/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 180 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 2357 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 145 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
(12) AND
    (13) IntTRS
        (14) TerminationGraphProcessor [EQUIVALENT, 0 ms]
        (15) YES
    (16) IntTRS
        (17) TerminationGraphProcessor [EQUIVALENT, 0 ms]
        (18) 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: true visibilityType: DEFAULT callingConvention: ccc
*BasicFunctionTypename: "f" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		store %x, %2
		%3 = load %2
		%4 = icmp sle %3 0
		br %4, %5, %6
	5:
		store 0, %1
		br %13
	6:
		%7 = load %2
		%8 = call i32 (...)* @g(i32 %7)
		%9 = load %2
		%10 = add %9 1
		%11 = call i32 (...)* @g(i32 %10)
		%12 = add %8 %11
		store %12, %1
		br %13
	13:
		%14 = load %1
		ret %14

*BasicFunctionTypename: "g" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		store %x, %2
		%3 = load %2
		%4 = icmp sle %3 0
		br %4, %5, %6
	5:
		store 0, %1
		br %14
	6:
		%7 = load %2
		%8 = sub %7 2
		%9 = call i32 @f(i32 %8)
		%10 = load %2
		%11 = sub %10 3
		%12 = call i32 @f(i32 %11)
		%13 = add %9 %12
		store %13, %1
		br %14
	14:
		%15 = load %1
		ret %15

*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
		store 0, %1
		%2 = call i32 (...)* @__VERIFIER_nondet_int()
		store %2, %x
		%3 = load %x
		%4 = call i32 @g(i32 %3)
		%5 = load %1
		ret %5


