YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 159 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 703 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 0 ms]
        (9) IntTRS
        (10) IRS2T2 [EQUIVALENT, 0 ms]
        (11) T2IntSys
        (12) T2 [EQUIVALENT, 1082 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 0 ms]
        (16) IntTRS
        (17) IRS2T2 [EQUIVALENT, 0 ms]
        (18) T2IntSys
        (19) T2 [EQUIVALENT, 1062 ms]
        (20) YES


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

(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
----------------------------------------

(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox2/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
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %x
		br %3
	3:
		%4 = load %x
		%5 = icmp ne %4 0
		br %5, %6, %16
	6:
		%7 = load %x
		%8 = icmp sgt %7 0
		br %8, %9, %12
	9:
		%10 = load %x
		%11 = sub %10 1
		store %11, %x
		br %15
	12:
		%13 = load %x
		%14 = add %13 1
		store %14, %x
		br %15
	15:
		br %3
	16:
		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 14 rulesP rules:
f_182(v91, v92, v93, v94, 1, 0, v97, v98, v99, 3, 4) -> f_185(v91, v92, v93, v97, 1, v94, 0, v98, v99, 3, 4) :|: 0 = 0
f_185(v91, v92, v93, v97, 1, v94, 0, v98, v99, 3, 4) -> f_188(v91, v92, v93, v97, 1, v94, 0, v98, v99, 3, 4) :|: v97 != 0
f_188(v91, v92, v93, v97, 1, v94, 0, v98, v99, 3, 4) -> f_191(v91, v92, v93, v97, 1, v94, 0, v98, v99, 3, 4) :|: 0 = 0
f_191(v91, v92, v93, v97, 1, v94, 0, v98, v99, 3, 4) -> f_194(v91, v92, v93, v97, 1, v94, 0, v98, v99, 3, 4) :|: TRUE
f_194(v91, v92, v93, v97, 1, v94, 0, v98, v99, 3, 4) -> f_197(v91, v92, v93, v97, 1, 0, v94, v98, v99, 3, 4) :|: 0 = 0
f_197(v91, v92, v93, v97, 1, 0, v94, v98, v99, 3, 4) -> f_200(v91, v92, v93, v97, 1, 0, v94, v98, v99, 3, 4) :|: v97 <= 0 && 1 + v94 <= 0 && 1 + v93 <= 0
f_200(v91, v92, v93, v97, 1, 0, v94, v98, v99, 3, 4) -> f_203(v91, v92, v93, v97, 1, 0, v94, v98, v99, 3, 4) :|: 0 = 0
f_203(v91, v92, v93, v97, 1, 0, v94, v98, v99, 3, 4) -> f_206(v91, v92, v93, v97, 1, 0, v94, v98, v99, 3, 4) :|: TRUE
f_206(v91, v92, v93, v97, 1, 0, v94, v98, v99, 3, 4) -> f_209(v91, v92, v93, v97, 1, 0, v98, v99, 3, 4) :|: 0 = 0
f_209(v91, v92, v93, v97, 1, 0, v98, v99, 3, 4) -> f_212(v91, v92, v93, v97, 1, 0, v128, v98, v99, 3, 4) :|: v128 = 1 + v97 && v128 <= 1
f_212(v91, v92, v93, v97, 1, 0, v128, v98, v99, 3, 4) -> f_214(v91, v92, v93, v97, 1, 0, v128, v98, v99, 3, 4) :|: TRUE
f_214(v91, v92, v93, v97, 1, 0, v128, v98, v99, 3, 4) -> f_216(v91, v92, v93, v97, 1, 0, v128, v98, v99, 3, 4) :|: TRUE
f_216(v91, v92, v93, v97, 1, 0, v128, v98, v99, 3, 4) -> f_179(v91, v92, v93, v97, 1, 0, v128, v98, v99, 3, 4) :|: TRUE
f_179(v91, v92, v93, v94, 1, 0, v97, v98, v99, 3, 4) -> f_182(v91, v92, v93, v94, 1, 0, v97, v98, v99, 3, 4) :|: TRUE
Combined rules. Obtained 2 rulesP rules:
f_182(v91:0, v92:0, v93:0, v94:0, 1, 0, v97:0, v98:0, v99:0, 3, 4) -> f_182(v91:0, v92:0, v93:0, v97:0, 1, 0, 1 + v97:0, v98:0, v99:0, 3, 4) :|: v97:0 < 0 && v94:0 < 0 && v97:0 < 1 && v93:0 < 0
f_182(v91:0, v92:0, v93:0, v94:0, 1, 0, v97:0, v98:0, v99:0, 3, 4) -> f_182(v91:0, v92:0, v93:0, v97:0, 1, 0, 1 + v97:0, v98:0, v99:0, 3, 4) :|: v97:0 > 0 && v94:0 < 0 && v97:0 < 1 && v93:0 < 0
Filtered unneeded arguments:
   f_182(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f_182(x3, x4, x7)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_182(v93:0, v94:0, v97:0) -> f_182(v93:0, v97:0, 1 + v97:0) :|: v94:0 < 0 && v97:0 < 0 && v93:0 < 0 && v97:0 < 1
f_182(v93:0, v94:0, v97:0) -> f_182(v93:0, v97:0, 1 + v97:0) :|: v94:0 < 0 && v97:0 > 0 && v93:0 < 0 && v97:0 < 1

