/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 176 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 2585 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToLassoProof [EQUIVALENT, 0 ms]
(6) LLVM Symbolic Execution Lasso
(7) Lasso2IRS [SOUND, 119 ms]
(8) IntTRS
(9) IRS2T2 [EQUIVALENT, 0 ms]
(10) T2IntSys
(11) T2 [EQUIVALENT, 1351 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, %5, %6
	5:
		store 0, %1
		br %26
	6:
		%7 = call i32 @__VERIFIER_nondet_int()
		store %7, %n
		%8 = load %n
		%9 = icmp sle %8 0
		br %9, %10, %11
	10:
		store 0, %1
		br %26
	11:
		%12 = load %m
		%13 = load %n
		%14 = call i32 @gcd(i32 %12, i32 %13)
		store %14, %z
		%15 = load %z
		%16 = icmp slt %15 1
		br %16, %17, %25
	17:
		%18 = load %m
		%19 = icmp sgt %18 0
		br %19, %20, %25
	20:
		%21 = load %n
		%22 = icmp sgt %21 0
		br %22, %23, %25
	23:
		br %24
	24:
		Unnamed Call-Instruction = call BasicVoidType (...)* @__VERIFIER_error() noreturn
		unreachable
	25:
		store 0, %1
		br %26
	26:
		%27 = load %1
		ret %27


