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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 175 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 5236 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 172 ms]
(8) IntTRS
(9) IRS2T2 [EQUIVALENT, 0 ms]
(10) T2IntSys
(11) T2 [EQUIVALENT, 1020 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: "__VERIFIER_error" returnParam: BasicVoidType parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc
*BasicFunctionTypename: "fibonacci" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (n i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		store %n, %2
		%3 = load %2
		%4 = icmp slt %3 1
		br %4, %5, %6
	5:
		store 0, %1
		br %18
	6:
		%7 = load %2
		%8 = icmp eq %7 1
		br %8, %9, %10
	9:
		store 1, %1
		br %18
	10:
		%11 = load %2
		%12 = sub %11 1
		%13 = call i32 @fibonacci(i32 %12)
		%14 = load %2
		%15 = sub %14 2
		%16 = call i32 @fibonacci(i32 %15)
		%17 = add %13 %16
		store %17, %1
		br %18
	18:
		%19 = load %1
		ret %19

*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
		%result = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %x
		%3 = load %x
		%4 = icmp slt %3 1
		br %4, %5, %6
	5:
		store 0, %1
		br %14
	6:
		%7 = load %x
		%8 = call i32 @fibonacci(i32 %7)
		store %8, %result
		%9 = load %result
		%10 = icmp sge %9 1
		br %10, %11, %12
	11:
		store 0, %1
		br %14
	12:
		br %13
	13:
		Unnamed Call-Instruction = call BasicVoidType (...)* @__VERIFIER_error() noreturn
		unreachable
	14:
		%15 = load %1
		ret %15


