/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToLLVMProof [EQUIVALENT, 81 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 1017 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToLassoProof [EQUIVALENT, 0 ms]
(6) LLVM Symbolic Execution Lasso
(7) Lasso2IRS [EQUIVALENT, 81 ms]
(8) IntTRS
(9) IRS2T2 [EQUIVALENT, 0 ms]
(10) T2IntSys
(11) T2 [EQUIVALENT, 1083 ms]
(12) 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
		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 = load %y
		%7 = sub %5 %6
		%8 = icmp sgt %7 0
		br %8, %9, %15
	9:
		%10 = load %y
		%11 = load %x
		%12 = sub %10 %11
		store %12, %x
		%13 = load %y
		%14 = add %13 1
		store %14, %y
		br %4
	15:
		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) SymbolicExecutionGraphToLassoProof (EQUIVALENT)
Converted SEGraph to 1 independent lasso.
----------------------------------------

(6)
Obligation:
Lasso
----------------------------------------

(7) Lasso2IRS (EQUIVALENT)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 40 rulesP rules:
f_135(v41, v42, v43, v44, v45, v50, v47, v48, 1, v46, v51, v52, v53, v54, 0, 3, 4) -> f_136(v41, v42, v43, v44, v45, v50, v51, v48, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: 0 = 0
f_136(v41, v42, v43, v44, v45, v50, v51, v48, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_137(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: v56 + v51 = v50
f_137(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_138(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: 0 < v56
f_138(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_140(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: 0 = 0
f_140(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_142(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: TRUE
f_142(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_144(v41, v42, v43, v44, v45, v50, v51, v56, 1, v46, v47, v52, v53, v54, 0, 3, 4) :|: 0 = 0
f_144(v41, v42, v43, v44, v45, v50, v51, v56, 1, v46, v47, v52, v53, v54, 0, 3, 4) -> f_145(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v52, v53, v54, 0, 3, 4) :|: 0 = 0
f_145(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v52, v53, v54, 0, 3, 4) -> f_146(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v47, v52, v53, v54, 0, 3, 4) :|: v57 + v50 = v51
f_146(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v47, v52, v53, v54, 0, 3, 4) -> f_147(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v47, v52, v53, v54, 0, 3, 4) :|: TRUE
f_147(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v47, v52, v53, v54, 0, 3, 4) -> f_148(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v52, v53, v54, 0, 3, 4) :|: 0 = 0
f_148(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v52, v53, v54, 0, 3, 4) -> f_149(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) :|: v59 = 1 + v51
f_149(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) -> f_150(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) :|: TRUE
f_150(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) -> f_151(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) :|: TRUE
f_151(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) -> f_134(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) :|: TRUE
f_134(v41, v42, v43, v44, v45, v46, v47, v48, 1, v50, v51, v52, v53, v54, 0, 3, 4) -> f_135(v41, v42, v43, v44, v45, v50, v47, v48, 1, v46, v51, v52, v53, v54, 0, 3, 4) :|: 0 = 0
f_72 -> f_73(v1, v2, 3, 1, 4) :|: 1 <= v1 && v2 = 3 + v1 && 4 <= v2
f_73(v1, v2, 3, 1, 4) -> f_74(v1, v3, v2, v4, 3, 1, 4) :|: 1 <= v3 && v4 = 3 + v3 && 4 <= v4
f_74(v1, v3, v2, v4, 3, 1, 4) -> f_75(v1, v3, v5, v2, v4, v6, 3, 1, 4) :|: 1 <= v5 && v6 = 3 + v5 && 4 <= v6
f_75(v1, v3, v5, v2, v4, v6, 3, 1, 4) -> f_76(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_76(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) -> f_77(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_77(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_78(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_78(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_79(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_79(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_80(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_80(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_81(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_81(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_82(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 = 0
f_82(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_83(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 = 0
f_83(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_84(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 1, 4) :|: v11 + v9 = v7
f_84(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 1, 4) -> f_85(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 1, 4) :|: 0 < v11
f_85(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 1, 4) -> f_87(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_87(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) -> f_89(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) :|: TRUE
f_89(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) -> f_91(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_91(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) -> f_92(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_92(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) -> f_93(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) :|: v12 + v7 = v9
f_93(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) -> f_94(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) :|: TRUE
f_94(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) -> f_95(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_95(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) -> f_96(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) :|: v14 = 1 + v9
f_96(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) -> f_97(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) :|: TRUE
f_97(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) -> f_98(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) :|: TRUE
f_98(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) -> f_116(v1, v3, v5, v7, v9, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) :|: TRUE
f_116(v21, v22, v23, v24, v25, v26, v27, v28, 1, v30, v31, v32, v33, v34, 0, 3, 4) -> f_134(v21, v22, v23, v24, v25, v26, v27, v28, 1, v30, v31, v32, v33, v34, 0, 3, 4) :|: TRUE
Combined rules. Obtained 2 rulesP rules:
f_135(v41:0, v42:0, v43:0, v44:0, v45:0, v50:0, v47:0, v48:0, 1, v46:0, v57:0 + v50:0, v52:0, v53:0, v54:0, 0, 3, 4) -> f_135(v41:0, v42:0, v43:0, v44:0, v45:0, v57:0, v57:0 + v50:0, v56:0, 1, v50:0, 1 + (v57:0 + v50:0), v52:0, v53:0, v54:0, 0, 3, 4) :|: v56:0 > 0 && v56:0 + (v57:0 + v50:0) = v50:0
f_72 -> f_135(v1:0, v3:0, v5:0, v7:0, v12:0 + v7:0, v12:0, v12:0 + v7:0, v11:0, 1, v7:0, 1 + (v12:0 + v7:0), 3 + v1:0, 3 + v3:0, 3 + v5:0, 0, 3, 4) :|: v3:0 > 0 && v1:0 > 0 && v5:0 > 0 && v11:0 > 0 && v7:0 = v11:0 + (v12:0 + v7:0)
Filtered unneeded arguments:
   f_135(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_135(x6, x7, x8, x10, x11)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_135(v50:0, v47:0, v48:0, v46:0, sum~v57:0~v50:0) -> f_135(v57:0, v57:0 + v50:0, v56:0, v50:0, 1 + (v57:0 + v50:0)) :|: v56:0 > 0 && v56:0 + (v57:0 + v50:0) = v50:0 && sum~v57:0~v50:0 = v57:0 + v50:0
f_72 -> f_135(v12:0, v12:0 + v7:0, v11:0, v7:0, 1 + (v12:0 + v7:0)) :|: v11:0 > 0 && v7:0 = v11:0 + (v12:0 + v7:0)

