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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 170 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 684 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToLassoProof [EQUIVALENT, 0 ms]
(6) LLVM Symbolic Execution Lasso
(7) Lasso2IRS [EQUIVALENT, 45 ms]
(8) IntTRS
(9) IRS2T2 [EQUIVALENT, 0 ms]
(10) T2IntSys
(11) T2 [EQUIVALENT, 1373 ms]
(12) YES


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

(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
----------------------------------------

(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM.
----------------------------------------

(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
		br %4
	4:
		%5 = load %x
		%6 = icmp sgt %5 0
		br %6, %7, %11
	7:
		%8 = load %x
		%9 = load %y
		%10 = icmp sgt %8 %9
		br %11
	11:
		%12 = phi [0, %4], [%10, %7]
		br %12, %13, %17
	13:
		%14 = load %y
		%15 = load %x
		%16 = add %14 %15
		store %16, %y
		br %4
	17:
		ret 0


Analyze Termination of all function calls matching the pattern:
main()
----------------------------------------

(3) LLVMToTerminationGraphProof (EQUIVALENT)
Constructed symbolic execution graph for LLVM program and proved memory safety.
----------------------------------------

(4)
Obligation:
SE Graph
----------------------------------------

(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 41 rulesP rules:
f_146(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) -> f_147(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) :|: 0 = 0
f_147(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) -> f_148(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) :|: TRUE
f_148(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) -> f_149(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) :|: 0 = 0
f_149(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) -> f_150(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) :|: 0 = 0
f_150(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) -> f_151(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) :|: v115 < v111 && 1 + v114 <= 0
f_151(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) -> f_153(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) :|: 0 = 0
f_153(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) -> f_155(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) :|: 0 = 0
f_155(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) -> f_157(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) :|: TRUE
f_157(v108, v109, v110, v111, v112, 1, v115, v114, v116, v117, v118, 0, 3, 4) -> f_159(v108, v109, v110, v111, v112, 1, v115, v116, v117, v118, 0, 3, 4) :|: 0 = 0
f_159(v108, v109, v110, v111, v112, 1, v115, v116, v117, v118, 0, 3, 4) -> f_160(v108, v109, v110, v111, v112, 1, v115, v116, v117, v118, 0, 3, 4) :|: 0 = 0
f_160(v108, v109, v110, v111, v112, 1, v115, v116, v117, v118, 0, 3, 4) -> f_161(v108, v109, v110, v111, v112, 1, v115, v153, v116, v117, v118, 0, 3, 4) :|: v153 = v115 + v111
f_161(v108, v109, v110, v111, v112, 1, v115, v153, v116, v117, v118, 0, 3, 4) -> f_162(v108, v109, v110, v111, v112, 1, v115, v153, v116, v117, v118, 0, 3, 4) :|: TRUE
f_162(v108, v109, v110, v111, v112, 1, v115, v153, v116, v117, v118, 0, 3, 4) -> f_163(v108, v109, v110, v111, v112, 1, v115, v153, v116, v117, v118, 0, 3, 4) :|: TRUE
f_163(v108, v109, v110, v111, v112, 1, v115, v153, v116, v117, v118, 0, 3, 4) -> f_145(v108, v109, v110, v111, v112, 1, v115, v153, v116, v117, v118, 0, 3, 4) :|: TRUE
f_145(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) -> f_146(v108, v109, v110, v111, v112, 1, v114, v115, v116, v117, v118, 0, 3, 4) :|: 0 = 0
f_75 -> f_76(v1, v2, 3, 1, 4) :|: 1 <= v1 && v2 = 3 + v1 && 4 <= v2
f_76(v1, v2, 3, 1, 4) -> f_77(v1, v3, v2, v4, 3, 1, 4) :|: 1 <= v3 && v4 = 3 + v3 && 4 <= v4
f_77(v1, v3, v2, v4, 3, 1, 4) -> f_78(v1, v3, v5, v2, v4, v6, 3, 1, 4) :|: 1 <= v5 && v6 = 3 + v5 && 4 <= v6
f_78(v1, v3, v5, v2, v4, v6, 3, 1, 4) -> f_79(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_79(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) -> f_80(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_80(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_81(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_81(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_82(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
