YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 2460 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 18 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 8 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: "gcd" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (y1 i32, y2 i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%3 = alloca i32, align 4
		store %y1, %2
		store %y2, %3
		%4 = load %2
		%5 = icmp sle %4 0
		br %5, %9, %6
	6:
		%7 = load %3
		%8 = icmp sle %7 0
		br %8, %9, %10
	9:
		store 0, %1
		br %32
	10:
		%11 = load %2
		%12 = load %3
		%13 = icmp eq %11 %12
		br %13, %14, %16
	14:
		%15 = load %2
		store %15, %1
		br %32
	16:
		%17 = load %2
		%18 = load %3
		%19 = icmp sgt %17 %18
		br %19, %20, %26
	20:
		%21 = load %2
		%22 = load %3
		%23 = sub %21 %22
		%24 = load %3
		%25 = call i32 @gcd(i32 %23, i32 %24)
		store %25, %1
		br %32
	26:
		%27 = load %2
		%28 = load %3
		%29 = load %2
		%30 = sub %28 %29
		%31 = call i32 @gcd(i32 %27, i32 %30)
		store %31, %1
		br %32
	32:
		%33 = load %1
		ret %33

*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%m = alloca i32, align 4
		%n = alloca i32, align 4
		%z = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %m
		%3 = load %m
		%4 = icmp sle %3 0
		br %4, %8, %5
	5:
		%6 = load %m
		%7 = icmp sgt %6 2147483647
		br %7, %8, %9
	8:
		store 0, %1
		br %32
	9:
		%10 = call i32 @__VERIFIER_nondet_int()
		store %10, %n
		%11 = load %n
		%12 = icmp sle %11 0
		br %12, %16, %13
	13:
		%14 = load %n
		%15 = icmp sgt %14 2147483647
		br %15, %16, %17
	16:
		store 0, %1
		br %32
	17:
		%18 = load %m
		%19 = load %n
		%20 = call i32 @gcd(i32 %18, i32 %19)
		store %20, %z
		%21 = load %z
		%22 = icmp slt %21 1
		br %22, %23, %31
	23:
		%24 = load %m
		%25 = icmp sgt %24 0
		br %25, %26, %31
	26:
		%27 = load %n
		%28 = icmp sgt %27 0
		br %28, %29, %31
	29:
		br %30
	30:
		Unnamed Call-Instruction = call BasicVoidType (...)* @__VERIFIER_error() noreturn
		unreachable
	31:
		store 0, %1
		br %32
	32:
		%33 = load %1
		ret %33


