4
18.98/16.82			%y = alloca i32, align 4
18.98/16.82			%z = alloca i32, align 4
18.98/16.82			store 0, %1
18.98/16.82			%2 = call i32 (...)* @__VERIFIER_nondet_int()
18.98/16.82			store %2, %x
18.98/16.82			%3 = call i32 (...)* @__VERIFIER_nondet_int()
18.98/16.82			store %3, %y
18.98/16.82			%4 = call i32 (...)* @__VERIFIER_nondet_int()
18.98/16.82			store %4, %z
18.98/16.82			br %5
18.98/16.82		5:
18.98/16.82			%6 = load %x
18.98/16.82			%7 = load %y
18.98/16.82			%8 = add %6 %7
18.98/16.82			%9 = icmp sge %8 0
18.98/16.82			br %9, %10, %14
18.98/16.82		10:
18.98/16.82			%11 = load %x
18.98/16.82			%12 = load %z
18.98/16.82			%13 = icmp sle %11 %12
18.98/16.82			br %14
18.98/16.82		14:
18.98/16.82			%15 = phi [0, %5], [%13, %10]
18.98/16.82			br %15, %16, %23
18.98/16.82		16:
18.98/16.82			%17 = load %x
18.98/16.82			%18 = mul 2 %17
18.98/16.82			%19 = load %y
18.98/16.82			%20 = add %18 %19
18.98/16.82			store %20, %x
18.98/16.82			%21 = load %y
18.98/16.82			%22 = add %21 1
18.98/16.82			store %22, %y
18.98/16.82			br %5
18.98/16.82		23:
18.98/16.82			ret 0
18.98/16.82	
18.98/16.82	
18.98/16.82	Analyze Termination of all function calls matching the pattern:
18.98/16.82	main()
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(3) LLVMToTerminationGraphProof (EQUIVALENT)
18.98/16.82	Constructed symbolic execution graph for LLVM program and proved memory safety.
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(4)
18.98/16.82	Obligation:
18.98/16.82	SE Graph
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(5) SymbolicExecutionGraphToSCCProof (SOUND)
18.98/16.82	Splitted symbolic execution graph to 1 SCC.
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(6)
18.98/16.82	Obligation:
18.98/16.82	SCC
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(7) SCC2IRS (SOUND)
18.98/16.82	Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
18.98/16.82	Generated rules. Obtained 22 rulesP rules:
18.98/16.82	f_204(v284, v285, v286, v287, v288, v289, v290, v296, v292, v293, 1, v291, v295, v297, v298, v299, v300, v301, 0, 3, 2, 4) -> f_205(v284, v285, v286, v287, v288, v289, v290, v296, v297, v293, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	f_205(v284, v285, v286, v287, v288, v289, v290, v296, v297, v293, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_206(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: v303 = v296 + v297
18.98/16.82	f_206(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_207(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 <= v303
18.98/16.82	f_207(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_209(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	f_209(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_211(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: TRUE
18.98/16.82	f_211(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_213(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	f_213(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_215(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	f_215(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_216(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: v296 <= v290
18.98/16.82	f_216(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_218(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	f_218(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_220(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	f_220(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_222(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: TRUE
18.98/16.82	f_222(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v291, v295, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_224(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v295, v292, v298, v299, v300, v301, 0, 3, 4) :|: 0 = 0
18.98/16.82	f_224(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v295, v292, v298, v299, v300, v301, 0, 3, 4) -> f_225(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: v406 = 2 * v296
18.98/16.82	f_225(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_226(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	f_226(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_227(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: v407 = v406 + v297
18.98/16.82	f_227(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_228(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v292, v298, v299, v300, v301, 0, 3, 2, 4) :|: TRUE
