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


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 178 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 1737 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 57 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
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(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM.
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(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 %11
	6:
		%7 = load %2
		%8 = add %7 1
		%9 = call i32 @rec1(i32 %8)
		%10 = call i32 @rec2(i32 %9)
		store %10, %1
		br %11
	11:
		%12 = load %1
		ret %12

*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 %11
	6:
		%7 = load %2
		%8 = sub %7 1
		%9 = call i32 @rec2(i32 %8)
		%10 = call i32 @rec1(i32 %9)
		store %10, %1
		br %11
	11:
		%12 = load %1
		ret %12

*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 @rec2(i32 %3)
		%5 = load %1
		ret %5


Analyze Termination of all function calls matching the pattern:
main()
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(3) LLVMToTerminationGraphProof (EQUIVALENT)
Constructed symbolic execution graph for LLVM program and proved memory safety.
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(4)
Obligation:
SE Graph
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(5) SymbolicExecutionGraphToSCCProof (SOUND)
Splitted symbolic execution graph to 1 SCC.
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(6)
Obligation:
SCC
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(7) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 12 rulesP rules:
f_179(v45, v52, v46, v47, v48, v49, v53, 0, v51, 3, 1, 4) -> f_180(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 1 <= v54 && v55 = 3 + v54 && 4 <= v55
f_180(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_181(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: TRUE
f_181(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_182(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 0 = 0
f_182(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_184(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 0 < v45 && 1 <= v51
f_184(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_186(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: 0 = 0
f_186(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_188(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: TRUE
f_188(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_190(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: 0 = 0
f_190(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_192(v45, v52, v54, 0, v57, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: 1 + v57 = v45 && 0 <= v57
f_192(v45, v52, v54, 0, v57, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_194(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 4) :|: 0 = 0
f_194(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 4) -> f_196(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 4) :|: TRUE
f_196(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 4) -> f_177(v57, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE
f_177(v45, v46, v47, v48, v49, 0, v51, 3, 1, 4) -> f_179(v45, v52, v46, v47, v48, v49, v53, 0, v51, 3, 1, 4) :|: 1 <= v52 && v53 = 3 + v52 && 4 <= v53
Combined rules. Obtained 1 rulesP rules:
f_179(1 + v57:0, v52:0, v46:0, v47:0, v48:0, v49:0, v53:0, 0, v51:0, 3, 1, 4) -> f_179(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 > -1 && v52:1 > 0
Filtered unneeded arguments:
   f_179(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f_179(x1, x9)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_179(sum~cons_1~v57:0, v51:0) -> f_179(v57:0, v51:0) :|: v51:0 > 0 && v57:0 > -1 && sum~cons_1~v57:0 = 1 + v57:0

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(8)
Obligation:
Rules:
f_179(sum~cons_1~v57:0, v51:0) -> f_179(v57:0, v51:0) :|: v51:0 > 0 && v57:0 > -1 && sum~cons_1~v57:0 = 1 + v57:0

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f_179(sum~cons_1~v57:0:0, v51:0:0) -> f_179(v57:0:0, v51:0:0) :|: v51:0:0 > 0 && v57:0:0 > -1 && sum~cons_1~v57:0:0 = 1 + v57:0:0

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_179(x, x1)] = x

The following rules are decreasing:
f_179(sum~cons_1~v57:0:0, v51:0:0) -> f_179(v57:0:0, v51:0:0) :|: v51:0:0 > 0 && v57:0:0 > -1 && sum~cons_1~v57:0:0 = 1 + v57:0:0
The following rules are bounded:
f_179(sum~cons_1~v57:0:0, v51:0:0) -> f_179(v57:0:0, v51:0:0) :|: v51:0:0 > 0 && v57:0:0 > -1 && sum~cons_1~v57:0:0 = 1 + v57:0:0

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(12)
YES