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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 174 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 5442 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 60 ms]
        (9) IntTRS
        (10) IRS2T2 [EQUIVALENT, 0 ms]
        (11) T2IntSys
        (12) T2 [EQUIVALENT, 1193 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 78 ms]
        (16) IntTRS
        (17) IRS2T2 [EQUIVALENT, 0 ms]
        (18) T2IntSys
        (19) T2 [EQUIVALENT, 1226 ms]
        (20) 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: "f" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (a i32, b i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%3 = alloca i32, align 4
		store %a, %2
		store %b, %3
		%4 = load %3
		%5 = icmp eq %4 0
		br %5, %6, %9
	6:
		%7 = load %2
		%8 = call i32 @g(i32 %7, i32 0)
		store %8, %1
		br %15
	9:
		%10 = load %2
		%11 = add 1 %10
		%12 = load %3
		%13 = sub %12 1
		%14 = call i32 @f(i32 %11, i32 %13)
		store %14, %1
		br %15
	15:
		%16 = load %1
		ret %16

*BasicFunctionTypename: "g" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (c i32, d i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%3 = alloca i32, align 4
		store %c, %2
		store %d, %3
		%4 = load %2
		%5 = icmp eq %4 0
		br %5, %6, %8
	6:
		%7 = load %3
		store %7, %1
		br %14
	8:
		%9 = load %2
		%10 = sub %9 1
		%11 = load %3
		%12 = add 1 %11
		%13 = call i32 @g(i32 %10, i32 %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
		%a = alloca i32, align 4
		%b = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %a
		%3 = call i32 @__VERIFIER_nondet_int()
		store %3, %b
		%4 = load %a
		%5 = icmp sge %4 0
		br %5, %6, %13
	6:
		%7 = load %b
		%8 = icmp sge %7 0
		br %8, %9, %13
	9:
		%10 = load %a
		%11 = load %b
		%12 = call i32 @f(i32 %10, i32 %11)
		br %13
	13:
		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) SymbolicExecutionGraphToSCCProof (SOUND)
Splitted symbolic execution graph to 2 SCCs.
----------------------------------------

(6)
Complex Obligation (AND)

