/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 179 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 1365 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 83 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 13 ms]
(12) AND
    (13) IntTRS
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IntTRS
        (16) RankingReductionPairProof [EQUIVALENT, 7 ms]
        (17) IntTRS
        (18) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (19) IntTRS
        (20) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
        (21) YES
    (22) IntTRS
        (23) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (26) IntTRS
        (27) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (28) IntTRS
        (29) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (30) 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: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%3 = alloca i32, align 4
		store %x, %2
		store %y, %3
		%4 = load %3
		%5 = icmp eq %4 0
		br %5, %6, %8
	6:
		%7 = load %2
		store %7, %1
		br %21
	8:
		%9 = load %2
		%10 = icmp eq %9 0
		br %10, %11, %16
	11:
		%12 = load %3
		%13 = load %3
		%14 = sub %13 1
		%15 = call i32 @f(i32 %12, i32 %14)
		store %15, %1
		br %21
	16:
		%17 = load %3
		%18 = load %2
		%19 = sub %18 1
		%20 = call i32 @f(i32 %17, i32 %19)
		store %20, %1
		br %21
	21:
		%22 = load %1
		ret %22

*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%x = alloca i32, align 4
		%y = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %x
		%3 = call i32 @__VERIFIER_nondet_int()
		store %3, %y
		%4 = load %x
		%5 = icmp sge %4 0
		br %5, %6, %13
	6:
		%7 = load %y
		%8 = icmp sge %7 0
		br %8, %9, %13
	9:
		%10 = load %x
		%11 = load %y
		%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 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_210(v50, v51, v52, v53, 3, 0, 1, 4) -> f_211(v50, v51, v52, v54, v53, v55, 3, 0, 1, 4) :|: 1 <= v54 && v55 = 3 + v54 && 4 <= v55
f_211(v50, v51, v52, v54, v53, v55, 3, 0, 1, 4) -> f_212(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: 1 <= v56 && v57 = 3 + v56 && 4 <= v57
f_212(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_213(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: TRUE
f_213(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_214(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: TRUE
f_214(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_215(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: 0 = 0
f_215(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_217(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: v51 != 0
f_217(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_219(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0
f_219(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_221(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: TRUE
f_221(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_223(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0
f_223(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_225(0, v51, v52, v54, v56, v53, v55, v57, 3, 1, 4) :|: v50 = 0
f_223(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_226(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: v50 != 0
f_225(0, v51, v52, v54, v56, v53, v55, v57, 3, 1, 4) -> f_228(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) :|: 0 = 0
f_228(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) -> f_231(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) :|: TRUE
f_231(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) -> f_234(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) :|: 0 = 0
f_234(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) -> f_237(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) :|: 0 = 0
f_237(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) -> f_240(0, v51, v52, v54, v56, 1, v72, v53, v55, v57, 3, 4) :|: 1 + v72 = v51 && 0 <= v72
f_240(0, v51, v52, v54, v56, 1, v72, v53, v55, v57, 3, 4) -> f_242(v51, v72, v52, v53, v54, v55, v56, v57, 0, 1, 3, 4) :|: 0 = 0
f_242(v51, v72, v52, v53, v54, v55, v56, v57, 0, 1, 3, 4) -> f_244(v51, v72, v52, v53, v54, v55, v56, v57, 0, 3, 1, 4) :|: TRUE
f_244(v51, v72, v52, v53, v54, v55, v56, v57, 0, 3, 1, 4) -> f_209(v51, v72, 0) :|: TRUE
f_209(v50, v51, 0) -> f_210(v50, v51, v52, v53, 3, 0, 1, 4) :|: 1 <= v52 && v53 = 3 + v52 && 4 <= v53
f_226(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_229(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0
f_229(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_232(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: TRUE
f_232(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_235(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0
f_235(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_238(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0
f_238(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_241(v50, v51, v52, v54, v56, 0, v73, v53, v55, v57, 3, 1, 4) :|: 1 + v73 = v50 && 0 <= v73
f_241(v50, v51, v52, v54, v56, 0, v73, v53, v55, v57, 3, 1, 4) -> f_243(v51, v73, v52, v53, v54, v55, v56, v57, v50, 0, 3, 1, 4) :|: 0 = 0
f_243(v51, v73, v52, v53, v54, v55, v56, v57, v50, 0, 3, 1, 4) -> f_245(v51, v73, v52, v53, v54, v55, v56, v57, v50, 3, 1, 4, 0) :|: TRUE
f_245(v51, v73, v52, v53, v54, v55, v56, v57, v50, 3, 1, 4, 0) -> f_209(v51, v73, 0) :|: TRUE
Combined rules. Obtained 3 rulesP rules:
f_210(0, 1 + v72:0, v52:0, v53:0, 3, 0, 1, 4) -> f_210(1 + v72:0, v72:0, v52:1, 3 + v52:1, 3, 0, 1, 4) :|: v56:0 > 0 && v54:0 > 0 && v72:0 > -1 && v52:1 > 0
f_210(1 + v73:0, v51:0, v52:0, v53:0, 3, 0, 1, 4) -> f_210(v51:0, v73:0, v52:1, 3 + v52:1, 3, 0, 1, 4) :|: v56:0 > 0 && v54:0 > 0 && v51:0 < 0 && v73:0 > -1 && v52:1 > 0
f_210(1 + v73:0, v51:0, v52:0, v53:0, 3, 0, 1, 4) -> f_210(v51:0, v73:0, v52:1, 3 + v52:1, 3, 0, 1, 4) :|: v56:0 > 0 && v54:0 > 0 && v51:0 > 0 && v73:0 > -1 && v52:1 > 0
Filtered unneeded arguments:
   f_210(x1, x2, x3, x4, x5, x6, x7, x8) -> f_210(x1, x2)
Removed division, modulo operations, cleaned up constraints. Obtained 3 rules.P rules:
f_210(cons_0, sum~cons_1~v72:0) -> f_210(1 + v72:0, v72:0) :|: v72:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0 = 1 + v72:0
f_210(sum~cons_1~v73:0, v51:0) -> f_210(v51:0, v73:0) :|: v51:0 < 0 && v73:0 > -1 && sum~cons_1~v73:0 = 1 + v73:0
f_210(sum~cons_1~v73:0, v51:0) -> f_210(v51:0, v73:0) :|: v51:0 > 0 && v73:0 > -1 && sum~cons_1~v73:0 = 1 + v73:0