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(8)
Obligation:
Rules:
f_135(v50:0, v47:0, v48:0, v46:0, sum~v57:0~v50:0) -> f_135(v57:0, v57:0 + v50:0, v56:0, v50:0, 1 + (v57:0 + v50:0)) :|: v56:0 > 0 && v56:0 + (v57:0 + v50:0) = v50:0 && sum~v57:0~v50:0 = v57:0 + v50:0
f_72 -> f_135(v12:0, v12:0 + v7:0, v11:0, v7:0, 1 + (v12:0 + v7:0)) :|: v11:0 > 0 && v7:0 = v11:0 + (v12:0 + v7:0)
Start term: f_72

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(9) IRS2T2 (EQUIVALENT)
Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs:

   (f_135_5,1)
   (f_72_5,2)

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(10)
Obligation:
START: 2;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := oldX4 - oldX0;
oldX6 := -(oldX5 + oldX0 - oldX0);
assume(oldX6 > 0 && oldX6 + (oldX5 + oldX0) = oldX0 && oldX4 = oldX5 + oldX0);
x0 := oldX4 - oldX0;
x1 := oldX5 + oldX0;
x2 := -(oldX5 + oldX0 - oldX0);
x3 := oldX0;
x4 := 1 + (oldX5 + oldX0);
TO: 1;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
oldX6 := nondet();
oldX7 := nondet();
assume(oldX7 > 0 && oldX6 = oldX7 + (oldX5 + oldX6));
x0 := oldX5;
x1 := oldX5 + oldX6;
x2 := oldX7;
x3 := oldX6;
x4 := 1 + (oldX5 + oldX6);
TO: 1;


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(11) T2 (EQUIVALENT)
No proof given by T2
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(12)
YES