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) 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 48 rulesP rules:
f_255(v97, v106, v98, v99, v100, v101, v102, v103, v107, 0, v105, 3, 1, 4) -> f_256(v97, v106, v108, v98, v99, v100, v101, v102, v103, v107, v109, 0, v105, 3, 1, 4) :|: 1 <= v108 && v109 = 3 + v108 && 4 <= v109
f_256(v97, v106, v108, v98, v99, v100, v101, v102, v103, v107, v109, 0, v105, 3, 1, 4) -> f_257(v97, v106, v108, v98, v99, v100, v101, v102, v103, v107, v109, 0, v105, 3, 1, 4) :|: TRUE
f_257(v97, v106, v108, v98, v99, v100, v101, v102, v103, v107, v109, 0, v105, 3, 1, 4) -> f_258(v97, v106, v108, v98, v99, v100, v101, v102, v103, v107, v109, 0, v105, 3, 1, 4) :|: 0 = 0
f_258(v97, v106, v108, v98, v99, v100, v101, v102, v103, v107, v109, 0, v105, 3, 1, 4) -> f_260(v97, v106, v108, v98, v99, v100, v101, v102, v103, v107, v109, 0, v105, 3, 1, 4) :|: 1 <= v97
f_260(v97, v106, v108, v98, v99, v100, v101, v102, v103, v107, v109, 0, v105, 3, 1, 4) -> f_262(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 4) :|: 0 = 0
f_262(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 4) -> f_264(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 4) :|: TRUE
f_264(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 4) -> f_266(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 4) :|: 0 = 0
f_266(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 4) -> f_269(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 2, 1, 4) :|: v97 != 1 && 2 <= v97 && 2 <= v105
f_269(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 2, 1, 4) -> f_272(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 2, 1, 4) :|: 0 = 0
f_272(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 2, 1, 4) -> f_275(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 2, 1, 4) :|: TRUE
f_275(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 2, 1, 4) -> f_277(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 2, 1, 4) :|: 0 = 0
f_277(v97, v106, v108, 0, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 2, 1, 4) -> f_279(v97, v106, v108, 0, v122, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 1 + v122 = v97 && 1 <= v122
f_279(v97, v106, v108, 0, v122, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_281(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: 0 = 0
f_281(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_283(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: TRUE
f_281(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_287(1, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, 2, 3, 4) :|: TRUE
f_281(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_616(v122, v1212, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: TRUE
f_281(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_643(v122, v1309, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: TRUE
f_281(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_680(v122, v1439, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: TRUE
f_281(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_717(v122, v1439, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: TRUE
f_281(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_737(v122, v1439, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: TRUE
f_283(v122, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_254(v122, v98, v99, v100, v101, v102, v103, 0, v105, 3, 1, 4) :|: TRUE
f_254(v97, v98, v99, v100, v101, v102, v103, 0, v105, 3, 1, 4) -> f_255(v97, v106, v98, v99, v100, v101, v102, v103, v107, 0, v105, 3, 1, 4) :|: 1 <= v106 && v107 = 3 + v106 && 4 <= v107
f_287(1, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, 2, 3, 4) -> f_289(2, v106, v108, 0, 1, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 4) :|: 0 = 0
f_289(2, v106, v108, 0, 1, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 4) -> f_291(2, v106, v108, 0, 1, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 4) :|: 0 = 0
f_291(2, v106, v108, 0, 1, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 4) -> f_293(2, v106, v108, 0, 1, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 4) :|: 0 = 0
f_293(2, v106, v108, 0, 1, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 4) -> f_295(0, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, v105, 2, 1, 3, 4) :|: 0 = 0
f_295(0, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, v105, 2, 1, 3, 4) -> f_297(0, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, v105, 2, 3, 1, 4) :|: TRUE
f_297(0, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, v105, 2, 3, 1, 4) -> f_254(0, v98, v99, v100, v101, v102, v103, 0, v105, 3, 1, 4) :|: TRUE
f_616(v122, v1212, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_623(v97, v106, v108, 0, v122, v1212, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 0 = 0
f_623(v97, v106, v108, 0, v122, v1212, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_626(v97, v106, v108, 0, v122, v1212, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 0 = 0
f_626(v97, v106, v108, 0, v122, v1212, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_629(v97, v106, v108, 0, v122, v1212, v1227, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 2 + v1227 = v97 && 0 <= v1227
f_629(v97, v106, v108, 0, v122, v1212, v1227, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_632(v1227, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, v122, v1212, 3, 1, 2, 4) :|: 0 = 0
f_632(v1227, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, v122, v1212, 3, 1, 2, 4) -> f_635(v1227, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 2, 1, 4) :|: TRUE
f_635(v1227, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 2, 1, 4) -> f_254(v1227, v98, v99, v100, v101, v102, v103, 0, v105, 3, 1, 4) :|: TRUE
f_643(v122, v1309, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_650(v97, v106, v108, 0, v122, v1309, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 0 = 0
f_650(v97, v106, v108, 0, v122, v1309, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_656(v97, v106, v108, 0, v122, v1309, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 0 = 0
f_656(v97, v106, v108, 0, v122, v1309, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_662(v97, v106, v108, 0, v122, v1309, v1329, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 2 + v1329 = v97 && 0 <= v1329
f_662(v97, v106, v108, 0, v122, v1309, v1329, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_668(v1329, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, v122, v1309, 3, 1, 2, 4) :|: 0 = 0
f_668(v1329, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, v122, v1309, 3, 1, 2, 4) -> f_674(v1329, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 2, 1, 4) :|: TRUE
f_674(v1329, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 2, 1, 4) -> f_254(v1329, v98, v99, v100, v101, v102, v103, 0, v105, 3, 1, 4) :|: TRUE
f_680(v122, v1439, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_687(v97, v106, v108, 0, v122, v1439, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 0 = 0
f_687(v97, v106, v108, 0, v122, v1439, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_694(v97, v106, v108, 0, v122, v1439, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 0 = 0
f_694(v97, v106, v108, 0, v122, v1439, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_701(v97, v106, v108, 0, v122, v1439, v1499, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) :|: 2 + v1499 = v97 && 0 <= v1499
f_701(v97, v106, v108, 0, v122, v1439, v1499, v98, v99, v100, v101, v102, v103, v107, v109, v105, 3, 1, 2, 4) -> f_708(v1499, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, v122, v1439, 3, 1, 2, 4) :|: 0 = 0
f_708(v1499, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, v122, v1439, 3, 1, 2, 4) -> f_715(v1499, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 2, 1, 4) :|: TRUE
f_715(v1499, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 2, 1, 4) -> f_254(v1499, v98, v99, v100, v101, v102, v103, 0, v105, 3, 1, 4) :|: TRUE
f_717(v122, v1439, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_680(v122, v1439, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: TRUE
f_737(v122, v1439, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) -> f_717(v122, v1439, v98, v99, v100, v101, v102, v103, v106, v107, v108, v109, 0, v105, v97, 3, 1, 2, 4) :|: TRUE
Combined rules. Obtained 3 rulesP rules:
f_255(2 + v1499:0, v106:0, v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, v107:0, 0, v105:0, 3, 1, 4) -> f_255(v1499:0, v106:1, v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, 3 + v106:1, 0, v105:0, 3, 1, 4) :|: v1499:0 > -1 && v108:0 > 0 && v105:0 > 1 && v122:0 > 0 && 2 + v1499:0 = 1 + v122:0 && v106:1 > 0
f_255(1 + v122:0, v106:0, v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, v107:0, 0, v105:0, 3, 1, 4) -> f_255(v122:0, v106:1, v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, 3 + v106:1, 0, v105:0, 3, 1, 4) :|: v122:0 > 0 && v108:0 > 0 && v105:0 > 1 && v106:1 > 0
f_255(1 + v122:0, v106:0, v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, v107:0, 0, v105:0, 3, 1, 4) -> f_255(0, v106:1, v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, 3 + v106:1, 0, v105:0, 3, 1, 4) :|: v122:0 > 0 && v108:0 > 0 && v105:0 > 1 && v106:1 > 0
Filtered unneeded arguments:
   f_255(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f_255(x1, x11)
Removed division, modulo operations, cleaned up constraints. Obtained 3 rules.P rules:
f_255(sum~cons_2~v1499:0, v105:0) -> f_255(v1499:0, v105:0) :|: v1499:0 > -1 && v105:0 > 1 && sum~cons_2~v1499:0 = 2 + v1499:0
f_255(sum~cons_1~v122:0, v105:0) -> f_255(v122:0, v105:0) :|: v122:0 > 0 && v105:0 > 1 && sum~cons_1~v122:0 = 1 + v122:0
f_255(sum~cons_1~v122:0, v105:0) -> f_255(0, v105:0) :|: v122:0 > 0 && v105:0 > 1 && sum~cons_1~v122:0 = 1 + v122:0