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) :|: TRUE
f_83(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_84(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE
f_84(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_85(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 = 0
f_85(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_86(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 < v7
f_86(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_88(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_88(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_90(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: TRUE
f_90(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_92(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_92(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_94(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_94(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_95(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: v9 < v7
f_95(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_97(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_97(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_99(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_99(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_101(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: TRUE
f_101(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_103(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_103(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_104(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0
f_104(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_105(v1, v3, v5, v7, v9, 1, v17, v2, v4, v6, 0, 3, 4) :|: v17 = v9 + v7
f_105(v1, v3, v5, v7, v9, 1, v17, v2, v4, v6, 0, 3, 4) -> f_106(v1, v3, v5, v7, v9, 1, v17, v2, v4, v6, 0, 3, 4) :|: TRUE
f_106(v1, v3, v5, v7, v9, 1, v17, v2, v4, v6, 0, 3, 4) -> f_107(v1, v3, v5, v7, v9, 1, v17, v2, v4, v6, 0, 3, 4) :|: TRUE
f_107(v1, v3, v5, v7, v9, 1, v17, v2, v4, v6, 0, 3, 4) -> f_126(v1, v3, v5, v7, v9, 1, v9, v17, v2, v4, v6, 0, 3, 4) :|: TRUE
f_126(v61, v62, v63, v64, v65, 1, v67, v68, v69, v70, v71, 0, 3, 4) -> f_145(v61, v62, v63, v64, v65, 1, v67, v68, v69, v70, v71, 0, 3, 4) :|: TRUE
Combined rules. Obtained 2 rulesP rules:
f_146(v108:0, v109:0, v110:0, v111:0, v112:0, 1, v114:0, v115:0, v116:0, v117:0, v118:0, 0, 3, 4) -> f_146(v108:0, v109:0, v110:0, v111:0, v112:0, 1, v115:0, v115:0 + v111:0, v116:0, v117:0, v118:0, 0, 3, 4) :|: v115:0 < v111:0 && v114:0 < 0
f_75 -> f_146(v1:0, v3:0, v5:0, v7:0, v9:0, 1, v9:0, v9:0 + v7:0, 3 + v1:0, 3 + v3:0, 3 + v5:0, 0, 3, 4) :|: v3:0 > 0 && v1:0 > 0 && v5:0 > 0 && v9:0 < v7:0 && v7:0 > 0
Filtered unneeded arguments:
   f_146(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f_146(x4, x7, x8)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_146(v111:0, v114:0, v115:0) -> f_146(v111:0, v115:0, v115:0 + v111:0) :|: v115:0 < v111:0 && v114:0 < 0
f_75 -> f_146(v7:0, v9:0, v9:0 + v7:0) :|: v9:0 < v7:0 && v7:0 > 0

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

(8)
Obligation:
Rules:
f_146(v111:0, v114:0, v115:0) -> f_146(v111:0, v115:0, v115:0 + v111:0) :|: v115:0 < v111:0 && v114:0 < 0
f_75 -> f_146(v7:0, v9:0, v9:0 + v7:0) :|: v9:0 < v7:0 && v7:0 > 0
Start term: f_75

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

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

   (f_146_3,1)
   (f_75_3,2)

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

(10)
Obligation:
START: 2;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 < oldX0 && oldX1 < 0);
x0 := oldX0;
x1 := oldX2;
x2 := oldX2 + oldX0;
TO: 1;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
oldX4 := nondet();
assume(oldX4 < oldX3 && oldX3 > 0);
x0 := oldX3;
x1 := oldX4;
x2 := oldX4 + oldX3;
TO: 1;


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

(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+x0, bound 1

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

(12)
YES