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 (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 61 rulesP rules:
f_330(v58, v59, v60, v61, 3, 1, 4) -> f_331(v58, v59, v60, v62, v61, v63, 3, 1, 4) :|: 1 <= v62 && v63 = 3 + v62 && 4 <= v63
f_331(v58, v59, v60, v62, v61, v63, 3, 1, 4) -> f_332(v58, v59, v60, v62, v64, v61, v63, v65, 3, 1, 4) :|: 1 <= v64 && v65 = 3 + v64 && 4 <= v65
f_332(v58, v59, v60, v62, v64, v61, v63, v65, 3, 1, 4) -> f_333(v58, v59, v60, v62, v64, v61, v63, v65, 3, 1, 4) :|: TRUE
f_333(v58, v59, v60, v62, v64, v61, v63, v65, 3, 1, 4) -> f_334(v58, v59, v60, v62, v64, v61, v63, v65, 3, 1, 4) :|: TRUE
f_334(v58, v59, v60, v62, v64, v61, v63, v65, 3, 1, 4) -> f_335(v58, v59, v60, v62, v64, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_335(v58, v59, v60, v62, v64, v61, v63, v65, 3, 1, 4) -> f_336(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_336(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_337(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: TRUE
f_337(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_338(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_338(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_339(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_339(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_340(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: TRUE
f_340(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_341(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_341(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_342(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_342(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_344(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: v58 != v59
f_344(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_346(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_346(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_348(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: TRUE
f_348(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_350(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_350(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_352(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) :|: 0 = 0
f_352(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_354(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 2, 1, 4) :|: v59 < v58 && 2 <= v58
f_352(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 4) -> f_355(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) :|: v58 <= v59 && 2 <= v59
f_354(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 2, 1, 4) -> f_357(v58, v59, v60, v62, v64, 0, 1, v61, v63, v65, 3, 2, 4) :|: 0 = 0
f_357(v58, v59, v60, v62, v64, 0, 1, v61, v63, v65, 3, 2, 4) -> f_360(v58, v59, v60, v62, v64, 0, 1, v61, v63, v65, 3, 2, 4) :|: TRUE
f_360(v58, v59, v60, v62, v64, 0, 1, v61, v63, v65, 3, 2, 4) -> f_363(v58, v59, v60, v62, v64, 0, 1, v61, v63, v65, 3, 2, 4) :|: 0 = 0
f_363(v58, v59, v60, v62, v64, 0, 1, v61, v63, v65, 3, 2, 4) -> f_366(v58, v59, v60, v62, v64, 0, 1, v61, v63, v65, 3, 2, 4) :|: 0 = 0
f_366(v58, v59, v60, v62, v64, 0, 1, v61, v63, v65, 3, 2, 4) -> f_369(v58, v59, v60, v62, v64, 0, 1, v77, v61, v63, v65, 3, 2, 4) :|: v77 + v59 = v58 && 1 <= v77
f_369(v58, v59, v60, v62, v64, 0, 1, v77, v61, v63, v65, 3, 2, 4) -> f_372(v58, v59, v60, v62, v64, 0, 1, v77, v61, v63, v65, 3, 2, 4) :|: 0 = 0
f_372(v58, v59, v60, v62, v64, 0, 1, v77, v61, v63, v65, 3, 2, 4) -> f_375(v77, v59, v60, v61, v62, v63, v64, v65, v58, 0, 1, 3, 2, 4) :|: 0 = 0
f_375(v77, v59, v60, v61, v62, v63, v64, v65, v58, 0, 1, 3, 2, 4) -> f_378(v77, v59, v60, v61, v62, v63, v64, v65, v58, 3, 2, 1, 4) :|: TRUE
f_378(v77, v59, v60, v61, v62, v63, v64, v65, v58, 3, 2, 1, 4) -> f_328(v77, v59, 1) :|: TRUE
f_328(v58, v59, 1) -> f_330(v58, v59, v60, v61, 3, 1, 4) :|: 1 <= v60 && v61 = 3 + v60 && 4 <= v61
f_355(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) -> f_358(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) :|: 0 = 0
f_358(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) -> f_361(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) :|: TRUE
f_361(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) -> f_364(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) :|: 0 = 0
f_364(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) -> f_367(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) :|: 0 = 0
f_367(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) -> f_370(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) :|: 0 = 0
f_370(v58, v59, v60, v62, v64, 0, v61, v63, v65, 3, 1, 2, 4) -> f_373(v58, v59, v60, v62, v64, 0, v78, v61, v63, v65, 3, 1, 2, 4) :|: v78 + v58 = v59 && 1 <= v78
f_373(v58, v59, v60, v62, v64, 0, v78, v61, v63, v65, 3, 1, 2, 4) -> f_376(v58, v78, v60, v61, v62, v63, v64, v65, v59, 0, 3, 1, 2, 4) :|: 0 = 0
f_376(v58, v78, v60, v61, v62, v63, v64, v65, v59, 0, 3, 1, 2, 4) -> f_379(v58, v78, v60, v61, v62, v63, v64, v65, v59, 3, 1, 2, 4) :|: TRUE
f_379(v58, v78, v60, v61, v62, v63, v64, v65, v59, 3, 1, 2, 4) -> f_328(v58, v78, 1) :|: TRUE
f_242 -> f_243(v1, v2, 3, 1, 4) :|: 1 <= v1 && v2 = 3 + v1 && 4 <= v2
f_243(v1, v2, 3, 1, 4) -> f_244(v1, v3, v2, v4, 3, 1, 4) :|: 1 <= v3 && v4 = 3 + v3 && 4 <= v4
f_244(v1, v3, v2, v4, 3, 1, 4) -> f_245(v1, v3, v5, v2, v4, v6, 3, 1, 4) :|: 1 <= v5 && v6 = 3 + v5 && 4 <= v6
f_245(v1, v3, v5, v2, v4, v6, 3, 1, 4) -> f_246(v1, v3, v5, v7, v2, v4, v6, v8, 3, 1, 4) :|: 1 <= v7 && v8 = 3 + v7 && 4 <= v8
f_246(v1, v3, v5, v7, v2, v4, v6, v8, 3, 1, 4) -> f_247(v1, v3, v5, v7, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_247(v1, v3, v5, v7, v2, v4, v6, v8, 0, 3, 1, 4) -> f_248(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_248(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) -> f_249(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_249(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) -> f_250(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) :|: 0 = 0
f_250(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) -> f_252(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) :|: 0 < v9
f_252(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) -> f_254(v1, v3, v5, v7, v9, 0, v2, v4, v6, v8, 3, 1, 4) :|: 0 = 0
f_254(v1, v3, v5, v7, v9, 0, v2, v4, v6, v8, 3, 1, 4) -> f_256(v1, v3, v5, v7, v9, 0, v2, v4, v6, v8, 3, 1, 4) :|: TRUE
f_256(v1, v3, v5, v7, v9, 0, v2, v4, v6, v8, 3, 1, 4) -> f_258(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) :|: TRUE
f_258(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) -> f_260(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) :|: TRUE
f_260(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) -> f_262(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) :|: 0 = 0
f_262(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) -> f_264(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) :|: 0 < v11
f_264(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) -> f_266(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) :|: 0 = 0
f_266(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) -> f_268(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) :|: TRUE
f_268(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) -> f_270(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) :|: 0 = 0
f_270(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) -> f_272(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) :|: 0 = 0
f_272(v1, v3, v5, v7, v9, 0, v11, v2, v4, v6, v8, 3, 1, 4) -> f_274(v9, v11, v1, v2, v3, v4, v5, v6, v7, v8, 0, 3, 1, 4) :|: 0 = 0
f_274(v9, v11, v1, v2, v3, v4, v5, v6, v7, v8, 0, 3, 1, 4) -> f_275(v9, v11, v1, v2, v3, v4, v5, v6, v7, v8, 0, 3, 1, 4) :|: TRUE
f_275(v9, v11, v1, v2, v3, v4, v5, v6, v7, v8, 0, 3, 1, 4) -> f_327(v9, v11, v1, v2, v3, v4, v5, v6, v7, v8, 0, v9, 3, 1, 4) :|: TRUE
f_327(v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, 0, v57, 3, 1, 4) -> f_328(v46, v47, 1) :|: TRUE
Combined rules. Obtained 3 rulesP rules:
f_242 -> f_330(v9:0, v11:0, v60:0, 3 + v60:0, 3, 1, 4) :|: v3:0 > 0 && v1:0 > 0 && v5:0 > 0 && v7:0 > 0 && v9:0 > 0 && v11:0 > 0 && v60:0 > 0
f_330(v58:0, v78:0 + v58:0, v60:0, v61:0, 3, 1, 4) -> f_330(v58:0, v78:0, v60:1, 3 + v60:1, 3, 1, 4) :|: v78:0 + v58:0 > v58:0 && v64:0 > 0 && v62:0 > 0 && v78:0 + v58:0 > 1 && v78:0 > 0 && v60:1 > 0
f_330(v77:0 + v59:0, v59:0, v60:0, v61:0, 3, 1, 4) -> f_330(v77:0, v59:0, v60:1, 3 + v60:1, 3, 1, 4) :|: v64:0 > 0 && v62:0 > 0 && v77:0 + v59:0 > v59:0 && v77:0 + v59:0 > 1 && v77:0 > 0 && v60:1 > 0
Filtered unneeded arguments:
   f_330(x1, x2, x3, x4, x5, x6, x7) -> f_330(x1, x2)
Removed division, modulo operations, cleaned up constraints. Obtained 3 rules.P rules:
f_242 -> f_330(v9:0, v11:0) :|: v9:0 > 0 && v11:0 > 0
f_330(v58:0, sum~v78:0~v58:0) -> f_330(v58:0, v78:0) :|: v78:0 + v58:0 > 1 && v78:0 > 0 && v78:0 + v58:0 > v58:0 && sum~v78:0~v58:0 = v78:0 + v58:0
f_330(sum~v77:0~v59:0, v59:0) -> f_330(v77:0, v59:0) :|: v77:0 + v59:0 > 1 && v77:0 > 0 && v77:0 + v59:0 > v59:0 && sum~v77:0~v59:0 = v77:0 + v59:0

