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


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 176 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 991 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 48 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) CaseAnalysis [EQUIVALENT, 14 ms]
(12) AND
    (13) IntTRS
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IntTRS
        (16) RankingReductionPairProof [EQUIVALENT, 4 ms]
        (17) YES
    (18) IntTRS
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES


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(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
----------------------------------------

(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox/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
		store 0, %1
		%2 = call i32 (...)* @__VERIFIER_nondet_int()
		store %2, %x
		%3 = call i32 (...)* @__VERIFIER_nondet_int()
		store %3, %y
		br %4
	4:
		%5 = load %x
		%6 = icmp sgt %5 0
		br %6, %7, %14
	7:
		%8 = load %x
		%9 = load %y
		%10 = mul 2 %9
		%11 = sub %8 %10
		store %11, %x
		%12 = load %y
		%13 = add %12 1
		store %13, %y
		br %4
	14:
		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.
----------------------------------------

(4)
Obligation:
SE Graph
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(5) SymbolicExecutionGraphToSCCProof (SOUND)
Splitted symbolic execution graph to 1 SCC.
----------------------------------------

(6)
Obligation:
SCC
----------------------------------------

(7) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 14 rulesP rules:
f_129(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_130(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: 0 < v50
f_130(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_132(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0
f_132(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_134(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: TRUE
f_134(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_136(v41, v42, v43, v44, v45, v50, 1, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0
f_136(v41, v42, v43, v44, v45, v50, 1, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_137(v41, v42, v43, v44, v45, v50, 1, v51, v49, v48, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0
f_137(v41, v42, v43, v44, v45, v50, 1, v51, v49, v48, v52, v53, v54, 0, 3, 2, 4) -> f_138(v41, v42, v43, v44, v45, v50, 1, v51, v56, v48, v52, v53, v54, 0, 3, 2, 4) :|: v56 = 2 * v51
f_138(v41, v42, v43, v44, v45, v50, 1, v51, v56, v48, v52, v53, v54, 0, 3, 2, 4) -> f_139(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v48, v52, v53, v54, 0, 3, 2, 4) :|: v57 + v56 = v50
f_139(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v48, v52, v53, v54, 0, 3, 2, 4) -> f_140(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v48, v52, v53, v54, 0, 3, 2, 4) :|: TRUE
f_140(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v48, v52, v53, v54, 0, 3, 2, 4) -> f_141(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0
f_141(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v52, v53, v54, 0, 3, 2, 4) -> f_142(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) :|: v59 = 1 + v51
f_142(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) -> f_143(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) :|: TRUE
f_143(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) -> f_144(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) :|: TRUE
f_144(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) -> f_128(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) :|: TRUE
f_128(v41, v42, v43, v44, v45, v46, 1, v48, v49, v50, v51, v52, v53, v54, 0, 3, 2, 4) -> f_129(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_129(v41:0, v42:0, v43:0, v44:0, v45:0, v57:0 + 2 * v51:0, 1, v46:0, v48:0, v49:0, v51:0, v52:0, v53:0, v54:0, 0, 3, 2, 4) -> f_129(v41:0, v42:0, v43:0, v44:0, v45:0, v57:0, 1, v57:0 + 2 * v51:0, v51:0, 2 * v51:0, 1 + v51:0, v52:0, v53:0, v54:0, 0, 3, 2, 4) :|: v57:0 + 2 * v51:0 > 0
Filtered unneeded arguments:
   f_129(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_129(x6, x11)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_129(sum~v57:0~times~cons_2~v51:0, v51:0) -> f_129(v57:0, 1 + v51:0) :|: v57:0 + 2 * v51:0 > 0 && sum~v57:0~times~cons_2~v51:0 = v57:0 + 2 * v51:0

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(8)
Obligation:
Rules:
f_129(sum~v57:0~times~cons_2~v51:0, v51:0) -> f_129(v57:0, 1 + v51:0) :|: v57:0 + 2 * v51:0 > 0 && sum~v57:0~times~cons_2~v51:0 = v57:0 + 2 * v51:0