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

(7)
Obligation:
SCC
----------------------------------------

(8) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 16 rulesP rules:
f_424(v319, v320, v337, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, 0, v334, v335, v336, 3, 1, 4) -> f_426(v319, v320, v337, v339, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, 0, v334, v335, v336, 3, 1, 4) :|: 1 <= v339 && v340 = 3 + v339 && 4 <= v340
f_426(v319, v320, v337, v339, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, 0, v334, v335, v336, 3, 1, 4) -> f_427(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) :|: 1 <= v341 && v342 = 3 + v341 && 4 <= v342
f_427(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) -> f_428(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) :|: TRUE
f_428(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) -> f_429(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) :|: TRUE
f_429(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) -> f_430(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) :|: 0 = 0
f_430(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) -> f_432(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) :|: v319 != 0 && 1 <= v336
f_432(v319, v320, v337, v339, v341, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, 0, v334, v335, v336, 3, 1, 4) -> f_434(v319, v320, v337, v339, v341, 0, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) :|: 0 = 0
f_434(v319, v320, v337, v339, v341, 0, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) -> f_436(v319, v320, v337, v339, v341, 0, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) :|: TRUE
f_436(v319, v320, v337, v339, v341, 0, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) -> f_438(v319, v320, v337, v339, v341, 0, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) :|: 0 = 0
f_438(v319, v320, v337, v339, v341, 0, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) -> f_440(v319, v320, v337, v339, v341, 0, v346, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) :|: 1 + v346 = v319 && 0 <= v346
f_440(v319, v320, v337, v339, v341, 0, v346, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) -> f_442(v319, v320, v337, v339, v341, 0, v346, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) :|: 0 = 0
f_442(v319, v320, v337, v339, v341, 0, v346, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) -> f_444(v319, v320, v337, v339, v341, 0, v346, v347, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) :|: v347 = 1 + v320 && 1 <= v347
f_444(v319, v320, v337, v339, v341, 0, v346, v347, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, v340, v342, v334, v335, v336, 3, 1, 4) -> f_446(v346, v347, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v337, v338, v339, v340, v341, v342, 0, v334, v335, v336, v319, v320, 3, 1, 4) :|: 0 = 0
f_446(v346, v347, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v337, v338, v339, v340, v341, v342, 0, v334, v335, v336, v319, v320, 3, 1, 4) -> f_448(v346, v347, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v337, v338, v339, v340, v341, v342, 0, v334, v335, v336, v319, v320, 3, 1, 4) :|: TRUE
f_448(v346, v347, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v337, v338, v339, v340, v341, v342, 0, v334, v335, v336, v319, v320, 3, 1, 4) -> f_422(v346, v347, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, 0, v334, v335, v336, 3, 1, 4) :|: TRUE
f_422(v319, v320, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, 0, v334, v335, v336, 3, 1, 4) -> f_424(v319, v320, v337, v321, v322, v323, v324, v325, v326, v327, v328, v329, v330, v331, v332, v338, 0, v334, v335, v336, 3, 1, 4) :|: 1 <= v337 && v338 = 3 + v337 && 4 <= v338
Combined rules. Obtained 1 rulesP rules:
f_424(1 + v346:0, v320:0, v337:0, v321:0, v322:0, v323:0, v324:0, v325:0, v326:0, v327:0, v328:0, v329:0, v330:0, v331:0, v332:0, v338:0, 0, v334:0, v335:0, v336:0, 3, 1, 4) -> f_424(v346:0, 1 + v320:0, v337:1, v321:0, v322:0, v323:0, v324:0, v325:0, v326:0, v327:0, v328:0, v329:0, v330:0, v331:0, v332:0, 3 + v337:1, 0, v334:0, v335:0, v336:0, 3, 1, 4) :|: v341:0 > 0 && v339:0 > 0 && v336:0 > 0 && v346:0 > -1 && v320:0 > -1 && v337:1 > 0
Filtered unneeded arguments:
   f_424(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f_424(x1, x2, x20)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_424(sum~cons_1~v346:0, v320:0, v336:0) -> f_424(v346:0, 1 + v320:0, v336:0) :|: v346:0 > -1 && v320:0 > -1 && v336:0 > 0 && sum~cons_1~v346:0 = 1 + v346:0

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

(9)
Obligation:
Rules:
f_424(sum~cons_1~v346:0, v320:0, v336:0) -> f_424(v346:0, 1 + v320:0, v336:0) :|: v346:0 > -1 && v320:0 > -1 && v336:0 > 0 && sum~cons_1~v346:0 = 1 + v346:0

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

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

   (f_424_3,1)

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

(11)
Obligation:
START: 0;

FROM: 0;
TO: 1;

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


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

(12) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 1, 3, 4 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: 2
    - Rank function 2:
      RF for loc. 5: 1+2*x0
      RF for loc. 6: 2*x0
      Bound for (chained) transitions 3: 2
    - Rank function 3:
      RF for loc. 5: 1
      RF for loc. 6: 0
      Bound for (chained) transitions 1: 1

