/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 150 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 2703 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 44 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 52 ms]
        (16) IntTRS
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 21 ms]
        (20) YES


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(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: "rec" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (a i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%res = alloca i32, align 4
		%rescopy = alloca i32, align 4
		store %a, %2
		%3 = load %2
		%4 = icmp eq %3 0
		br %4, %5, %6
	5:
		store 0, %1
		br %20
	6:
		%7 = load %2
		%8 = sub %7 1
		%9 = call i32 @rec(i32 %8)
		store %9, %res
		%10 = load %res
		store %10, %rescopy
		br %11
	11:
		%12 = load %rescopy
		%13 = icmp sgt %12 0
		br %13, %14, %17
	14:
		%15 = load %rescopy
		%16 = add %15 -1
		store %16, %rescopy
		br %11
	17:
		%18 = load %res
		%19 = add 1 %18
		store %19, %1
		br %20
	20:
		%21 = load %1
		ret %21

*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%i = alloca i32, align 4
		%res = alloca i32, align 4
		store 0, %1
		%2 = call i32 (...)* @__VERIFIER_nondet_int()
		store %2, %i
		%3 = load %i
		%4 = icmp sle %3 0
		br %4, %5, %6
	5:
		store 0, %1
		br %9
	6:
		%7 = load %i
		%8 = call i32 @rec(i32 %7)
		store %8, %res
		br %9
	9:
		%10 = load %1
		ret %10


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 9 rulesP rules:
f_398(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 4) -> f_399(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) :|: 0 < v617 && 2 <= v615 && 2 <= v614 && 2 <= v607 && 1 <= v613
f_399(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_401(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) :|: 0 = 0
f_401(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_403(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) :|: TRUE
f_403(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_405(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v618, v619, v620, v621, 3, 2, 4) :|: 0 = 0
f_405(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v618, v619, v620, v621, 3, 2, 4) -> f_407(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: 1 + v630 = v617 && 0 <= v630
f_407(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_409(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: TRUE
f_409(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_411(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: TRUE
f_411(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_397(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 4) :|: TRUE
f_397(v607, v608, v609, v610, v611, 0, v613, v614, v615, 1, v617, v618, v619, v620, v621, 3, 4) -> f_398(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_398(v607:0, v608:0, v609:0, v610:0, v611:0, 0, v613:0, v614:0, 1 + v630:0, 1, v615:0, v618:0, v619:0, v620:0, v621:0, 3, 4) -> f_398(v607:0, v608:0, v609:0, v610:0, v611:0, 0, v613:0, v614:0, v630:0, 1, 1 + v630:0, v618:0, v619:0, v620:0, v621:0, 3, 4) :|: v615:0 > 1 && v630:0 > -1 && v614:0 > 1 && v607:0 > 1 && v613:0 > 0
Filtered unneeded arguments:
   f_398(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_398(x1, x7, x8, x9, x11)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_398(v607:0, v613:0, v614:0, sum~cons_1~v630:0, v615:0) -> f_398(v607:0, v613:0, v614:0, v630:0, 1 + v630:0) :|: v630:0 > -1 && v615:0 > 1 && v614:0 > 1 && v613:0 > 0 && v607:0 > 1 && sum~cons_1~v630:0 = 1 + v630:0

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

(9)
Obligation:
Rules:
f_398(v607:0, v613:0, v614:0, sum~cons_1~v630:0, v615:0) -> f_398(v607:0, v613:0, v614:0, v630:0, 1 + v630:0) :|: v630:0 > -1 && v615:0 > 1 && v614:0 > 1 && v613:0 > 0 && v607:0 > 1 && sum~cons_1~v630:0 = 1 + v630:0

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

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

(11)
Obligation:
Rules:
f_398(v607:0:0, v613:0:0, v614:0:0, sum~cons_1~v630:0:0, v615:0:0) -> f_398(v607:0:0, v613:0:0, v614:0:0, v630:0:0, 1 + v630:0:0) :|: v613:0:0 > 0 && v607:0:0 > 1 && v614:0:0 > 1 && v615:0:0 > 1 && v630:0:0 > -1 && sum~cons_1~v630:0:0 = 1 + v630:0:0

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_398(x, x1, x2, x3, x4)] = x3

