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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 155 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 592 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 0 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 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: "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
		%z = 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 = call i32 @__VERIFIER_nondet_int()
		store %4, %z
		%5 = load %y
		%6 = icmp sgt %5 0
		br %6, %7, %17
	7:
		br %8
	8:
		%9 = load %x
		%10 = load %z
		%11 = icmp sge %9 %10
		br %11, %12, %16
	12:
		%13 = load %z
		%14 = load %y
		%15 = add %13 %14
		store %15, %z
		br %8
	16:
		br %17
	17:
		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 11 rulesP rules:
f_130(v28, v29, v30, v31, v32, v33, v34, 1, v36, v37, v38, v39, v40, v41, 0, 3, 4) -> f_131(v28, v29, v30, v31, v32, v33, v34, 1, v37, v36, v38, v39, v40, v41, 0, 3, 4) :|: 0 = 0
f_131(v28, v29, v30, v31, v32, v33, v34, 1, v37, v36, v38, v39, v40, v41, 0, 3, 4) -> f_132(v28, v29, v30, v31, v32, v33, v34, 1, v37, v36, v38, v39, v40, v41, 0, 3, 4) :|: v37 <= v32
f_132(v28, v29, v30, v31, v32, v33, v34, 1, v37, v36, v38, v39, v40, v41, 0, 3, 4) -> f_134(v28, v29, v30, v31, v32, v33, v34, 1, v37, v36, v38, v39, v40, v41, 0, 3, 4) :|: 0 = 0
f_134(v28, v29, v30, v31, v32, v33, v34, 1, v37, v36, v38, v39, v40, v41, 0, 3, 4) -> f_136(v28, v29, v30, v31, v32, v33, v34, 1, v37, v36, v38, v39, v40, v41, 0, 3, 4) :|: TRUE
f_136(v28, v29, v30, v31, v32, v33, v34, 1, v37, v36, v38, v39, v40, v41, 0, 3, 4) -> f_138(v28, v29, v30, v31, v32, v33, v34, 1, v37, v38, v39, v40, v41, 0, 3, 4) :|: 0 = 0
f_138(v28, v29, v30, v31, v32, v33, v34, 1, v37, v38, v39, v40, v41, 0, 3, 4) -> f_140(v28, v29, v30, v31, v32, v33, v34, 1, v37, v38, v39, v40, v41, 0, 3, 4) :|: 0 = 0
f_140(v28, v29, v30, v31, v32, v33, v34, 1, v37, v38, v39, v40, v41, 0, 3, 4) -> f_141(v28, v29, v30, v31, v32, v33, v34, 1, v37, v52, v38, v39, v40, v41, 0, 3, 4) :|: v52 = v37 + v33
f_141(v28, v29, v30, v31, v32, v33, v34, 1, v37, v52, v38, v39, v40, v41, 0, 3, 4) -> f_142(v28, v29, v30, v31, v32, v33, v34, 1, v37, v52, v38, v39, v40, v41, 0, 3, 4) :|: TRUE
f_142(v28, v29, v30, v31, v32, v33, v34, 1, v37, v52, v38, v39, v40, v41, 0, 3, 4) -> f_143(v28, v29, v30, v31, v32, v33, v34, 1, v37, v52, v38, v39, v40, v41, 0, 3, 4) :|: TRUE
f_143(v28, v29, v30, v31, v32, v33, v34, 1, v37, v52, v38, v39, v40, v41, 0, 3, 4) -> f_129(v28, v29, v30, v31, v32, v33, v34, 1, v37, v52, v38, v39, v40, v41, 0, 3, 4) :|: v34 <= v32 && v37 <= v32 && 1 <= v28 && 1 <= v29 && 1 <= v30 && 1 <= v31 && 1 <= v33 && 4 <= v38 && 4 <= v39 && 4 <= v40 && 4 <= v41 && v28 <= v38 && v29 <= v39 && v30 <= v40 && v31 <= v41
f_129(v28, v29, v30, v31, v32, v33, v34, 1, v36, v37, v38, v39, v40, v41, 0, 3, 4) -> f_130(v28, v29, v30, v31, v32, v33, v34, 1, v36, v37, v38, v39, v40, v41, 0, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_130(v28:0, v29:0, v30:0, v31:0, v32:0, v33:0, v34:0, 1, v36:0, v37:0, v38:0, v39:0, v40:0, v41:0, 0, 3, 4) -> f_130(v28:0, v29:0, v30:0, v31:0, v32:0, v33:0, v34:0, 1, v37:0, v37:0 + v33:0, v38:0, v39:0, v40:0, v41:0, 0, 3, 4) :|: v37:0 <= v32:0 && v34:0 <= v32:0 && v28:0 > 0 && v29:0 > 0 && v30:0 > 0 && v31:0 > 0 && v33:0 > 0 && v38:0 > 3 && v39:0 > 3 && v40:0 > 3 && v41:0 > 3 && v38:0 >= v28:0 && v39:0 >= v29:0 && v41:0 >= v31:0 && v40:0 >= v30:0
Filtered unneeded arguments:
   f_130(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_130(x1, x2, x3, x4, x5, x6, x7, x10, x11, x12, x13, x14)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_130(v28:0, v29:0, v30:0, v31:0, v32:0, v33:0, v34:0, v37:0, v38:0, v39:0, v40:0, v41:0) -> f_130(v28:0, v29:0, v30:0, v31:0, v32:0, v33:0, v34:0, v37:0 + v33:0, v38:0, v39:0, v40:0, v41:0) :|: v34:0 <= v32:0 && v37:0 <= v32:0 && v28:0 > 0 && v29:0 > 0 && v30:0 > 0 && v31:0 > 0 && v33:0 > 0 && v38:0 > 3 && v39:0 > 3 && v40:0 > 3 && v41:0 > 3 && v38:0 >= v28:0 && v39:0 >= v29:0 && v40:0 >= v30:0 && v41:0 >= v31:0

