/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 179 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 4612 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 56 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 24 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 46 ms]
        (16) IntTRS
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 9 ms]
        (20) 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: "subxy" 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
		%z = alloca i32, align 4
		%i = alloca i32, align 4
		store %x, %2
		store %y, %3
		store 0, %z
		%4 = load %2
		store %4, %i
		%5 = load %3
		%6 = icmp sle %5 0
		br %6, %10, %7
	7:
		%8 = load %2
		%9 = icmp sle %8 0
		br %9, %10, %11
	10:
		store 0, %1
		br %32
	11:
		br %12
	12:
		%13 = load %i
		%14 = icmp sgt %13 0
		br %14, %15, %20
	15:
		%16 = load %i
		%17 = add %16 -1
		store %17, %i
		%18 = load %z
		%19 = add %18 1
		store %19, %z
		br %12
	20:
		br %21
	21:
		%22 = load %i
		%23 = load %3
		%24 = icmp slt %22 %23
		br %24, %25, %30
	25:
		%26 = load %i
		%27 = add %26 1
		store %27, %i
		%28 = load %z
		%29 = add %28 -1
		store %29, %z
		br %21
	30:
		%31 = load %z
		store %31, %1
		br %32
	32:
		%33 = load %1
		ret %33

*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 = load %y
		%6 = call i32 @subxy(i32 %4, i32 %5)
		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 13 rulesP rules:
f_469(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 4) -> f_470(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 4) :|: 0 = 0
f_470(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 4) -> f_471(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: v454 < v443 && 2 <= v443
f_471(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_473(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: 0 = 0
f_473(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_475(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: TRUE
f_475(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_477(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: 0 = 0
f_477(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_479(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: v479 = 1 + v454 && 2 <= v479
f_479(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_481(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: TRUE
f_481(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_483(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: 0 = 0
f_483(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_485(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v482, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: 1 + v482 = v456
f_485(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v482, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_487(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v482, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: TRUE
f_487(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v482, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_488(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v482, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) :|: TRUE
f_488(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v482, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 2, 4) -> f_468(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v479, v456, v482, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 4) :|: TRUE
f_468(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v453, v454, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 4) -> f_469(v442, v443, v444, v445, v446, v447, v448, 0, 1, v451, v452, v454, v453, v455, v456, v457, v460, v458, v461, v459, v462, v463, v464, v465, v466, v467, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_469(v442:0, v443:0, v444:0, v445:0, v446:0, v447:0, v448:0, 0, 1, v451:0, v452:0, v454:0, v453:0, v455:0, 1 + v482:0, v457:0, v460:0, v458:0, v461:0, v459:0, v462:0, v463:0, v464:0, v465:0, v466:0, v467:0, 3, 4) -> f_469(v442:0, v443:0, v444:0, v445:0, v446:0, v447:0, v448:0, 0, 1, v451:0, v452:0, 1 + v454:0, v454:0, 1 + v482:0, v482:0, v457:0, v460:0, v458:0, v461:0, v459:0, v462:0, v463:0, v464:0, v465:0, v466:0, v467:0, 3, 4) :|: v443:0 > 1 && v454:0 > 0 && v454:0 < v443:0
Filtered unneeded arguments:
   f_469(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28) -> f_469(x2, x12, x15)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_469(v443:0, v454:0, sum~cons_1~v482:0) -> f_469(v443:0, 1 + v454:0, v482:0) :|: v454:0 > 0 && v454:0 < v443:0 && v443:0 > 1 && sum~cons_1~v482:0 = 1 + v482:0

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

(9)
Obligation:
Rules:
f_469(v443:0, v454:0, sum~cons_1~v482:0) -> f_469(v443:0, 1 + v454:0, v482:0) :|: v454:0 > 0 && v454:0 < v443:0 && v443:0 > 1 && sum~cons_1~v482:0 = 1 + v482:0

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

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

(11)
Obligation:
Rules:
f_469(v443:0:0, v454:0:0, sum~cons_1~v482:0:0) -> f_469(v443:0:0, 1 + v454:0:0, v482:0:0) :|: v454:0:0 > 0 && v454:0:0 < v443:0:0 && v443:0:0 > 1 && sum~cons_1~v482:0:0 = 1 + v482:0:0

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_469 ] = -1*f_469_2 + f_469_1

The following rules are decreasing:
f_469(v443:0:0, v454:0:0, sum~cons_1~v482:0:0) -> f_469(v443:0:0, 1 + v454:0:0, v482:0:0) :|: v454:0:0 > 0 && v454:0:0 < v443:0:0 && v443:0:0 > 1 && sum~cons_1~v482:0:0 = 1 + v482:0:0