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

(13)
YES

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

(14)
Obligation:
SCC
----------------------------------------

(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 16 rulesP rules:
f_264(v55, v56, v67, v57, v58, v59, v60, v61, v62, v68, 0, v64, v65, 3, 1, 4) -> f_265(v55, v56, v67, v69, v57, v58, v59, v60, v61, v62, v68, v70, 0, v64, v65, 3, 1, 4) :|: 1 <= v69 && v70 = 3 + v69 && 4 <= v70
f_265(v55, v56, v67, v69, v57, v58, v59, v60, v61, v62, v68, v70, 0, v64, v65, 3, 1, 4) -> f_266(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) :|: 1 <= v71 && v72 = 3 + v71 && 4 <= v72
f_266(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) -> f_267(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) :|: TRUE
f_267(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) -> f_268(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) :|: TRUE
f_268(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) -> f_269(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) :|: 0 = 0
f_269(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) -> f_271(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) :|: v56 != 0 && 1 <= v65
f_271(v55, v56, v67, v69, v71, v57, v58, v59, v60, v61, v62, v68, v70, v72, 0, v64, v65, 3, 1, 4) -> f_273(v55, v56, v67, v69, v71, 0, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) :|: 0 = 0
f_273(v55, v56, v67, v69, v71, 0, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) -> f_275(v55, v56, v67, v69, v71, 0, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) :|: TRUE
f_275(v55, v56, v67, v69, v71, 0, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) -> f_277(v55, v56, v67, v69, v71, 0, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) :|: 0 = 0
f_277(v55, v56, v67, v69, v71, 0, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) -> f_279(v55, v56, v67, v69, v71, 0, v75, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) :|: v75 = 1 + v55 && 1 <= v75
f_279(v55, v56, v67, v69, v71, 0, v75, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) -> f_281(v55, v56, v67, v69, v71, 0, v75, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) :|: 0 = 0
f_281(v55, v56, v67, v69, v71, 0, v75, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) -> f_282(v55, v56, v67, v69, v71, 0, v75, v76, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) :|: 1 + v76 = v56 && 0 <= v76
f_282(v55, v56, v67, v69, v71, 0, v75, v76, v57, v58, v59, v60, v61, v62, v68, v70, v72, v64, v65, 3, 1, 4) -> f_284(v75, v76, v57, v58, v59, v60, v61, v62, v67, v68, v69, v70, v71, v72, 0, v64, v65, v55, v56, 3, 1, 4) :|: 0 = 0
f_284(v75, v76, v57, v58, v59, v60, v61, v62, v67, v68, v69, v70, v71, v72, 0, v64, v65, v55, v56, 3, 1, 4) -> f_286(v75, v76, v57, v58, v59, v60, v61, v62, v67, v68, v69, v70, v71, v72, 0, v64, v65, v55, v56, 3, 1, 4) :|: TRUE
f_286(v75, v76, v57, v58, v59, v60, v61, v62, v67, v68, v69, v70, v71, v72, 0, v64, v65, v55, v56, 3, 1, 4) -> f_262(v75, v76, v57, v58, v59, v60, v61, v62, 0, v64, v65, 3, 1, 4) :|: TRUE
f_262(v55, v56, v57, v58, v59, v60, v61, v62, 0, v64, v65, 3, 1, 4) -> f_264(v55, v56, v67, v57, v58, v59, v60, v61, v62, v68, 0, v64, v65, 3, 1, 4) :|: 1 <= v67 && v68 = 3 + v67 && 4 <= v68
Combined rules. Obtained 1 rulesP rules:
f_264(v55:0, 1 + v76:0, v67:0, v57:0, v58:0, v59:0, v60:0, v61:0, v62:0, v68:0, 0, v64:0, v65:0, 3, 1, 4) -> f_264(1 + v55:0, v76:0, v67:1, v57:0, v58:0, v59:0, v60:0, v61:0, v62:0, 3 + v67:1, 0, v64:0, v65:0, 3, 1, 4) :|: v71:0 > 0 && v69:0 > 0 && v65:0 > 0 && v76:0 > -1 && v55:0 > -1 && v67:1 > 0
Filtered unneeded arguments:
   f_264(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_264(x1, x2, x13)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_264(v55:0, sum~cons_1~v76:0, v65:0) -> f_264(1 + v55:0, v76:0, v65:0) :|: v76:0 > -1 && v55:0 > -1 && v65:0 > 0 && sum~cons_1~v76:0 = 1 + v76:0

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

(16)
Obligation:
Rules:
f_264(v55:0, sum~cons_1~v76:0, v65:0) -> f_264(1 + v55:0, v76:0, v65:0) :|: v76:0 > -1 && v55:0 > -1 && v65:0 > 0 && sum~cons_1~v76:0 = 1 + v76:0

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

   (f_264_3,1)

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(18)
Obligation:
START: 0;

FROM: 0;
TO: 1;

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


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(19) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 1, 3, 4 using the following rank functions:
    - Rank function 1:
      RF for loc. 5: 1+2*x1
      RF for loc. 6: 2*x1
      Bound for (chained) transitions 4: 2
    - Rank function 2:
      RF for loc. 5: 1+2*x1
      RF for loc. 6: 2*x1
      Bound for (chained) transitions 3: 2
    - Rank function 3:
      RF for loc. 5: 0
      RF for loc. 6: -1
      Bound for (chained) transitions 1: 0

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(20)
YES