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

(8)
Obligation:
Rules:
f_130(v28:0, v29:0, v30:0, v31:0, v32:0, v33:0, v34:0, v37:0, v38:0, v39:0, v40:0, v41:0) -> f_130(v28:0, v29:0, v30:0, v31:0, v32:0, v33:0, v34:0, v37:0 + v33:0, v38:0, v39:0, v40:0, v41:0) :|: v34:0 <= v32:0 && v37:0 <= v32:0 && v28:0 > 0 && v29:0 > 0 && v30:0 > 0 && v31:0 > 0 && v33:0 > 0 && v38:0 > 3 && v39:0 > 3 && v40:0 > 3 && v41:0 > 3 && v38:0 >= v28:0 && v39:0 >= v29:0 && v40:0 >= v30:0 && v41:0 >= v31:0

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

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

(10)
Obligation:
Rules:
f_130(v28:0:0, v29:0:0, v30:0:0, v31:0:0, v32:0:0, v33:0:0, v34:0:0, v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0) -> f_130(v28:0:0, v29:0:0, v30:0:0, v31:0:0, v32:0:0, v33:0:0, v34:0:0, v37:0:0 + v33:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0) :|: v40:0:0 >= v30:0:0 && v41:0:0 >= v31:0:0 && v39:0:0 >= v29:0:0 && v38:0:0 >= v28:0:0 && v41:0:0 > 3 && v40:0:0 > 3 && v39:0:0 > 3 && v38:0:0 > 3 && v33:0:0 > 0 && v31:0:0 > 0 && v30:0:0 > 0 && v29:0:0 > 0 && v28:0:0 > 0 && v37:0:0 <= v32:0:0 && v34:0:0 <= v32:0:0

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

(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_130 ] = -1*f_130_8 + f_130_5

The following rules are decreasing:
f_130(v28:0:0, v29:0:0, v30:0:0, v31:0:0, v32:0:0, v33:0:0, v34:0:0, v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0) -> f_130(v28:0:0, v29:0:0, v30:0:0, v31:0:0, v32:0:0, v33:0:0, v34:0:0, v37:0:0 + v33:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0) :|: v40:0:0 >= v30:0:0 && v41:0:0 >= v31:0:0 && v39:0:0 >= v29:0:0 && v38:0:0 >= v28:0:0 && v41:0:0 > 3 && v40:0:0 > 3 && v39:0:0 > 3 && v38:0:0 > 3 && v33:0:0 > 0 && v31:0:0 > 0 && v30:0:0 > 0 && v29:0:0 > 0 && v28:0:0 > 0 && v37:0:0 <= v32:0:0 && v34:0:0 <= v32:0:0

The following rules are bounded:
f_130(v28:0:0, v29:0:0, v30:0:0, v31:0:0, v32:0:0, v33:0:0, v34:0:0, v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0) -> f_130(v28:0:0, v29:0:0, v30:0:0, v31:0:0, v32:0:0, v33:0:0, v34:0:0, v37:0:0 + v33:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0) :|: v40:0:0 >= v30:0:0 && v41:0:0 >= v31:0:0 && v39:0:0 >= v29:0:0 && v38:0:0 >= v28:0:0 && v41:0:0 > 3 && v40:0:0 > 3 && v39:0:0 > 3 && v38:0:0 > 3 && v33:0:0 > 0 && v31:0:0 > 0 && v30:0:0 > 0 && v29:0:0 > 0 && v28:0:0 > 0 && v37:0:0 <= v32:0:0 && v34:0:0 <= v32:0:0


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

(12)
YES