The following rules are bounded:
f_469(v443:0:0, v454:0:0, sum~cons_1~v482:0:0) -> f_469(v443:0:0, 1 + v454:0:0, v482:0:0) :|: v454:0:0 > 0 && v454:0:0 < v443:0:0 && v443:0:0 > 1 && sum~cons_1~v482:0:0 = 1 + v482:0:0


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

(13)
YES

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

(14)
Obligation:
SCC
----------------------------------------

(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 12 rulesP rules:
f_338(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v148, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 4) -> f_339(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v148, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: 0 < v150 && 2 <= v148 && 2 <= v140
f_339(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v148, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_341(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v148, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: 0 = 0
f_341(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v148, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_343(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v148, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: TRUE
f_343(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v148, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_345(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: 0 = 0
f_345(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_347(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: 1 + v164 = v150 && 0 <= v164
f_347(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_349(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: TRUE
f_349(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_351(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: 0 = 0
f_351(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_353(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v166, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: v166 = 1 + v152 && 2 <= v166
f_353(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v166, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_355(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v166, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: TRUE
f_355(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v166, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_357(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v166, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) :|: TRUE
f_357(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v166, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 2, 4) -> f_337(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v164, v152, v166, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 4) :|: TRUE
f_337(v140, v141, v142, v143, v144, v145, v146, 0, v148, 1, v150, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 4) -> f_338(v140, v141, v142, v143, v144, v145, v146, 0, v150, 1, v148, v151, v152, v153, v156, v154, v157, v155, v158, v159, v160, v161, v162, v163, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_338(v140:0, v141:0, v142:0, v143:0, v144:0, v145:0, v146:0, 0, 1 + v164:0, 1, v148:0, v151:0, v152:0, v153:0, v156:0, v154:0, v157:0, v155:0, v158:0, v159:0, v160:0, v161:0, v162:0, v163:0, 3, 4) -> f_338(v140:0, v141:0, v142:0, v143:0, v144:0, v145:0, v146:0, 0, v164:0, 1, 1 + v164:0, v152:0, 1 + v152:0, v153:0, v156:0, v154:0, v157:0, v155:0, v158:0, v159:0, v160:0, v161:0, v162:0, v163:0, 3, 4) :|: v148:0 > 1 && v164:0 > -1 && v140:0 > 1 && v152:0 > 0
Filtered unneeded arguments:
   f_338(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f_338(x1, x9, x11, x13)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_338(v140:0, sum~cons_1~v164:0, v148:0, v152:0) -> f_338(v140:0, v164:0, 1 + v164:0, 1 + v152:0) :|: v164:0 > -1 && v148:0 > 1 && v152:0 > 0 && v140:0 > 1 && sum~cons_1~v164:0 = 1 + v164:0

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

(16)
Obligation:
Rules:
f_338(v140:0, sum~cons_1~v164:0, v148:0, v152:0) -> f_338(v140:0, v164:0, 1 + v164:0, 1 + v152:0) :|: v164:0 > -1 && v148:0 > 1 && v152:0 > 0 && v140:0 > 1 && sum~cons_1~v164:0 = 1 + v164:0

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

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

(18)
Obligation:
Rules:
f_338(v140:0:0, sum~cons_1~v164:0:0, v148:0:0, v152:0:0) -> f_338(v140:0:0, v164:0:0, 1 + v164:0:0, 1 + v152:0:0) :|: v152:0:0 > 0 && v140:0:0 > 1 && v148:0:0 > 1 && v164:0:0 > -1 && sum~cons_1~v164:0:0 = 1 + v164:0:0

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

(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_338 ] = f_338_2

The following rules are decreasing:
f_338(v140:0:0, sum~cons_1~v164:0:0, v148:0:0, v152:0:0) -> f_338(v140:0:0, v164:0:0, 1 + v164:0:0, 1 + v152:0:0) :|: v152:0:0 > 0 && v140:0:0 > 1 && v148:0:0 > 1 && v164:0:0 > -1 && sum~cons_1~v164:0:0 = 1 + v164:0:0

The following rules are bounded:
f_338(v140:0:0, sum~cons_1~v164:0:0, v148:0:0, v152:0:0) -> f_338(v140:0:0, v164:0:0, 1 + v164:0:0, 1 + v152:0:0) :|: v152:0:0 > 0 && v140:0:0 > 1 && v148:0:0 > 1 && v164:0:0 > -1 && sum~cons_1~v164:0:0 = 1 + v164:0:0


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(20)
YES