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 74 rulesP rules:
f_293(v177, v178, v179, 3, 1, 4) -> f_294(v177, v178, v180, v179, v181, 3, 1, 4) :|: 1 <= v180 && v181 = 3 + v180 && 4 <= v181
f_294(v177, v178, v180, v179, v181, 3, 1, 4) -> f_295(v177, v178, v180, v179, v181, 3, 1, 4) :|: TRUE
f_295(v177, v178, v180, v179, v181, 3, 1, 4) -> f_296(v177, v178, v180, v179, v181, 3, 1, 4) :|: 0 = 0
f_296(v177, v178, v180, v179, v181, 3, 1, 4) -> f_298(v177, v178, v180, v179, v181, 3, 1, 4) :|: 0 < v177
f_298(v177, v178, v180, v179, v181, 3, 1, 4) -> f_300(v177, v178, v180, 0, v179, v181, 3, 1, 4) :|: 0 = 0
f_300(v177, v178, v180, 0, v179, v181, 3, 1, 4) -> f_302(v177, v178, v180, 0, v179, v181, 3, 1, 4) :|: TRUE
f_302(v177, v178, v180, 0, v179, v181, 3, 1, 4) -> f_304(v177, v178, v180, 0, v179, v181, 3, 1, 4) :|: 0 = 0
f_304(v177, v178, v180, 0, v179, v181, 3, 1, 4) -> f_306(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 2 + v183 = v177 && 0 <= 1 + v183
f_306(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) :|: 0 = 0
f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_310(v183, v178, v179, v180, v181, v177, 3, 2, 1, 4, 0) :|: TRUE
f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_377(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_484(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_497(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_530(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_553(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
f_310(v183, v178, v179, v180, v181, v177, 3, 2, 1, 4, 0) -> f_336(v183, v178, v179, v180, v181, v177, 3, 2, 0, 1, 4) :|: TRUE
f_336(v211, v212, v213, v214, v215, v216, 3, 2, 0, 1, 4) -> f_360(v211, 0, 2) :|: TRUE
f_360(v239, 0, 2) -> f_361(v239, v240, v241, 3, 0, 2, 1, 4) :|: 1 <= v240 && v241 = 3 + v240 && 4 <= v241
f_361(v239, v240, v241, 3, 0, 2, 1, 4) -> f_362(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) :|: 1 <= v242 && v243 = 3 + v242 && 4 <= v243
f_362(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) -> f_363(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) :|: TRUE
f_363(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) -> f_364(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) :|: 0 = 0
f_364(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) -> f_366(v239, v240, v242, v241, v243, 3, 1, 4) :|: 0 < v239
f_366(v239, v240, v242, v241, v243, 3, 1, 4) -> f_368(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
f_368(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_370(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: TRUE
f_370(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_372(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
f_372(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) :|: 0 = 0
f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_376(v239, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_435(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_470(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_512(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_548(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_567(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
f_376(v239, v240, v241, v242, v243, 3, 1, 4) -> f_291(v239) :|: TRUE
f_291(v177) -> f_293(v177, v178, v179, 3, 1, 4) :|: 1 <= v178 && v179 = 3 + v178 && 4 <= v179
f_435(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_437(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
f_437(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_439(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
f_439(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_440(v239, v240, v242, 0, v348, v241, v243, 3, 1, 4, 2) :|: v348 = 1 + v239 && 2 <= v348
f_440(v239, v240, v242, 0, v348, v241, v243, 3, 1, 4, 2) -> f_441(v348, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) :|: 0 = 0
f_441(v348, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) -> f_442(v348, v240, v241, v242, v243, v239, 3, 1, 4, 2) :|: TRUE
f_442(v348, v240, v241, v242, v243, v239, 3, 1, 4, 2) -> f_291(v348) :|: TRUE
f_470(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_473(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
f_473(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_476(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
f_476(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_478(v239, v240, v242, 0, v424, v241, v243, 3, 1, 4, 2) :|: v424 = 1 + v239 && 2 <= v424
f_478(v239, v240, v242, 0, v424, v241, v243, 3, 1, 4, 2) -> f_480(v424, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) :|: 0 = 0
f_480(v424, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) -> f_482(v424, v240, v241, v242, v243, v239, 3, 1, 4, 2) :|: TRUE
f_482(v424, v240, v241, v242, v243, v239, 3, 1, 4, 2) -> f_291(v424) :|: TRUE
f_512(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_516(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
f_516(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_520(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
f_520(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_523(v239, v240, v242, 0, v520, v241, v243, 3, 1, 4, 2) :|: v520 = 1 + v239 && 2 <= v520
f_523(v239, v240, v242, 0, v520, v241, v243, 3, 1, 4, 2) -> f_526(v520, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) :|: 0 = 0
f_526(v520, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) -> f_529(v520, v240, v241, v242, v243, v239, 3, 1, 4, 2) :|: TRUE
f_529(v520, v240, v241, v242, v243, v239, 3, 1, 4, 2) -> f_291(v520) :|: TRUE
f_548(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_512(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
f_567(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_548(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
f_377(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_378(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
f_378(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_380(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
f_380(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_381(v177, v178, v180, 0, v183, v256, v179, v181, 3, 2, 1, 4) :|: 3 + v256 = v177 && 0 <= 2 + v256 && 1 + v256 <= 0
f_381(v177, v178, v180, 0, v183, v256, v179, v181, 3, 2, 1, 4) -> f_382(v256, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) :|: 0 = 0
f_382(v256, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) -> f_383(v256, v178, v179, v180, v181, v177, 3, 1, 2, 4, 0) :|: TRUE
f_383(v256, v178, v179, v180, v181, v177, 3, 1, 2, 4, 0) -> f_360(v256, 0, 2) :|: TRUE
f_484(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_488(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
f_488(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_490(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
f_490(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_492(v177, v178, v180, 0, v183, v450, v179, v181, 3, 2, 1, 4) :|: 3 + v450 = v177 && 0 <= v450
f_492(v177, v178, v180, 0, v183, v450, v179, v181, 3, 2, 1, 4) -> f_494(v450, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) :|: 0 = 0
f_494(v450, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) -> f_496(v450, v178, v179, v180, v181, v177, 3, 1, 4, 0) :|: TRUE
f_496(v450, v178, v179, v180, v181, v177, 3, 1, 4, 0) -> f_360(v450, 0, 2) :|: TRUE
f_497(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_484(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
f_530(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_533(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
f_533(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_537(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
f_537(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_540(v177, v178, v180, 0, v183, v566, v179, v181, 3, 2, 1, 4) :|: 3 + v566 = v177 && 0 <= v566
f_540(v177, v178, v180, 0, v183, v566, v179, v181, 3, 2, 1, 4) -> f_543(v566, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) :|: 0 = 0
f_543(v566, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) -> f_546(v566, v178, v179, v180, v181, v177, 3, 1, 4, 0) :|: TRUE
f_546(v566, v178, v179, v180, v181, v177, 3, 1, 4, 0) -> f_360(v566, 0, 2) :|: TRUE
f_553(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_530(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
Combined rules. Obtained 4 rulesP rules:
f_374(v239:0, v240:0, v241:0, v242:0, v243:0, 0, 3, 1, 4) -> f_293(1 + v239:0, v178:0, 3 + v178:0, 3, 1, 4) :|: v239:0 > 0 && v178:0 > 0
f_293(3 + v450:0, v178:0, v179:0, 3, 1, 4) -> f_374(v450:0, v240:0, 3 + v240:0, v242:0, 3 + v242:0, 0, 3, 1, 4) :|: v450:0 > 0 && v180:0 > 0 && v240:0 > 0 && v242:0 > 0 && 3 + v450:0 = 2 + v183:0 && v183:0 > -2
f_374(v239:0, v240:0, v241:0, v242:0, v243:0, 0, 3, 1, 4) -> f_293(v239:0, v178:0, 3 + v178:0, 3, 1, 4) :|: v178:0 > 0
f_293(2 + v183:0, v178:0, v179:0, 3, 1, 4) -> f_374(v183:0, v240:0, 3 + v240:0, v242:0, 3 + v242:0, 0, 3, 1, 4) :|: v183:0 > 0 && v180:0 > 0 && v240:0 > 0 && v242:0 > 0
Filtered unneeded arguments:
   f_374(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f_374(x1)
   f_293(x1, x2, x3, x4, x5, x6) -> f_293(x1)
Removed division, modulo operations, cleaned up constraints. Obtained 4 rules.P rules:
f_374(v239:0) -> f_293(1 + v239:0) :|: v239:0 > 0
f_293(sum~cons_3~v450:0) -> f_374(v450:0) :|: v450:0 > 0 && sum~cons_3~v450:0 = 3 + v450:0
f_374(v239:0) -> f_293(v239:0) :|: TRUE
f_293(sum~cons_2~v183:0) -> f_374(v183:0) :|: v183:0 > 0 && sum~cons_2~v183:0 = 2 + v183:0