The following rules are decreasing:
f_398(v607:0:0, v613:0:0, v614:0:0, sum~cons_1~v630:0:0, v615:0:0) -> f_398(v607:0:0, v613:0:0, v614:0:0, v630:0:0, 1 + v630:0:0) :|: v613:0:0 > 0 && v607:0:0 > 1 && v614:0:0 > 1 && v615:0:0 > 1 && v630:0:0 > -1 && sum~cons_1~v630:0:0 = 1 + v630:0:0
The following rules are bounded:
f_398(v607:0:0, v613:0:0, v614:0:0, sum~cons_1~v630:0:0, v615:0:0) -> f_398(v607:0:0, v613:0:0, v614:0:0, v630:0:0, 1 + v630:0:0) :|: v613:0:0 > 0 && v607:0:0 > 1 && v614:0:0 > 1 && v615:0:0 > 1 && v630:0:0 > -1 && sum~cons_1~v630:0:0 = 1 + v630:0:0

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

(13)
YES

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

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

(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 14 rulesP rules:
f_199(v52, v61, v53, v54, v55, v56, v57, v58, v62, 0, v60, 3, 1, 4) -> f_200(v52, v61, v63, v53, v54, v55, v56, v57, v58, v62, v64, 0, v60, 3, 1, 4) :|: 1 <= v63 && v64 = 3 + v63 && 4 <= v64
f_200(v52, v61, v63, v53, v54, v55, v56, v57, v58, v62, v64, 0, v60, 3, 1, 4) -> f_201(v52, v61, v63, v65, v53, v54, v55, v56, v57, v58, v62, v64, v66, 0, v60, 3, 1, 4) :|: 1 <= v65 && v66 = 3 + v65 && 4 <= v66
f_201(v52, v61, v63, v65, v53, v54, v55, v56, v57, v58, v62, v64, v66, 0, v60, 3, 1, 4) -> f_202(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: 1 <= v67 && v68 = 3 + v67 && 4 <= v68
f_202(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_203(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: TRUE
f_203(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_204(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: 0 = 0
f_204(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_206(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: v52 != 0
f_206(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_208(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: 0 = 0
f_208(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_210(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: TRUE
f_210(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_212(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: 0 = 0
f_212(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_214(v52, v61, v63, v65, v67, 0, v70, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: 1 + v70 = v52 && 0 <= v70
f_214(v52, v61, v63, v65, v67, 0, v70, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_216(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) :|: 0 = 0
f_216(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) -> f_218(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) :|: TRUE
f_218(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) -> f_198(v70, v53, v54, v55, v56, v57, v58, 0, v60, 3, 1, 4) :|: TRUE
f_198(v52, v53, v54, v55, v56, v57, v58, 0, v60, 3, 1, 4) -> f_199(v52, v61, v53, v54, v55, v56, v57, v58, v62, 0, v60, 3, 1, 4) :|: 1 <= v61 && v62 = 3 + v61 && 4 <= v62
Combined rules. Obtained 1 rulesP rules:
f_199(1 + v70:0, v61:0, v53:0, v54:0, v55:0, v56:0, v57:0, v58:0, v62:0, 0, v60:0, 3, 1, 4) -> f_199(v70:0, v61:1, v53:0, v54:0, v55:0, v56:0, v57:0, v58:0, 3 + v61:1, 0, v60:0, 3, 1, 4) :|: v65:0 > 0 && v63:0 > 0 && v67:0 > 0 && v70:0 > -1 && v61:1 > 0
Filtered unneeded arguments:
   f_199(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f_199(x1)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_199(sum~cons_1~v70:0) -> f_199(v70:0) :|: v70:0 > -1 && sum~cons_1~v70:0 = 1 + v70:0

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

(16)
Obligation:
Rules:
f_199(sum~cons_1~v70:0) -> f_199(v70:0) :|: v70:0 > -1 && sum~cons_1~v70:0 = 1 + v70:0

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

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

(18)
Obligation:
Rules:
f_199(sum~cons_1~v70:0:0) -> f_199(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0

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

(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_199 ] = f_199_1

The following rules are decreasing:
f_199(sum~cons_1~v70:0:0) -> f_199(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0

The following rules are bounded:
f_199(sum~cons_1~v70:0:0) -> f_199(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0


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

(20)
YES