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

(9)
Obligation:
Rules:
f_182(v93:0, v94:0, v97:0) -> f_182(v93:0, v97:0, 1 + v97:0) :|: v94:0 < 0 && v97:0 < 0 && v93:0 < 0 && v97:0 < 1
f_182(x, x1, x2) -> f_182(x, x2, 1 + x2) :|: x1 < 0 && x2 > 0 && x < 0 && x2 < 1

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

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

   (f_182_3,1)

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

(11)
Obligation:
START: 0;

FROM: 0;
TO: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 < 0 && oldX2 < 0 && oldX0 < 0 && oldX2 < 1);
x0 := oldX0;
x1 := oldX2;
x2 := 1 + oldX2;
TO: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 < 0 && oldX2 > 0 && oldX0 < 0 && oldX2 < 1);
x0 := oldX0;
x1 := oldX2;
x2 := 1 + oldX2;
TO: 1;


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

(12) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 1, 4, 5 using the following rank functions:
    - Rank function 1:
      RF for loc. 5: 1-2*x2
      RF for loc. 6: -2*x2
      Bound for (chained) transitions 4: 0
      Bound for (chained) transitions 5: 0
    - Rank function 2:
      RF for loc. 5: 0
      RF for loc. 6: -1
      Bound for (chained) transitions 1: 0

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

(13)
YES

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

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

(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 13 rulesP rules:
f_176(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 4) -> f_180(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) :|: v76 != 0 && 2 <= v74 && 2 <= v73
f_180(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) -> f_183(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) :|: 0 = 0
f_183(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) -> f_186(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) :|: TRUE
f_186(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) -> f_190(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) :|: 0 = 0
f_190(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) -> f_193(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) :|: 0 = 0
f_193(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) -> f_196(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) :|: TRUE
f_196(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 2, 4) -> f_198(v71, v72, v73, v76, 1, v77, v78, 0, 3, 2, 4) :|: 0 = 0
f_198(v71, v72, v73, v76, 1, v77, v78, 0, 3, 2, 4) -> f_201(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 2, 4) :|: 1 + v111 = v76 && 0 <= v111
f_201(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 2, 4) -> f_204(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 2, 4) :|: TRUE
f_204(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 2, 4) -> f_207(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 2, 4) :|: TRUE
f_207(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 2, 4) -> f_210(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 2, 4) :|: TRUE
f_210(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 2, 4) -> f_173(v71, v72, v73, v76, 1, v111, v77, v78, 0, 3, 4) :|: TRUE
f_173(v71, v72, v73, v74, 1, v76, v77, v78, 0, 3, 4) -> f_176(v71, v72, v73, v76, 1, v74, v77, v78, 0, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_176(v71:0, v72:0, v73:0, 1 + v111:0, 1, v74:0, v77:0, v78:0, 0, 3, 4) -> f_176(v71:0, v72:0, v73:0, v111:0, 1, 1 + v111:0, v77:0, v78:0, 0, 3, 4) :|: v74:0 > 1 && v111:0 > -1 && v73:0 > 1
Filtered unneeded arguments:
   f_176(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f_176(x3, x4, x6)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_176(v73:0, sum~cons_1~v111:0, v74:0) -> f_176(v73:0, v111:0, 1 + v111:0) :|: v111:0 > -1 && v73:0 > 1 && v74:0 > 1 && sum~cons_1~v111:0 = 1 + v111:0

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

(16)
Obligation:
Rules:
f_176(v73:0, sum~cons_1~v111:0, v74:0) -> f_176(v73:0, v111:0, 1 + v111:0) :|: v111:0 > -1 && v73:0 > 1 && v74:0 > 1 && sum~cons_1~v111:0 = 1 + v111:0

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

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

   (f_176_3,1)

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

(18)
Obligation:
START: 0;

FROM: 0;
TO: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := oldX1 - 1;
assume(oldX3 > -1 && oldX0 > 1 && oldX2 > 1 && oldX1 = 1 + oldX3);
x0 := oldX0;
x1 := oldX1 - 1;
x2 := 1 + oldX3;
TO: 1;


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

(19) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 1, 3, 4 using the following rank functions:
    - Rank function 1:
      RF for loc. 5: 1+2*x1
      RF for loc. 6: 2*x1
      Bound for (chained) transitions 4: 2
    - Rank function 2:
      RF for loc. 5: 1+2*x1
      RF for loc. 6: 2*x1
      Bound for (chained) transitions 3: 2
    - Rank function 3:
      RF for loc. 5: 1
      RF for loc. 6: 0
      Bound for (chained) transitions 1: 1

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

(20)
YES