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

(8)
Obligation:
Rules:
f_374(v239:0) -> f_293(1 + v239:0) :|: v239:0 > 0
f_293(sum~cons_3~v450:0) -> f_374(v450:0) :|: v450:0 > 0 && sum~cons_3~v450:0 = 3 + v450:0
f_374(x) -> f_293(x) :|: TRUE
f_293(sum~cons_2~v183:0) -> f_374(v183:0) :|: v183:0 > 0 && sum~cons_2~v183:0 = 2 + v183:0

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

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

(10)
Obligation:
Rules:
f_293(sum~cons_2~v183:0:0) -> f_374(v183:0:0) :|: v183:0:0 > 0 && sum~cons_2~v183:0:0 = 2 + v183:0:0
f_374(x:0) -> f_293(x:0) :|: TRUE
f_374(v239:0:0) -> f_293(1 + v239:0:0) :|: v239:0:0 > 0
f_293(sum~cons_3~v450:0:0) -> f_374(v450:0:0) :|: v450:0:0 > 0 && sum~cons_3~v450:0:0 = 3 + v450:0:0

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

(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_293(x)] = -2 + x
[f_374(x1)] = -1 + x1

The following rules are decreasing:
f_293(sum~cons_2~v183:0:0) -> f_374(v183:0:0) :|: v183:0:0 > 0 && sum~cons_2~v183:0:0 = 2 + v183:0:0
f_374(x:0) -> f_293(x:0) :|: TRUE
f_293(sum~cons_3~v450:0:0) -> f_374(v450:0:0) :|: v450:0:0 > 0 && sum~cons_3~v450:0:0 = 3 + v450:0:0
The following rules are bounded:
f_293(sum~cons_2~v183:0:0) -> f_374(v183:0:0) :|: v183:0:0 > 0 && sum~cons_2~v183:0:0 = 2 + v183:0:0
f_374(v239:0:0) -> f_293(1 + v239:0:0) :|: v239:0:0 > 0
f_293(sum~cons_3~v450:0:0) -> f_374(v450:0:0) :|: v450:0:0 > 0 && sum~cons_3~v450:0:0 = 3 + v450:0:0

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

(12)
Complex Obligation (AND)

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

(13)
Obligation:
Rules:
f_374(v239:0:0) -> f_293(1 + v239:0:0) :|: v239:0:0 > 0

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

(14) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained no non-trivial SCC(s).

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

(15)
YES

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

(16)
Obligation:
Rules:
f_374(x:0) -> f_293(x:0) :|: TRUE

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

(17) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained no non-trivial SCC(s).

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

(18)
YES