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 38 rulesP rules:
f_364(v89, v90, v91, v92, 3, 1, 4) -> f_365(v89, v90, v91, v93, v92, v94, 3, 1, 4) :|: 1 <= v93 && v94 = 3 + v93 && 4 <= v94
f_365(v89, v90, v91, v93, v92, v94, 3, 1, 4) -> f_366(v89, v90, v91, v93, v95, v92, v94, v96, 3, 1, 4) :|: 1 <= v95 && v96 = 3 + v95 && 4 <= v96
f_366(v89, v90, v91, v93, v95, v92, v94, v96, 3, 1, 4) -> f_367(v89, v90, v91, v93, v95, v92, v94, v96, 3, 1, 4) :|: TRUE
f_367(v89, v90, v91, v93, v95, v92, v94, v96, 3, 1, 4) -> f_368(v89, v90, v91, v93, v95, v92, v94, v96, 3, 1, 4) :|: TRUE
f_368(v89, v90, v91, v93, v95, v92, v94, v96, 3, 1, 4) -> f_369(v89, v90, v91, v93, v95, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_369(v89, v90, v91, v93, v95, v92, v94, v96, 3, 1, 4) -> f_370(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_370(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_371(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: TRUE
f_371(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_372(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_372(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_373(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_373(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_374(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: TRUE
f_374(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_375(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_375(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_376(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_376(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_378(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: v89 != v90
f_378(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_380(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_380(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_382(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: TRUE
f_382(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_384(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_384(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_386(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) :|: 0 = 0
f_386(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_388(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 2, 1, 4) :|: v90 < v89 && 2 <= v89
f_386(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 4) -> f_389(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) :|: v89 <= v90 && 2 <= v90
f_388(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 2, 1, 4) -> f_391(v89, v90, v91, v93, v95, 0, 1, v92, v94, v96, 3, 2, 4) :|: 0 = 0
f_391(v89, v90, v91, v93, v95, 0, 1, v92, v94, v96, 3, 2, 4) -> f_394(v89, v90, v91, v93, v95, 0, 1, v92, v94, v96, 3, 2, 4) :|: TRUE
f_394(v89, v90, v91, v93, v95, 0, 1, v92, v94, v96, 3, 2, 4) -> f_397(v89, v90, v91, v93, v95, 0, 1, v92, v94, v96, 3, 2, 4) :|: 0 = 0
f_397(v89, v90, v91, v93, v95, 0, 1, v92, v94, v96, 3, 2, 4) -> f_400(v89, v90, v91, v93, v95, 0, 1, v92, v94, v96, 3, 2, 4) :|: 0 = 0
f_400(v89, v90, v91, v93, v95, 0, 1, v92, v94, v96, 3, 2, 4) -> f_403(v89, v90, v91, v93, v95, 0, 1, v108, v92, v94, v96, 3, 2, 4) :|: v108 + v90 = v89 && 1 <= v108
f_403(v89, v90, v91, v93, v95, 0, 1, v108, v92, v94, v96, 3, 2, 4) -> f_406(v89, v90, v91, v93, v95, 0, 1, v108, v92, v94, v96, 3, 2, 4) :|: 0 = 0
f_406(v89, v90, v91, v93, v95, 0, 1, v108, v92, v94, v96, 3, 2, 4) -> f_409(v108, v90, v91, v92, v93, v94, v95, v96, v89, 0, 1, 3, 2, 4) :|: 0 = 0
f_409(v108, v90, v91, v92, v93, v94, v95, v96, v89, 0, 1, 3, 2, 4) -> f_412(v108, v90, v91, v92, v93, v94, v95, v96, v89, 3, 2, 1, 4) :|: TRUE
f_412(v108, v90, v91, v92, v93, v94, v95, v96, v89, 3, 2, 1, 4) -> f_362(v108, v90, 1) :|: 1 <= v108 && 1 <= v90
f_362(v89, v90, 1) -> f_364(v89, v90, v91, v92, 3, 1, 4) :|: 1 <= v91 && v92 = 3 + v91 && 4 <= v92
f_389(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) -> f_392(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) :|: 0 = 0
f_392(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) -> f_395(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) :|: TRUE
f_395(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) -> f_398(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) :|: 0 = 0
f_398(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) -> f_401(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) :|: 0 = 0
f_401(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) -> f_404(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) :|: 0 = 0
f_404(v89, v90, v91, v93, v95, 0, v92, v94, v96, 3, 1, 2, 4) -> f_407(v89, v90, v91, v93, v95, 0, v109, v92, v94, v96, 3, 1, 2, 4) :|: v109 + v89 = v90 && 1 <= v109
f_407(v89, v90, v91, v93, v95, 0, v109, v92, v94, v96, 3, 1, 2, 4) -> f_410(v89, v109, v91, v92, v93, v94, v95, v96, v90, 0, 3, 1, 2, 4) :|: 0 = 0
f_410(v89, v109, v91, v92, v93, v94, v95, v96, v90, 0, 3, 1, 2, 4) -> f_413(v89, v109, v91, v92, v93, v94, v95, v96, v90, 3, 1, 2, 4) :|: TRUE
f_413(v89, v109, v91, v92, v93, v94, v95, v96, v90, 3, 1, 2, 4) -> f_362(v89, v109, 1) :|: 1 <= v89 && 1 <= v109
Combined rules. Obtained 2 rulesP rules:
f_364(v89:0, v109:0 + v89:0, v91:0, v92:0, 3, 1, 4) -> f_364(v89:0, v109:0, v91:1, 3 + v91:1, 3, 1, 4) :|: v89:0 < v109:0 + v89:0 && v95:0 > 0 && v93:0 > 0 && v109:0 + v89:0 > 1 && v109:0 > 0 && v91:1 > 0 && v89:0 > 0
f_364(v108:0 + v90:0, v90:0, v91:0, v92:0, 3, 1, 4) -> f_364(v108:0, v90:0, v91:1, 3 + v91:1, 3, 1, 4) :|: v95:0 > 0 && v93:0 > 0 && v90:0 < v108:0 + v90:0 && v108:0 + v90:0 > 1 && v108:0 > 0 && v91:1 > 0 && v90:0 > 0
Filtered unneeded arguments:
   f_364(x1, x2, x3, x4, x5, x6, x7) -> f_364(x1, x2)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_364(v89:0, sum~v109:0~v89:0) -> f_364(v89:0, v109:0) :|: v109:0 + v89:0 > 1 && v89:0 < v109:0 + v89:0 && v89:0 > 0 && v109:0 > 0 && sum~v109:0~v89:0 = v109:0 + v89:0
f_364(sum~v108:0~v90:0, v90:0) -> f_364(v108:0, v90:0) :|: v108:0 + v90:0 > 1 && v90:0 < v108:0 + v90:0 && v90:0 > 0 && v108:0 > 0 && sum~v108:0~v90:0 = v108:0 + v90:0