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

(8)
Obligation:
Rules:
f_255(sum~cons_2~v1499:0, v105:0) -> f_255(v1499:0, v105:0) :|: v1499:0 > -1 && v105:0 > 1 && sum~cons_2~v1499:0 = 2 + v1499:0
f_255(x, x1) -> f_255(x2, x1) :|: x2 > 0 && x1 > 1 && x = 1 + x2
f_255(x3, x4) -> f_255(0, x4) :|: x5 > 0 && x4 > 1 && x3 = 1 + x5

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

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

   (f_255_2,1)

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

(10)
Obligation:
START: 0;

FROM: 0;
TO: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := oldX0 - 2;
assume(oldX2 > -1 && oldX1 > 1 && oldX0 = 2 + oldX2);
x0 := oldX0 - 2;
x1 := oldX1;
TO: 1;

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

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


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

(11) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 1, 4, 5, 6 using the following rank functions:
    - Rank function 1:
      RF for loc. 5: 1+2*x0
      RF for loc. 6: 2*x0
      Bound for (chained) transitions 4: 4
      Bound for (chained) transitions 5: 4
      Bound for (chained) transitions 6: 4
    - Rank function 2:
      RF for loc. 5: 1
      RF for loc. 6: 0
      Bound for (chained) transitions 1: 1

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

(12)
YES