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

(8)
Obligation:
Rules:
f_242 -> f_330(v9:0, v11:0) :|: v9:0 > 0 && v11:0 > 0
f_330(v58:0, sum~v78:0~v58:0) -> f_330(v58:0, v78:0) :|: v78:0 + v58:0 > 1 && v78:0 > 0 && v78:0 + v58:0 > v58:0 && sum~v78:0~v58:0 = v78:0 + v58:0
f_330(sum~v77:0~v59:0, v59:0) -> f_330(v77:0, v59:0) :|: v77:0 + v59:0 > 1 && v77:0 > 0 && v77:0 + v59:0 > v59:0 && sum~v77:0~v59:0 = v77:0 + v59:0
Start term: f_242

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

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

   (f_242_2,1)
   (f_330_2,2)

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

(10)
Obligation:
START: 1;

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

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := oldX1 - oldX0;
assume(oldX2 + oldX0 > 1 && oldX2 > 0 && oldX2 + oldX0 > oldX0 && oldX1 = oldX2 + oldX0);
x0 := oldX0;
x1 := oldX1 - oldX0;
TO: 2;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := oldX0 - oldX1;
assume(oldX2 + oldX1 > 1 && oldX2 > 0 && oldX2 + oldX1 > oldX1 && oldX0 = oldX2 + oldX1);
x0 := oldX0 - oldX1;
x1 := oldX1;
TO: 2;


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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 x1+x0, bound 3
    - RF x1+oldX3, bound 2

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(12)
YES