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

(10)
Obligation:
Rules:
f_129(sum~v57:0:0~times~cons_2~v51:0:0, v51:0:0) -> f_129(v57:0:0, 1 + v51:0:0) :|: v57:0:0 + 2 * v51:0:0 > 0 && sum~v57:0:0~times~cons_2~v51:0:0 = v57:0:0 + 2 * v51:0:0

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(11) CaseAnalysis (EQUIVALENT)
Found the following inductive condition: 
f_129(x, x1): -1 + 6*x1>=0

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(12)
Complex Obligation (AND)

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(13)
Obligation:
Rules:
f_129(sum~v57:0:0~times~cons_2~v51:0:0, v51:0:0) -> f_129(v57:0:0, 1 + v51:0:0) :|: v57:0:0 + 2 * v51:0:0 > 0 && sum~v57:0:0~times~cons_2~v51:0:0 = v57:0:0 + 2 * v51:0:0 && -1 + 6 * v51:0:0 >= 0

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

(15)
Obligation:
Rules:
f_129(sum~v57:0:0:0~times~cons_2~v51:0:0:0, v51:0:0:0) -> f_129(v57:0:0:0, 1 + v51:0:0:0) :|: 6 * v51:0:0:0 >= 1 && v57:0:0:0 + 2 * v51:0:0:0 > 0 && sum~v57:0:0:0~times~cons_2~v51:0:0:0 = v57:0:0:0 + 2 * v51:0:0:0

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(16) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_129 ] = 1/2*f_129_1

The following rules are decreasing:
f_129(sum~v57:0:0:0~times~cons_2~v51:0:0:0, v51:0:0:0) -> f_129(v57:0:0:0, 1 + v51:0:0:0) :|: 6 * v51:0:0:0 >= 1 && v57:0:0:0 + 2 * v51:0:0:0 > 0 && sum~v57:0:0:0~times~cons_2~v51:0:0:0 = v57:0:0:0 + 2 * v51:0:0:0

The following rules are bounded:
f_129(sum~v57:0:0:0~times~cons_2~v51:0:0:0, v51:0:0:0) -> f_129(v57:0:0:0, 1 + v51:0:0:0) :|: 6 * v51:0:0:0 >= 1 && v57:0:0:0 + 2 * v51:0:0:0 > 0 && sum~v57:0:0:0~times~cons_2~v51:0:0:0 = v57:0:0:0 + 2 * v51:0:0:0


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(17)
YES

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(18)
Obligation:
Rules:
f_129(sum~v57:0:0~times~cons_2~v51:0:0, v51:0:0) -> f_129(v57:0:0, 1 + v51:0:0) :|: v57:0:0 + 2 * v51:0:0 > 0 && sum~v57:0:0~times~cons_2~v51:0:0 = v57:0:0 + 2 * v51:0:0 && -1 + 6 * v51:0:0 < 0

----------------------------------------

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

(20)
Obligation:
Rules:
f_129(sum~v57:0:0:0~times~cons_2~v51:0:0:0, v51:0:0:0) -> f_129(v57:0:0:0, 1 + v51:0:0:0) :|: 6 * v51:0:0:0 < 1 && v57:0:0:0 + 2 * v51:0:0:0 > 0 && sum~v57:0:0:0~times~cons_2~v51:0:0:0 = v57:0:0:0 + 2 * v51:0:0:0

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_129(x, x1)] = -x1

The following rules are decreasing:
f_129(sum~v57:0:0:0~times~cons_2~v51:0:0:0, v51:0:0:0) -> f_129(v57:0:0:0, 1 + v51:0:0:0) :|: 6 * v51:0:0:0 < 1 && v57:0:0:0 + 2 * v51:0:0:0 > 0 && sum~v57:0:0:0~times~cons_2~v51:0:0:0 = v57:0:0:0 + 2 * v51:0:0:0
The following rules are bounded:
f_129(sum~v57:0:0:0~times~cons_2~v51:0:0:0, v51:0:0:0) -> f_129(v57:0:0:0, 1 + v51:0:0:0) :|: 6 * v51:0:0:0 < 1 && v57:0:0:0 + 2 * v51:0:0:0 > 0 && sum~v57:0:0:0~times~cons_2~v51:0:0:0 = v57:0:0:0 + 2 * v51:0:0:0

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(22)
YES