YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 6257 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 109 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
(12) YES


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

(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
----------------------------------------

(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox/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: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%x_ref = alloca *i32, align 8
		%y_ref = alloca *i32, align 8
		%c = alloca *i32, align 8
		store %x, %1
		store %y, %2
		%3 = alloca i8, numElementsLit: 4
		%4 = bitcast *i8 %3 to *i32
		store %4, %x_ref
		%5 = alloca i8, numElementsLit: 4
		%6 = bitcast *i8 %5 to *i32
		store %6, %y_ref
		%7 = alloca i8, numElementsLit: 4
		%8 = bitcast *i8 %7 to *i32
		store %8, %c
		%9 = load %1
		%10 = load %x_ref
		store %9, %10
		%11 = load %2
		%12 = load %y_ref
		store %11, %12
		%13 = load %c
		store 0, %13
		br %14
	14:
		%15 = load %x_ref
		%16 = load %15
		%17 = icmp sgt %16 0
		br %17, %18, %22
	18:
		%19 = load %y_ref
		%20 = load %19
		%21 = icmp sgt %20 0
		br %22
	22:
		%23 = phi [0, %14], [%21, %18]
		br %23, %24, %37
	24:
		%25 = load %x_ref
		%26 = load %25
		%27 = sub %26 1
		%28 = load %x_ref
		store %27, %28
		%29 = load %y_ref
		%30 = load %29
		%31 = sub %30 1
		%32 = load %y_ref
		store %31, %32
		%33 = load %c
		%34 = load %33
		%35 = add %34 1
		%36 = load %c
		store %35, %36
		br %14
	37:
		%38 = load %c
		%39 = load %38
		ret %39

*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		%3 = call i32 @__VERIFIER_nondet_int()
		%4 = call i32 @test_fun(i32 %2, i32 %3)
		ret %4


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 28 rulesP rules:
f_508(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v639, 1, v641, v642, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 4, 8) -> f_509(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 4, 8) :|: 0 = 0
f_509(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 4, 8) -> f_510(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 < v642 && 2 <= v639 && 2 <= v629
f_510(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_512(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_512(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_514(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: TRUE
f_514(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_516(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_516(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v641, v639, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_518(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_518(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_520(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 < v643 && 2 <= v641 && 2 <= v630
f_520(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_523(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_523(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_526(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_526(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_528(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: TRUE
f_528(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_530(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_530(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v639, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_532(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_532(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_534(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 1 + v725 = v642 && 0 <= v725
f_534(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_536(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_536(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_537(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: TRUE
f_537(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_538(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_538(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v641, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_539(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_539(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_540(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 1 + v727 = v643 && 0 <= v727
f_540(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_541(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_541(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_542(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: TRUE
f_542(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_543(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_543(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_544(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_544(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_545(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: v729 = 1 + v645 && 2 <= v729
f_545(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_546(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: 0 = 0
f_546(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_547(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: TRUE
f_547(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_548(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) :|: TRUE
f_548(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 2, 4, 8) -> f_507(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v642, 1, v643, v725, v727, v645, v729, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 4, 8) :|: TRUE
f_507(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v639, 1, v641, v642, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 4, 8) -> f_508(v629, v630, v631, v632, v633, v634, v635, v636, v637, v638, v639, 1, v641, v642, v643, v644, v645, v646, v647, v648, v649, v650, v651, v652, v653, v654, v655, 0, 3, 7, 4, 8) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_508(v629:0, v630:0, v631:0, v632:0, v633:0, v634:0, v635:0, v636:0, v637:0, v638:0, v639:0, 1, v641:0, 1 + v725:0, 1 + v727:0, v644:0, v645:0, v646:0, v647:0, v648:0, v649:0, v650:0, v651:0, v652:0, v653:0, v654:0, v655:0, 0, 3, 7, 4, 8) -> f_508(v629:0, v630:0, v631:0, v632:0, v633:0, v634:0, v635:0, v636:0, v637:0, v638:0, 1 + v725:0, 1, 1 + v727:0, v725:0, v727:0, v645:0, 1 + v645:0, v646:0, v647:0, v648:0, v649:0, v650:0, v651:0, v652:0, v653:0, v654:0, v655:0, 0, 3, 7, 4, 8) :|: v639:0 > 1 && v725:0 > -1 && v629:0 > 1 && v641:0 > 1 && v727:0 > -1 && v630:0 > 1 && v645:0 > 0
Filtered unneeded arguments:
   f_508(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> f_508(x1, x2, x11, x13, x14, x15, x17)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_508(v629:0, v630:0, v639:0, v641:0, sum~cons_1~v725:0, sum~cons_1~v727:0, v645:0) -> f_508(v629:0, v630:0, 1 + v725:0, 1 + v727:0, v725:0, v727:0, 1 + v645:0) :|: v725:0 > -1 && v639:0 > 1 && v629:0 > 1 && v641:0 > 1 && v727:0 > -1 && v645:0 > 0 && v630:0 > 1 && sum~cons_1~v725:0 = 1 + v725:0 && sum~cons_1~v727:0 = 1 + v727:0

