/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 790 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToLassoProof [EQUIVALENT, 0 ms]
(6) LLVM Symbolic Execution Lasso
(7) Lasso2IRS [EQUIVALENT, 87 ms]
(8) IntTRS
(9) IRS2T2 [EQUIVALENT, 0 ms]
(10) T2IntSys
(11) T2 [EQUIVALENT, 1283 ms]
(12) YES


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(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
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(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: false 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
		%4 = load %y
		%5 = mul 2 %4
		%6 = icmp slt %5 1
		br %6, %7, %8
	7:
		store 0, %1
		br %19
	8:
		br %9
	9:
		%10 = load %x
		%11 = icmp sge %10 0
		br %11, %12, %18
	12:
		%13 = load %x
		%14 = load %y
		%15 = mul 2 %14
		%16 = sub %13 %15
		%17 = add %16 1
		store %17, %x
		br %9
	18:
		store 0, %1
		br %19
	19:
		%20 = load %1
		ret %20


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.
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(6)
Obligation:
Lasso
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(7) Lasso2IRS (EQUIVALENT)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 38 rulesP rules:
f_146(v21, v22, v23, v24, v25, v26, 0, v31, 1, v28, v30, v32, v33, v34, 3, 2, 4) -> f_147(v21, v22, v23, v24, v25, v26, 0, v31, 1, v28, v30, v32, v33, v34, 3, 2, 4) :|: 0 <= v31 && 0 <= 1 + v30 && 1 <= v28
f_147(v21, v22, v23, v24, v25, v26, 0, v31, 1, v28, v30, v32, v33, v34, 3, 2, 4) -> f_149(v21, v22, v23, v24, v25, v26, 0, v31, 1, v28, v30, v32, v33, v34, 3, 2, 4) :|: 0 = 0
f_149(v21, v22, v23, v24, v25, v26, 0, v31, 1, v28, v30, v32, v33, v34, 3, 2, 4) -> f_151(v21, v22, v23, v24, v25, v26, 0, v31, 1, v28, v30, v32, v33, v34, 3, 2, 4) :|: TRUE
f_151(v21, v22, v23, v24, v25, v26, 0, v31, 1, v28, v30, v32, v33, v34, 3, 2, 4) -> f_153(v21, v22, v23, v24, v25, v26, 0, v31, 1, v30, v32, v33, v34, 3, 2, 4) :|: 0 = 0
f_153(v21, v22, v23, v24, v25, v26, 0, v31, 1, v30, v32, v33, v34, 3, 2, 4) -> f_155(v21, v22, v23, v24, v25, v26, 0, v31, 1, v30, v32, v33, v34, 3, 2, 4) :|: 0 = 0
f_155(v21, v22, v23, v24, v25, v26, 0, v31, 1, v30, v32, v33, v34, 3, 2, 4) -> f_157(v21, v22, v23, v24, v25, v26, 0, v31, 1, v30, v32, v33, v34, 3, 2, 4) :|: v26 = 2 * v25
f_157(v21, v22, v23, v24, v25, v26, 0, v31, 1, v30, v32, v33, v34, 3, 2, 4) -> f_159(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v32, v33, v34, 3, 2, 4) :|: v38 + v26 = v31
f_159(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v32, v33, v34, 3, 2, 4) -> f_160(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v39, v32, v33, v34, 3, 2, 4) :|: v39 = 1 + v38
f_160(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v39, v32, v33, v34, 3, 2, 4) -> f_161(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v39, v32, v33, v34, 3, 2, 4) :|: TRUE
f_161(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v39, v32, v33, v34, 3, 2, 4) -> f_162(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v39, v32, v33, v34, 3, 2, 4) :|: TRUE
f_162(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v39, v32, v33, v34, 3, 2, 4) -> f_145(v21, v22, v23, v24, v25, v26, 0, v31, 1, v38, v39, v32, v33, v34, 3, 2, 4) :|: TRUE
f_145(v21, v22, v23, v24, v25, v26, 0, v28, 1, v30, v31, v32, v33, v34, 3, 2, 4) -> f_146(v21, v22, v23, v24, v25, v26, 0, v31, 1, v28, v30, v32, v33, v34, 3, 2, 4) :|: 0 = 0
f_90 -> f_91(v1, v2, 3, 1, 4) :|: 1 <= v1 && v2 = 3 + v1 && 4 <= v2
f_91(v1, v2, 3, 1, 4) -> f_92(v1, v3, v2, v4, 3, 1, 4) :|: 1 <= v3 && v4 = 3 + v3 && 4 <= v4
f_92(v1, v3, v2, v4, 3, 1, 4) -> f_93(v1, v3, v5, v2, v4, v6, 3, 1, 4) :|: 1 <= v5 && v6 = 3 + v5 && 4 <= v6
f_93(v1, v3, v5, v2, v4, v6, 3, 1, 4) -> f_94(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_94(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) -> f_95(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_95(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_96(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_96(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_97(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_97(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_98(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_98(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_99(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 = 0
f_99(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_100(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 2, 1, 4) :|: v11 = 2 * v9