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

(8)
Obligation:
Rules:
f_210(cons_0, sum~cons_1~v72:0) -> f_210(1 + v72:0, v72:0) :|: v72:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0 = 1 + v72:0
f_210(sum~cons_1~v73:0, v51:0) -> f_210(v51:0, v73:0) :|: v51:0 < 0 && v73:0 > -1 && sum~cons_1~v73:0 = 1 + v73:0
f_210(x, x1) -> f_210(x1, x2) :|: x1 > 0 && x2 > -1 && x = 1 + x2

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

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

(10)
Obligation:
Rules:
f_210(cons_0, sum~cons_1~v72:0:0) -> f_210(1 + v72:0:0, v72:0:0) :|: v72:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0 = 1 + v72:0:0
f_210(sum~cons_1~x2:0, x1:0) -> f_210(x1:0, x2:0) :|: x1:0 > 0 && x2:0 > -1 && sum~cons_1~x2:0 = 1 + x2:0
f_210(sum~cons_1~v73:0:0, v51:0:0) -> f_210(v51:0:0, v73:0:0) :|: v51:0:0 < 0 && v73:0:0 > -1 && sum~cons_1~v73:0:0 = 1 + v73:0:0

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

(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_210(x, x1)] = -4 - 2*x - 3*x*x1 + 2*x^2 + x1 + 2*x1^2

The following rules are decreasing:
f_210(cons_0, sum~cons_1~v72:0:0) -> f_210(1 + v72:0:0, v72:0:0) :|: v72:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0 = 1 + v72:0:0
The following rules are bounded:
f_210(sum~cons_1~v73:0:0, v51:0:0) -> f_210(v51:0:0, v73:0:0) :|: v51:0:0 < 0 && v73:0:0 > -1 && sum~cons_1~v73:0:0 = 1 + v73:0:0

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

(12)
Complex Obligation (AND)

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

(13)
Obligation:
Rules:
f_210(sum~cons_1~x2:0, x1:0) -> f_210(x1:0, x2:0) :|: x1:0 > 0 && x2:0 > -1 && sum~cons_1~x2:0 = 1 + x2:0
f_210(sum~cons_1~v73:0:0, v51:0:0) -> f_210(v51:0:0, v73:0:0) :|: v51:0:0 < 0 && v73:0:0 > -1 && sum~cons_1~v73:0:0 = 1 + v73:0:0

