/export/starexec/sandbox2/solver/bin/starexec_run_c /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToLLVMProof [EQUIVALENT, 172 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 2188 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 66 ms]
(8) IntTRS
(9) TerminationGraphProcessor [EQUIVALENT, 3 ms]
(10) IntTRS
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IntTRS
(13) RankingReductionPairProof [EQUIVALENT, 6 ms]
(14) YES


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(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
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(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM.
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(2)
Obligation:
LLVM Problem

Aliases:

Data layout:

"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"

Machine:

"x86_64-pc-linux-gnu"

Type definitions:

Global variables:

Function declarations and definitions:

*BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc
*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%x = alloca i32, align 4
		%y = alloca i32, align 4
		%z = alloca i32, align 4
		store 0, %1
		%2 = call i32 (...)* @__VERIFIER_nondet_int()
		store %2, %x
		%3 = call i32 (...)* @__VERIFIER_nondet_int()
		store %3, %y
		%4 = call i32 (...)* @__VERIFIER_nondet_int()
		store %4, %z
		br %5
	5:
		%6 = load %x
		%7 = load %y
		%8 = add %6 %7
		%9 = icmp sge %8 0
		br %9, %10, %14
	10:
		%11 = load %x
		%12 = load %z
		%13 = icmp sle %11 %12
		br %14
	14:
		%15 = phi [0, %5], [%13, %10]
		br %15, %16, %23
	16:
		%17 = load %x
		%18 = mul 2 %17
		%19 = load %y
		%20 = add %18 %19
		store %20, %x
		%21 = load %y
		%22 = add %21 1
		store %22, %y
		br %5
	23:
		ret 0


Analyze Termination of all function calls matching the pattern:
main()
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(3) LLVMToTerminationGraphProof (EQUIVALENT)
Constructed symbolic execution graph for LLVM program and proved memory safety.
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(4)
Obligation:
SE Graph
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(5) SymbolicExecutionGraphToSCCProof (SOUND)
Splitted symbolic execution graph to 1 SCC.
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(6)
Obligation:
SCC
----------------------------------------

(7) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 22 rulesP rules:
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Combined rules. Obtained 1 rulesP rules:
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
Filtered unneeded arguments:
   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)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
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

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(8)
Obligation:
Rules:
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

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(9) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

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
has been transformed into
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.


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 
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
have been merged into the new rule
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)


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(10)
Obligation:
Rules:
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

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(11) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(12)
Obligation:
Rules:
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

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(13) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_204 ] = -1/4*f_204_2 + 1/4*f_204_1

The following rules are decreasing:
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

The following rules are bounded:
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


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(14)
YES