f_100(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 2, 1, 4) -> f_102(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 2, 1, 4) :|: 1 <= v11 && 2 <= v11 && 1 <= v9
f_102(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 2, 1, 4) -> f_104(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) :|: 0 = 0
f_104(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) -> f_106(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) :|: TRUE
f_106(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) -> f_108(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) :|: TRUE
f_108(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) -> f_110(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) :|: 0 = 0
f_110(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) -> f_112(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) :|: 0 <= v7
f_112(v1, v3, v5, v7, v9, v11, 0, v2, v4, v6, 3, 2, 1, 4) -> f_114(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) :|: 0 = 0
f_114(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) -> f_116(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) :|: TRUE
f_116(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) -> f_118(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) :|: 0 = 0
f_118(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) -> f_120(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) :|: 0 = 0
f_120(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) -> f_122(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) :|: v11 = 2 * v9
f_122(v1, v3, v5, v7, v9, v11, 0, 1, v2, v4, v6, 3, 2, 4) -> f_124(v1, v3, v5, v7, v9, v11, 0, 1, v12, v2, v4, v6, 3, 2, 4) :|: v12 + v11 = v7
f_124(v1, v3, v5, v7, v9, v11, 0, 1, v12, v2, v4, v6, 3, 2, 4) -> f_125(v1, v3, v5, v7, v9, v11, 0, 1, v12, v13, v2, v4, v6, 3, 2, 4) :|: v13 = 1 + v12
f_125(v1, v3, v5, v7, v9, v11, 0, 1, v12, v13, v2, v4, v6, 3, 2, 4) -> f_126(v1, v3, v5, v7, v9, v11, 0, 1, v12, v13, v2, v4, v6, 3, 2, 4) :|: TRUE
f_126(v1, v3, v5, v7, v9, v11, 0, 1, v12, v13, v2, v4, v6, 3, 2, 4) -> f_127(v1, v3, v5, v7, v9, v11, 0, 1, v12, v13, v2, v4, v6, 3, 2, 4) :|: TRUE
f_127(v1, v3, v5, v7, v9, v11, 0, 1, v12, v13, v2, v4, v6, 3, 2, 4) -> f_145(v1, v3, v5, v7, v9, v11, 0, v7, 1, v12, v13, v2, v4, v6, 3, 2, 4) :|: TRUE
Combined rules. Obtained 2 rulesP rules:
f_146(v21:0, v22:0, v23:0, v24:0, v25:0, 2 * v25:0, 0, v38:0 + 2 * v25:0, 1, v28:0, v30:0, v32:0, v33:0, v34:0, 3, 2, 4) -> f_146(v21:0, v22:0, v23:0, v24:0, v25:0, 2 * v25:0, 0, 1 + v38:0, 1, v38:0 + 2 * v25:0, v38:0, v32:0, v33:0, v34:0, 3, 2, 4) :|: v30:0 > -2 && v28:0 > 0 && v38:0 + 2 * v25:0 > -1
f_90 -> f_146(v1:0, v3:0, v5:0, v12:0 + 2 * v9:0, v9:0, 2 * v9:0, 0, 1 + v12:0, 1, v12:0 + 2 * v9:0, v12:0, 3 + v1:0, 3 + v3:0, 3 + v5:0, 3, 2, 4) :|: 2 * v9:0 > 1 && v3:0 > 0 && v1:0 > 0 && v5:0 > 0 && v12:0 + 2 * v9:0 > -1 && v9:0 > 0
Filtered unneeded arguments:
   f_146(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_146(x5, x6, x8, x10, x11)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_146(v25:0, times~cons_2~v25:0, sum~v38:0~times~cons_2~v25:0, v28:0, v30:0) -> f_146(v25:0, 2 * v25:0, 1 + v38:0, v38:0 + 2 * v25:0, v38:0) :|: v28:0 > 0 && v38:0 + 2 * v25:0 > -1 && v30:0 > -2 && times~cons_2~v25:0 = 2 * v25:0 && sum~v38:0~times~cons_2~v25:0 = v38:0 + 2 * v25:0
f_90 -> f_146(v9:0, 2 * v9:0, 1 + v12:0, v12:0 + 2 * v9:0, v12:0) :|: v12:0 + 2 * v9:0 > -1 && v9:0 > 0 && 2 * v9:0 > 1

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(8)
Obligation:
Rules:
f_146(v25:0, times~cons_2~v25:0, sum~v38:0~times~cons_2~v25:0, v28:0, v30:0) -> f_146(v25:0, 2 * v25:0, 1 + v38:0, v38:0 + 2 * v25:0, v38:0) :|: v28:0 > 0 && v38:0 + 2 * v25:0 > -1 && v30:0 > -2 && times~cons_2~v25:0 = 2 * v25:0 && sum~v38:0~times~cons_2~v25:0 = v38:0 + 2 * v25:0
f_90 -> f_146(v9:0, 2 * v9:0, 1 + v12:0, v12:0 + 2 * v9:0, v12:0) :|: v12:0 + 2 * v9:0 > -1 && v9:0 > 0 && 2 * v9:0 > 1
Start term: f_90

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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_146_5,1)
   (f_90_5,2)

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(10)
Obligation:
START: 2;

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

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


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(11) T2 (EQUIVALENT)
Used the following cutpoint-specific lexicographic rank functions:
 * For cutpoint 5, used the following rank functions/bounds (in descending priority order):
    - RF x2, bound 0

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(12)
YES