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

(8)
Obligation:
Rules:
f_364(v89:0, sum~v109:0~v89:0) -> f_364(v89:0, v109:0) :|: v109:0 + v89:0 > 1 && v89:0 < v109:0 + v89:0 && v89:0 > 0 && v109:0 > 0 && sum~v109:0~v89:0 = v109:0 + v89:0
f_364(sum~v108:0~v90:0, v90:0) -> f_364(v108:0, v90:0) :|: v108:0 + v90:0 > 1 && v90:0 < v108:0 + v90:0 && v90:0 > 0 && v108:0 > 0 && sum~v108:0~v90:0 = v108:0 + v90:0

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

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

(10)
Obligation:
Rules:
f_364(v89:0:0, sum~v109:0:0~v89:0:0) -> f_364(v89:0:0, v109:0:0) :|: v89:0:0 > 0 && v109:0:0 > 0 && v89:0:0 < v109:0:0 + v89:0:0 && v109:0:0 + v89:0:0 > 1 && sum~v109:0:0~v89:0:0 = v109:0:0 + v89:0:0
f_364(sum~v108:0:0~v90:0:0, v90:0:0) -> f_364(v108:0:0, v90:0:0) :|: v90:0:0 > 0 && v108:0:0 > 0 && v90:0:0 < v108:0:0 + v90:0:0 && v108:0:0 + v90:0:0 > 1 && sum~v108:0:0~v90:0:0 = v108:0:0 + v90:0:0

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

(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_364 ] = f_364_1 + f_364_2

The following rules are decreasing:
f_364(v89:0:0, sum~v109:0:0~v89:0:0) -> f_364(v89:0:0, v109:0:0) :|: v89:0:0 > 0 && v109:0:0 > 0 && v89:0:0 < v109:0:0 + v89:0:0 && v109:0:0 + v89:0:0 > 1 && sum~v109:0:0~v89:0:0 = v109:0:0 + v89:0:0
f_364(sum~v108:0:0~v90:0:0, v90:0:0) -> f_364(v108:0:0, v90:0:0) :|: v90:0:0 > 0 && v108:0:0 > 0 && v90:0:0 < v108:0:0 + v90:0:0 && v108:0:0 + v90:0:0 > 1 && sum~v108:0:0~v90:0:0 = v108:0:0 + v90:0:0

The following rules are bounded:
f_364(v89:0:0, sum~v109:0:0~v89:0:0) -> f_364(v89:0:0, v109:0:0) :|: v89:0:0 > 0 && v109:0:0 > 0 && v89:0:0 < v109:0:0 + v89:0:0 && v109:0:0 + v89:0:0 > 1 && sum~v109:0:0~v89:0:0 = v109:0:0 + v89:0:0
f_364(sum~v108:0:0~v90:0:0, v90:0:0) -> f_364(v108:0:0, v90:0:0) :|: v90:0:0 > 0 && v108:0:0 > 0 && v90:0:0 < v108:0:0 + v90:0:0 && v108:0:0 + v90:0:0 > 1 && sum~v108:0:0~v90:0:0 = v108:0:0 + v90:0:0


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

(12)
YES