/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 177 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 2338 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 146 ms]
(8) IntTRS
(9) IRS2T2 [EQUIVALENT, 0 ms]
(10) T2IntSys
(11) T2 [EQUIVALENT, 944 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: true visibilityType: DEFAULT callingConvention: ccc
*BasicFunctionTypename: "rec1" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (i i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		store %i, %2
		%3 = load %2
		%4 = icmp sle %3 0
		br %4, %5, %6
	5:
		store 0, %1
		br %14
	6:
		%7 = load %2
		%8 = sub %7 2
		%9 = call i32 @rec1(i32 %8)
		%10 = sub %9 1
		%11 = call i32 @rec1(i32 %10)
		%12 = call i32 @rec1(i32 %11)
		%13 = add %12 1
		store %13, %1
		br %14
	14:
		%15 = load %1
		ret %15

*BasicFunctionTypename: "rec2" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (j i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		store %j, %2
		%3 = load %2
		%4 = icmp sle %3 0
		br %4, %5, %6
	5:
		store 0, %1
		br %12
	6:
		%7 = load %2
		%8 = add %7 1
		%9 = call i32 @rec1(i32 %8)
		%10 = call i32 @rec2(i32 %9)
		%11 = sub %10 1
		store %11, %1
		br %12
	12:
		%13 = load %1
		ret %13

*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
		store 0, %1
		%2 = call i32 (...)* @__VERIFIER_nondet_int()
		store %2, %x
		%3 = load %x
		%4 = call i32 @rec1(i32 %3)
		%5 = load %1
		ret %5


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 47 rulesP rules:
f_191(v45, v52, v46, v47, v48, v49, v53, 0, v51, 3, 1, 4) -> f_192(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 1 <= v54 && v55 = 3 + v54 && 4 <= v55
f_192(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_193(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: TRUE
f_193(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_194(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 0 = 0
f_194(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_196(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 0 < v45 && 1 <= v51
f_196(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_198(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: 0 = 0
f_198(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_200(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: TRUE
f_200(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_202(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: 0 = 0
f_202(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_204(v45, v52, v54, 0, v57, v46, v47, v48, v49, v53, v55, v51, 3, 2, 1, 4) :|: 2 + v57 = v45 && 0 <= 1 + v57
f_204(v45, v52, v54, 0, v57, v46, v47, v48, v49, v53, v55, v51, 3, 2, 1, 4) -> f_206(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 1, 4) :|: 0 = 0
f_206(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 1, 4) -> f_208(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 1, 4) :|: TRUE
f_206(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 1, 4) -> f_211(v57, 0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 2, 1, 4) :|: TRUE
f_206(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 1, 4) -> f_318(v57, 1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 4) :|: TRUE
f_206(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 1, 4) -> f_342(v57, 1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 4) :|: TRUE
f_206(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 1, 4) -> f_365(v57, 1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 4) :|: TRUE
f_208(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 1, 4) -> f_189(v57, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE
f_189(v45, v46, v47, v48, v49, 0, v51, 3, 1, 4) -> f_191(v45, v52, v46, v47, v48, v49, v53, 0, v51, 3, 1, 4) :|: 1 <= v52 && v53 = 3 + v52 && 4 <= v53
f_211(v57, 0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 2, 1, 4) -> f_212(v45, v52, v54, 0, v57, v46, v47, v48, v49, v53, v55, v51, 3, 2, 1, 4) :|: 0 = 0
f_212(v45, v52, v54, 0, v57, v46, v47, v48, v49, v53, v55, v51, 3, 2, 1, 4) -> f_213(v45, v52, v54, 0, v57, -1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 1, 4) :|: 0 = 0
f_213(v45, v52, v54, 0, v57, -1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 1, 4) -> f_214(-1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, v57, 3, 2, 1, 4) :|: 0 = 0
f_214(-1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, v57, 3, 2, 1, 4) -> f_215(-1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 2, 4) :|: TRUE
f_214(-1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, v57, 3, 2, 1, 4) -> f_216(-1, 0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 3, 2, 1, 4) :|: TRUE
f_215(-1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 2, 4) -> f_189(-1, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE
f_216(-1, 0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 3, 2, 1, 4) -> f_217(v45, v52, v54, 0, v57, -1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 1, 4) :|: 0 = 0
f_217(v45, v52, v54, 0, v57, -1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 1, 4) -> f_218(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, -1, 3, 2, 1, 4) :|: 0 = 0
f_218(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, -1, 3, 2, 1, 4) -> f_219(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 2, 4) :|: TRUE
f_219(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 2, 4) -> f_189(0, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE
f_318(v57, 1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 4) -> f_324(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) :|: 0 = 0
f_324(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) -> f_326(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) :|: 0 = 0
f_326(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) -> f_327(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) :|: 0 = 0
f_327(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) -> f_328(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 4) :|: TRUE
f_327(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) -> f_329(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) :|: TRUE
f_328(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 4) -> f_189(0, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE
f_329(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) -> f_331(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) :|: 0 = 0
f_331(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) -> f_332(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) :|: 0 = 0
f_332(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) -> f_333(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 4) :|: TRUE
f_333(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 4) -> f_189(0, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE
f_342(v57, 1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 4) -> f_348(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) :|: 0 = 0
f_348(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) -> f_350(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) :|: 0 = 0
f_350(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) -> f_351(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) :|: 0 = 0
f_351(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) -> f_352(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 4) :|: TRUE
f_351(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) -> f_353(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) :|: TRUE
f_352(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 4) -> f_189(0, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE
f_353(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) -> f_355(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) :|: 0 = 0
f_355(v45, v52, v54, 0, v57, 1, v46, v47, v48, v49, v53, v55, v51, 3, 2, 4) -> f_356(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) :|: 0 = 0
f_356(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, v57, 1, 3, 2, 4) -> f_357(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 4) :|: TRUE
f_357(0, v46, v47, v48, v49, v52, v53, v54, v55, v51, v45, 3, 1, 4) -> f_189(0, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE
f_365(v57, 1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 4) -> f_342(v57, 1, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 2, 4) :|: TRUE
Combined rules. Obtained 5 rulesP rules:
f_191(2 + v57:0, v52:0, v46:0, v47:0, v48:0, v49:0, v53:0, 0, v51:0, 3, 1, 4) -> f_351(0, v46:0, v47:0, v48:0, v49:0, v52:0, v53:0, v54:0, 3 + v54:0, v51:0, 2 + v57:0, v57:0, 1, 3, 2, 4) :|: v54:0 > 0 && v51:0 > 0 && v57:0 > -2
f_191(2 + v57:0, v52:0, v46:0, v47:0, v48:0, v49:0, v53:0, 0, v51:0, 3, 1, 4) -> f_191(0, v52:1, v46:0, v47:0, v48:0, v49:0, 3 + v52:1, 0, v51:0, 3, 1, 4) :|: v54:0 > 0 && v51:0 > 0 && v57:0 > -2 && v52:1 > 0
f_351(0, v46:0, v47:0, v48:0, v49:0, v52:0, v53:0, v54:0, v55:0, v51:0, v45:0, v57:0, 1, 3, 2, 4) -> f_191(0, v52:1, v46:0, v47:0, v48:0, v49:0, 3 + v52:1, 0, v51:0, 3, 1, 4) :|: v52:1 > 0
f_191(2 + v57:0, v52:0, v46:0, v47:0, v48:0, v49:0, v53:0, 0, v51:0, 3, 1, 4) -> f_191(-1, v52:1, v46:0, v47:0, v48:0, v49:0, 3 + v52:1, 0, v51:0, 3, 1, 4) :|: v54:0 > 0 && v51:0 > 0 && v57:0 > -2 && v52:1 > 0
f_191(2 + v57:0, v52:0, v46:0, v47:0, v48:0, v49:0, v53:0, 0, v51:0, 3, 1, 4) -> f_191(v57:0, v52:1, v46:0, v47:0, v48:0, v49:0, 3 + v52:1, 0, v51:0, 3, 1, 4) :|: v54:0 > 0 && v51:0 > 0 && v57:0 > -2 && v52:1 > 0
Filtered unneeded arguments:
   f_191(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f_191(x1, x9)
   f_351(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_351(x10)
Removed division, modulo operations, cleaned up constraints. Obtained 5 rules.P rules:
f_191(sum~cons_2~v57:0, v51:0) -> f_351(v51:0) :|: v51:0 > 0 && v57:0 > -2 && sum~cons_2~v57:0 = 2 + v57:0
f_191(sum~cons_2~v57:0, v51:0) -> f_191(0, v51:0) :|: v51:0 > 0 && v57:0 > -2 && sum~cons_2~v57:0 = 2 + v57:0
f_351(v51:0) -> f_191(0, v51:0) :|: TRUE
f_191(sum~cons_2~v57:0, v51:0) -> f_191(-1, v51:0) :|: v51:0 > 0 && v57:0 > -2 && sum~cons_2~v57:0 = 2 + v57:0
f_191(sum~cons_2~v57:0, v51:0) -> f_191(v57:0, v51:0) :|: v51:0 > 0 && v57:0 > -2 && sum~cons_2~v57:0 = 2 + v57:0