18.98/16.82	f_228(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v292, v298, v299, v300, v301, 0, 3, 2, 4) -> f_229(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	f_229(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v298, v299, v300, v301, 0, 3, 2, 4) -> f_230(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v409, v298, v299, v300, v301, 0, 3, 2, 4) :|: v409 = 1 + v297
18.98/16.82	f_230(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v409, v298, v299, v300, v301, 0, 3, 2, 4) -> f_231(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v409, v298, v299, v300, v301, 0, 3, 2, 4) :|: TRUE
18.98/16.82	f_231(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v409, v298, v299, v300, v301, 0, 3, 2, 4) -> f_232(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v409, v298, v299, v300, v301, 0, 3, 2, 4) :|: TRUE
18.98/16.82	f_232(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v409, v298, v299, v300, v301, 0, 3, 2, 4) -> f_203(v284, v285, v286, v287, v288, v289, v290, v296, v297, v303, 1, v406, v407, v409, v298, v299, v300, v301, 0, 3, 2, 4) :|: TRUE
18.98/16.82	f_203(v284, v285, v286, v287, v288, v289, v290, v291, v292, v293, 1, v295, v296, v297, v298, v299, v300, v301, 0, 3, 2, 4) -> f_204(v284, v285, v286, v287, v288, v289, v290, v296, v292, v293, 1, v291, v295, v297, v298, v299, v300, v301, 0, 3, 2, 4) :|: 0 = 0
18.98/16.82	Combined rules. Obtained 1 rulesP rules:
18.98/16.82	f_204(v284:0, v285:0, v286:0, v287:0, v288:0, v289:0, v290:0, v296:0, v292:0, v293:0, 1, v291:0, v295:0, v297:0, v298:0, v299:0, v300:0, v301:0, 0, 3, 2, 4) -> f_204(v284:0, v285:0, v286:0, v287:0, v288:0, v289:0, v290:0, 2 * v296:0 + v297:0, v297:0, v296:0 + v297:0, 1, v296:0, 2 * v296:0, 1 + v297:0, v298:0, v299:0, v300:0, v301:0, 0, 3, 2, 4) :|: v296:0 <= v290:0 && v296:0 + v297:0 > -1
18.98/16.82	Filtered unneeded arguments:
18.98/16.82	   f_204(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f_204(x7, x8, x14)
18.98/16.82	Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
18.98/16.82	f_204(v290:0, v296:0, v297:0) -> f_204(v290:0, 2 * v296:0 + v297:0, 1 + v297:0) :|: v296:0 <= v290:0 && v296:0 + v297:0 > -1
18.98/16.82	
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(8)
18.98/16.82	Obligation:
18.98/16.82	Rules:
18.98/16.82	f_204(v290:0, v296:0, v297:0) -> f_204(v290:0, 2 * v296:0 + v297:0, 1 + v297:0) :|: v296:0 <= v290:0 && v296:0 + v297:0 > -1
18.98/16.82	
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(9) TerminationGraphProcessor (EQUIVALENT)
18.98/16.82	Constructed the termination graph and obtained one non-trivial SCC.
18.98/16.82	
18.98/16.82	f_204(v290:0, v296:0, v297:0) -> f_204(v290:0, 2 * v296:0 + v297:0, 1 + v297:0) :|: v296:0 <= v290:0 && v296:0 + v297:0 > -1
18.98/16.82	has been transformed into
18.98/16.82	f_204(v290:0, v296:0, v297:0) -> f_204(v290:0, 2 * v296:0 + v297:0, 1 + v297:0) :|: v297:0 = 1 + x8 && (v296:0 = 2 * x7 + x8 && (v290:0 = x6 && (v296:0 <= v290:0 && v296:0 + v297:0 > -1))) && x7 <= x6 && x7 + x8 > -1.
18.98/16.82	
18.98/16.82	
18.98/16.82	f_204(v290:0, v296:0, v297:0) -> f_204(v290:0, 2 * v296:0 + v297:0, 1 + v297:0) :|: v297:0 = 1 + x8 && (v296:0 = 2 * x7 + x8 && (v290:0 = x6 && (v296:0 <= v290:0 && v296:0 + v297:0 > -1))) && x7 <= x6 && x7 + x8 > -1 and 
18.98/16.82	f_204(v290:0, v296:0, v297:0) -> f_204(v290:0, 2 * v296:0 + v297:0, 1 + v297:0) :|: v297:0 = 1 + x8 && (v296:0 = 2 * x7 + x8 && (v290:0 = x6 && (v296:0 <= v290:0 && v296:0 + v297:0 > -1))) && x7 <= x6 && x7 + x8 > -1
18.98/16.82	have been merged into the new rule
18.98/16.82	f_204(x21, x22, x23) -> f_204(x21, 2 * (2 * x22 + x23) + (1 + x23), 1 + (1 + x23)) :|: x23 = 1 + x24 && (x22 = 2 * x25 + x24 && (x21 = x26 && (x22 <= x21 && x22 + x23 > -1))) && x25 <= x26 && x25 + x24 > -1 && (1 + x23 = 1 + x27 && (2 * x22 + x23 = 2 * x28 + x27 && (x21 = x29 && (2 * x22 + x23 <= x21 && 2 * x22 + x23 + (1 + x23) > -1))) && x28 <= x29 && x28 + x27 > -1)
18.98/16.82	
18.98/16.82	
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(10)
18.98/16.82	Obligation:
18.98/16.82	Rules:
18.98/16.82	f_204(x30, x31, x32) -> f_204(x30, 4 * x31 + 3 * x32 + 1, 2 + x32) :|: TRUE && x32 + -1 * x33 = 1 && x31 + -2 * x34 + -1 * x33 = 0 && x30 + -1 * x35 = 0 && x31 + -1 * x30 <= 0 && x31 + x32 >= 0 && x34 + -1 * x35 <= 0 && x34 + x33 >= 0 && x32 + -1 * x36 = 0 && 2 * x31 + x32 + -2 * x37 + -1 * x36 = 0 && x30 + -1 * x38 = 0 && 2 * x31 + x32 + -1 * x30 <= 0 && x37 + -1 * x38 <= 0 && x37 + x36 >= 0
18.98/16.82	
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(11) IntTRSCompressionProof (EQUIVALENT)
18.98/16.82	Compressed rules.