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

(8)
Obligation:
Rules:
f_508(v629:0, v630:0, v639:0, v641:0, sum~cons_1~v725:0, sum~cons_1~v727:0, v645:0) -> f_508(v629:0, v630:0, 1 + v725:0, 1 + v727:0, v725:0, v727:0, 1 + v645:0) :|: v725:0 > -1 && v639:0 > 1 && v629:0 > 1 && v641:0 > 1 && v727:0 > -1 && v645:0 > 0 && v630:0 > 1 && sum~cons_1~v725:0 = 1 + v725:0 && sum~cons_1~v727:0 = 1 + v727:0

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f_508(v629:0:0, v630:0:0, v639:0:0, v641:0:0, sum~cons_1~v725:0:0, sum~cons_1~v727:0:0, v645:0:0) -> f_508(v629:0:0, v630:0:0, 1 + v725:0:0, 1 + v727:0:0, v725:0:0, v727:0:0, 1 + v645:0:0) :|: v645:0:0 > 0 && v630:0:0 > 1 && v727:0:0 > -1 && v641:0:0 > 1 && v629:0:0 > 1 && v639:0:0 > 1 && v725:0:0 > -1 && sum~cons_1~v725:0:0 = 1 + v725:0:0 && sum~cons_1~v727:0:0 = 1 + v727:0:0

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_508(x, x1, x2, x3, x4, x5, x6)] = x4

The following rules are decreasing:
f_508(v629:0:0, v630:0:0, v639:0:0, v641:0:0, sum~cons_1~v725:0:0, sum~cons_1~v727:0:0, v645:0:0) -> f_508(v629:0:0, v630:0:0, 1 + v725:0:0, 1 + v727:0:0, v725:0:0, v727:0:0, 1 + v645:0:0) :|: v645:0:0 > 0 && v630:0:0 > 1 && v727:0:0 > -1 && v641:0:0 > 1 && v629:0:0 > 1 && v639:0:0 > 1 && v725:0:0 > -1 && sum~cons_1~v725:0:0 = 1 + v725:0:0 && sum~cons_1~v727:0:0 = 1 + v727:0:0
The following rules are bounded:
f_508(v629:0:0, v630:0:0, v639:0:0, v641:0:0, sum~cons_1~v725:0:0, sum~cons_1~v727:0:0, v645:0:0) -> f_508(v629:0:0, v630:0:0, 1 + v725:0:0, 1 + v727:0:0, v725:0:0, v727:0:0, 1 + v645:0:0) :|: v645:0:0 > 0 && v630:0:0 > 1 && v727:0:0 > -1 && v641:0:0 > 1 && v629:0:0 > 1 && v639:0:0 > 1 && v725:0:0 > -1 && sum~cons_1~v725:0:0 = 1 + v725:0:0 && sum~cons_1~v727:0:0 = 1 + v727:0:0

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(12)
YES