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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 174 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 1089 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 46 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 12 ms]
        (13) IntTRS
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IntTRS
        (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (17) IntTRS
        (18) RankingReductionPairProof [EQUIVALENT, 4 ms]
        (19) YES
    (20) LLVM Symbolic Execution SCC
        (21) SCC2IRS [SOUND, 35 ms]
        (22) IntTRS
        (23) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
        (26) 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
		%N = alloca i32, align 4
		%j = alloca i32, align 4
		%i = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %N
		%3 = load %N
		store %3, %i
		br %4
	4:
		%5 = load %i
		%6 = icmp sgt %5 0
		br %6, %7, %18
	7:
		%8 = load %N
		store %8, %j
		br %9
	9:
		%10 = load %j
		%11 = icmp sgt %10 0
		br %11, %12, %15
	12:
		%13 = load %j
		%14 = add %13 -1
		store %14, %j
		br %9
	15:
		%16 = load %i
		%17 = add %16 -1
		store %17, %i
		br %4
	18:
		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 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 28 rulesP rules:
f_211(v231, v232, v233, v234, v235, v236, 1, v238, v240, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_212(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 1 + v247 = v238 && 0 <= v247
f_212(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_213(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: TRUE
f_213(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_214(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: TRUE
f_214(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_215(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 0 = 0
f_215(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_216(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 0 < v247 && 2 <= v238
f_215(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_217(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) :|: v247 <= 0 && v238 = 1 && v247 = 0 && 0 = 0
f_216(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_218(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 0 = 0
f_218(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_220(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: TRUE
f_220(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_210(v231, v232, v233, v234, v235, v236, 1, v247, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: TRUE
f_210(v231, v232, v233, v234, v235, v236, 1, v238, v239, v240, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_211(v231, v232, v233, v234, v235, v236, 1, v238, v240, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 0 = 0
f_217(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) -> f_219(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0
f_219(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) -> f_221(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) :|: TRUE
f_221(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) -> f_222(v231, v232, v233, v234, v235, v236, 1, 0, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0
f_222(v231, v232, v233, v234, v235, v236, 1, 0, v242, v243, v244, v245, 3, 2, 4) -> f_223(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) :|: 1 + v297 = v236 && 0 <= v297
f_223(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) -> f_224(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) :|: TRUE
f_224(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) -> f_225(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) :|: TRUE
f_225(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) -> f_226(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0
f_226(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_227(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: 0 < v297 && 2 <= v236 && 3 <= v235
f_227(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_229(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0
f_229(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_231(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: TRUE
f_231(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_233(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0
f_233(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_234(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: TRUE
f_234(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_235(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: TRUE
f_235(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_236(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: TRUE
f_236(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) -> f_237(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) :|: 0 = 0
f_237(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) -> f_238(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) :|: 0 = 0
f_238(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) -> f_239(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) :|: TRUE
f_239(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) -> f_210(v327, v328, v329, v330, v331, v332, 1, v331, 1, 0, v335, v336, v337, v338, v339, 0, 3, 2, 4) :|: TRUE
Combined rules. Obtained 2 rulesP rules:
f_211(v231:0, v232:0, v233:0, v234:0, v235:0, v236:0, 1, 1 + v247:0, v240:0, v241:0, v242:0, v243:0, v244:0, v245:0, 0, 3, 2, 4) -> f_211(v231:0, v232:0, v233:0, v234:0, v235:0, v236:0, 1, v247:0, v247:0, v241:0, v242:0, v243:0, v244:0, v245:0, 0, 3, 2, 4) :|: v247:0 > 0
f_211(v231:0, v232:0, v233:0, v234:0, v235:0, 1 + v297:0, 1, 1, v240:0, v241:0, v242:0, v243:0, v244:0, v245:0, 0, 3, 2, 4) -> f_211(v231:0, v232:0, v233:0, v234:0, v235:0, v297:0, 1, v235:0, 0, 1 + v297:0, v242:0, v243:0, v244:0, v245:0, 0, 3, 2, 4) :|: v297:0 > 0 && v235:0 > 2
Filtered unneeded arguments:
   f_211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_211(x5, x6, x8)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_211(v235:0, v236:0, sum~cons_1~v247:0) -> f_211(v235:0, v236:0, v247:0) :|: v247:0 > 0 && sum~cons_1~v247:0 = 1 + v247:0
f_211(v235:0, sum~cons_1~v297:0, cons_1) -> f_211(v235:0, v297:0, v235:0) :|: v297:0 > 0 && v235:0 > 2 && sum~cons_1~v297:0 = 1 + v297:0 && cons_1 = 1

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

(9)
Obligation:
Rules:
f_211(v235:0, v236:0, sum~cons_1~v247:0) -> f_211(v235:0, v236:0, v247:0) :|: v247:0 > 0 && sum~cons_1~v247:0 = 1 + v247:0
f_211(x, x1, x2) -> f_211(x, x3, x) :|: x3 > 0 && x > 2 && x1 = 1 + x3 && x2 = 1

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

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

(11)
Obligation:
Rules:
f_211(v235:0:0, v236:0:0, sum~cons_1~v247:0:0) -> f_211(v235:0:0, v236:0:0, v247:0:0) :|: v247:0:0 > 0 && sum~cons_1~v247:0:0 = 1 + v247:0:0
f_211(x:0, sum~cons_1~x3:0, cons_1) -> f_211(x:0, x3:0, x:0) :|: x3:0 > 0 && x:0 > 2 && sum~cons_1~x3:0 = 1 + x3:0 && cons_1 = 1