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(12)
18.98/16.82	Obligation:
18.98/16.82	Rules:
18.98/16.82	f_204(x30:0, x31:0, x32:0) -> f_204(x30:0, 4 * x31:0 + 3 * x32:0 + 1, 2 + x32:0) :|: x37:0 + -1 * x38:0 <= 0 && x37:0 + x36:0 >= 0 && 2 * x31:0 + x32:0 + -1 * x30:0 <= 0 && x30:0 + -1 * x38:0 = 0 && 2 * x31:0 + x32:0 + -2 * x37:0 + -1 * x36:0 = 0 && x32:0 + -1 * x36:0 = 0 && x34:0 + x33:0 >= 0 && x34:0 + -1 * x35:0 <= 0 && x31:0 + x32:0 >= 0 && x31:0 + -1 * x30:0 <= 0 && x30:0 + -1 * x35:0 = 0 && x32:0 + -1 * x33:0 = 1 && x31:0 + -2 * x34:0 + -1 * x33:0 = 0
18.98/16.82	
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(13) RankingReductionPairProof (EQUIVALENT)
18.98/16.82	Interpretation:
18.98/16.82	[ f_204 ] = -1/4*f_204_2 + 1/4*f_204_1
18.98/16.82	
18.98/16.82	The following rules are decreasing:
18.98/16.82	f_204(x30:0, x31:0, x32:0) -> f_204(x30:0, 4 * x31:0 + 3 * x32:0 + 1, 2 + x32:0) :|: x37:0 + -1 * x38:0 <= 0 && x37:0 + x36:0 >= 0 && 2 * x31:0 + x32:0 + -1 * x30:0 <= 0 && x30:0 + -1 * x38:0 = 0 && 2 * x31:0 + x32:0 + -2 * x37:0 + -1 * x36:0 = 0 && x32:0 + -1 * x36:0 = 0 && x34:0 + x33:0 >= 0 && x34:0 + -1 * x35:0 <= 0 && x31:0 + x32:0 >= 0 && x31:0 + -1 * x30:0 <= 0 && x30:0 + -1 * x35:0 = 0 && x32:0 + -1 * x33:0 = 1 && x31:0 + -2 * x34:0 + -1 * x33:0 = 0
18.98/16.82	
18.98/16.82	The following rules are bounded:
18.98/16.82	f_204(x30:0, x31:0, x32:0) -> f_204(x30:0, 4 * x31:0 + 3 * x32:0 + 1, 2 + x32:0) :|: x37:0 + -1 * x38:0 <= 0 && x37:0 + x36:0 >= 0 && 2 * x31:0 + x32:0 + -1 * x30:0 <= 0 && x30:0 + -1 * x38:0 = 0 && 2 * x31:0 + x32:0 + -2 * x37:0 + -1 * x36:0 = 0 && x32:0 + -1 * x36:0 = 0 && x34:0 + x33:0 >= 0 && x34:0 + -1 * x35:0 <= 0 && x31:0 + x32:0 >= 0 && x31:0 + -1 * x30:0 <= 0 && x30:0 + -1 * x35:0 = 0 && x32:0 + -1 * x33:0 = 1 && x31:0 + -2 * x34:0 + -1 * x33:0 = 0
18.98/16.82	
18.98/16.82	
18.98/16.82	----------------------------------------
18.98/16.82	
18.98/16.82	(14)
18.98/16.82	YES
19.07/16.95	EOF