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

(8)
Obligation:
Rules:
f_191(sum~cons_2~v57:0, v51:0) -> f_351(v51:0) :|: v51:0 > 0 && v57:0 > -2 && sum~cons_2~v57:0 = 2 + v57:0
f_191(x, x1) -> f_191(0, x1) :|: x1 > 0 && x2 > -2 && x = 2 + x2
f_351(x3) -> f_191(0, x3) :|: TRUE
f_191(x4, x5) -> f_191(-1, x5) :|: x5 > 0 && x6 > -2 && x4 = 2 + x6
f_191(x7, x8) -> f_191(x9, x8) :|: x8 > 0 && x9 > -2 && x7 = 2 + x9

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

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

   (f_191_2,1)
   (f_351_2,2)

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

(10)
Obligation:
START: 0;

FROM: 0;
TO: 1;

FROM: 0;
TO: 2;

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

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

FROM: 2;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := 0;
x1 := oldX0;
TO: 1;

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

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


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

(11) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 2, 5, 6, 7, 8, 20, 22, 23 using the following rank functions:
    - Rank function 1:
      RF for loc. 6: 3*x0
      RF for loc. 8: -1+3*x0
      RF for loc. 12: 1
      Bound for (chained) transitions 5, 20: 2
      Bound for (chained) transitions 6: 2
      Bound for (chained) transitions 7: 2
      Bound for (chained) transitions 8: 2
      Bound for (chained) transitions 22: 1
      Bound for (chained) transitions 23: 1
    - Rank function 2:
      RF for loc. 6: 0
      RF for loc. 8: -1
      Bound for (chained) transitions 2: 0

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

(12)
YES