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

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

(15)
Obligation:
Rules:
f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0
f_210(sum~cons_1~v73:0:0:0, v51:0:0:0) -> f_210(v51:0:0:0, v73:0:0:0) :|: v51:0:0:0 < 0 && v73:0:0:0 > -1 && sum~cons_1~v73:0:0:0 = 1 + v73:0:0:0

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

(16) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_210 ] = 3*f_210_2 + 3*f_210_1

The following rules are decreasing:
f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0
f_210(sum~cons_1~v73:0:0:0, v51:0:0:0) -> f_210(v51:0:0:0, v73:0:0:0) :|: v51:0:0:0 < 0 && v73:0:0:0 > -1 && sum~cons_1~v73:0:0:0 = 1 + v73:0:0:0

The following rules are bounded:
f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0


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

(17)
Obligation:
Rules:
f_210(sum~cons_1~v73:0:0:0, v51:0:0:0) -> f_210(v51:0:0:0, v73:0:0:0) :|: v51:0:0:0 < 0 && v73:0:0:0 > -1 && sum~cons_1~v73:0:0:0 = 1 + v73:0:0:0

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

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

(19)
Obligation:
Rules:
f_210(sum~cons_1~v73:0:0:0:0, v51:0:0:0:0) -> f_210(v51:0:0:0:0, v73:0:0:0:0) :|: v51:0:0:0:0 < 0 && v73:0:0:0:0 > -1 && sum~cons_1~v73:0:0:0:0 = 1 + v73:0:0:0:0

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

(20) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_210(x, x1)] = -x1

The following rules are decreasing:
f_210(sum~cons_1~v73:0:0:0:0, v51:0:0:0:0) -> f_210(v51:0:0:0:0, v73:0:0:0:0) :|: v51:0:0:0:0 < 0 && v73:0:0:0:0 > -1 && sum~cons_1~v73:0:0:0:0 = 1 + v73:0:0:0:0
The following rules are bounded:
f_210(sum~cons_1~v73:0:0:0:0, v51:0:0:0:0) -> f_210(v51:0:0:0:0, v73:0:0:0:0) :|: v51:0:0:0:0 < 0 && v73:0:0:0:0 > -1 && sum~cons_1~v73:0:0:0:0 = 1 + v73:0:0:0:0

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

(21)
YES

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

(22)
Obligation:
Rules:
f_210(cons_0, sum~cons_1~v72:0:0) -> f_210(1 + v72:0:0, v72:0:0) :|: v72:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0 = 1 + v72:0:0
f_210(sum~cons_1~x2:0, x1:0) -> f_210(x1:0, x2:0) :|: x1:0 > 0 && x2:0 > -1 && sum~cons_1~x2:0 = 1 + x2:0

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

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

(24)
Obligation:
Rules:
f_210(cons_0, sum~cons_1~v72:0:0:0) -> f_210(1 + v72:0:0:0, v72:0:0:0) :|: v72:0:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0:0 = 1 + v72:0:0:0
f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0

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

(25) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_210(x, x1)] = -2*x - x*x1 + x^2 + x1^2

The following rules are decreasing:
f_210(cons_0, sum~cons_1~v72:0:0:0) -> f_210(1 + v72:0:0:0, v72:0:0:0) :|: v72:0:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0:0 = 1 + v72:0:0:0
The following rules are bounded:
f_210(cons_0, sum~cons_1~v72:0:0:0) -> f_210(1 + v72:0:0:0, v72:0:0:0) :|: v72:0:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0:0 = 1 + v72:0:0:0

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

(26)
Obligation:
Rules:
f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0

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

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

(28)
Obligation:
Rules:
f_210(sum~cons_1~x2:0:0:0, x1:0:0:0) -> f_210(x1:0:0:0, x2:0:0:0) :|: x1:0:0:0 > 0 && x2:0:0:0 > -1 && sum~cons_1~x2:0:0:0 = 1 + x2:0:0:0

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

(29) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_210(x, x1)] = x + x1

The following rules are decreasing:
f_210(sum~cons_1~x2:0:0:0, x1:0:0:0) -> f_210(x1:0:0:0, x2:0:0:0) :|: x1:0:0:0 > 0 && x2:0:0:0 > -1 && sum~cons_1~x2:0:0:0 = 1 + x2:0:0:0
The following rules are bounded:
f_210(sum~cons_1~x2:0:0:0, x1:0:0:0) -> f_210(x1:0:0:0, x2:0:0:0) :|: x1:0:0:0 > 0 && x2:0:0:0 > -1 && sum~cons_1~x2:0:0:0 = 1 + x2:0:0:0

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

(30)
YES