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_211 ] = 2*f_211_1 + f_211_2

The following rules are decreasing:
f_211(x:0, sum~cons_1~x3:0, cons_1) -> f_211(x:0, x3:0, x:0) :|: x3:0 > 0 && x:0 > 2 && sum~cons_1~x3:0 = 1 + x3:0 && cons_1 = 1

The following rules are bounded:
f_211(x:0, sum~cons_1~x3:0, cons_1) -> f_211(x:0, x3:0, x:0) :|: x3:0 > 0 && x:0 > 2 && sum~cons_1~x3:0 = 1 + x3:0 && cons_1 = 1


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

(13)
Obligation:
Rules:
f_211(v235:0:0, v236:0:0, sum~cons_1~v247:0:0) -> f_211(v235:0:0, v236:0:0, v247:0:0) :|: v247:0:0 > 0 && sum~cons_1~v247:0:0 = 1 + v247:0:0

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

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

(15)
Obligation:
Rules:
f_211(v235:0:0:0, v236:0:0:0, sum~cons_1~v247:0:0:0) -> f_211(v235:0:0:0, v236:0:0:0, v247:0:0:0) :|: v247:0:0:0 > 0 && sum~cons_1~v247:0:0:0 = 1 + v247:0:0:0

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

(16) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f_211(x1, x2, x3) -> f_211(x3)

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

(17)
Obligation:
Rules:
f_211(sum~cons_1~v247:0:0:0) -> f_211(v247:0:0:0) :|: v247:0:0:0 > 0 && sum~cons_1~v247:0:0:0 = 1 + v247:0:0:0

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

(18) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_211 ] = f_211_1

The following rules are decreasing:
f_211(sum~cons_1~v247:0:0:0) -> f_211(v247:0:0:0) :|: v247:0:0:0 > 0 && sum~cons_1~v247:0:0:0 = 1 + v247:0:0:0

The following rules are bounded:
f_211(sum~cons_1~v247:0:0:0) -> f_211(v247:0:0:0) :|: v247:0:0:0 > 0 && sum~cons_1~v247:0:0:0 = 1 + v247:0:0:0


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

(19)
YES

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

(20)
Obligation:
SCC
----------------------------------------

(21) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 9 rulesP rules:
f_145(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 4) -> f_146(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) :|: 0 < v41 && 2 <= v40 && 2 <= v38
f_146(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) -> f_148(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) :|: 0 = 0
f_148(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) -> f_150(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) :|: TRUE
f_150(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) -> f_152(v34, v35, v36, v37, v38, 1, v41, v42, v43, v44, v45, 0, 3, 2, 4) :|: 0 = 0
f_152(v34, v35, v36, v37, v38, 1, v41, v42, v43, v44, v45, 0, 3, 2, 4) -> f_154(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) :|: 1 + v47 = v41 && 0 <= v47
f_154(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) -> f_156(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) :|: TRUE
f_156(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) -> f_158(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) :|: TRUE
f_158(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) -> f_144(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 4) :|: TRUE
f_144(v34, v35, v36, v37, v38, 1, v40, v41, v42, v43, v44, v45, 0, 3, 4) -> f_145(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_145(v34:0, v35:0, v36:0, v37:0, v38:0, 1, 1 + v47:0, v40:0, v42:0, v43:0, v44:0, v45:0, 0, 3, 4) -> f_145(v34:0, v35:0, v36:0, v37:0, v38:0, 1, v47:0, 1 + v47:0, v42:0, v43:0, v44:0, v45:0, 0, 3, 4) :|: v40:0 > 1 && v47:0 > -1 && v38:0 > 1
Filtered unneeded arguments:
   f_145(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_145(x5, x7, x8)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_145(v38:0, sum~cons_1~v47:0, v40:0) -> f_145(v38:0, v47:0, 1 + v47:0) :|: v47:0 > -1 && v38:0 > 1 && v40:0 > 1 && sum~cons_1~v47:0 = 1 + v47:0

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

(22)
Obligation:
Rules:
f_145(v38:0, sum~cons_1~v47:0, v40:0) -> f_145(v38:0, v47:0, 1 + v47:0) :|: v47:0 > -1 && v38:0 > 1 && v40:0 > 1 && sum~cons_1~v47:0 = 1 + v47:0

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

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

(24)
Obligation:
Rules:
f_145(v38:0:0, sum~cons_1~v47:0:0, v40:0:0) -> f_145(v38:0:0, v47:0:0, 1 + v47:0:0) :|: v47:0:0 > -1 && v38:0:0 > 1 && v40:0:0 > 1 && sum~cons_1~v47:0:0 = 1 + v47:0:0

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

(25) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_145(x, x1, x2)] = x1

The following rules are decreasing:
f_145(v38:0:0, sum~cons_1~v47:0:0, v40:0:0) -> f_145(v38:0:0, v47:0:0, 1 + v47:0:0) :|: v47:0:0 > -1 && v38:0:0 > 1 && v40:0:0 > 1 && sum~cons_1~v47:0:0 = 1 + v47:0:0
The following rules are bounded:
f_145(v38:0:0, sum~cons_1~v47:0:0, v40:0:0) -> f_145(v38:0:0, v47:0:0, 1 + v47:0:0) :|: v47:0:0 > -1 && v38:0:0 > 1 && v40:0:0 > 1 && sum~cons_1~v47:0:0 = 1 + v47:0:0

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

(26)
YES