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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 149 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 811 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToLassoProof [EQUIVALENT, 0 ms]
(6) LLVM Symbolic Execution Lasso
(7) Lasso2IRS [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IRS2T2 [EQUIVALENT, 0 ms]
(10) T2IntSys
(11) T2 [EQUIVALENT, 1372 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 = mul 2 %5
		%7 = load %z
		%8 = icmp sge %6 %7
		br %8, %9, %25
	9:
		br %10
	10:
		%11 = load %x
		%12 = icmp sge %11 0
		br %12, %13, %16
	13:
		%14 = load %z
		%15 = icmp eq %14 1
		br %16
	16:
		%17 = phi [0, %10], [%15, %13]
		br %17, %18, %24
	18:
		%19 = load %x
		%20 = load %y
		%21 = mul 2 %20
		%22 = sub %19 %21
		%23 = add %22 1
		store %23, %x
		br %10
	24:
		br %25
	25:
		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) SymbolicExecutionGraphToLassoProof (EQUIVALENT)
Converted SEGraph to 1 independent lasso.
----------------------------------------

(6)
Obligation:
Lasso
----------------------------------------

(7) Lasso2IRS (EQUIVALENT)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 51 rulesP rules:
f_174(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_175(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: 0 <= v110 && 0 <= 1 + v109 && 1 <= v108
f_175(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_177(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: 0 = 0
f_177(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_179(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: TRUE
f_179(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_181(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: 0 = 0
f_181(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_183(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: 0 = 0
f_183(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_185(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: 0 = 0
f_185(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_186(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: TRUE
f_186(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_187(v100, v101, v102, v103, v104, v105, 1, v107, v110, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: 0 = 0
f_187(v100, v101, v102, v103, v104, v105, 1, v107, v110, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_188(v100, v101, v102, v103, v104, v105, 1, v107, v110, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: 0 = 0
f_188(v100, v101, v102, v103, v104, v105, 1, v107, v110, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_189(v100, v101, v102, v103, v104, v105, 1, v107, v110, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: v107 = 2 * v105
f_189(v100, v101, v102, v103, v104, v105, 1, v107, v110, v109, v111, v112, v113, v114, 0, 3, 2, 4) -> f_190(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v111, v112, v113, v114, 0, 3, 2, 4) :|: v182 + v107 = v110
f_190(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v111, v112, v113, v114, 0, 3, 2, 4) -> f_191(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v183, v111, v112, v113, v114, 0, 3, 2, 4) :|: v183 = 1 + v182
f_191(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v183, v111, v112, v113, v114, 0, 3, 2, 4) -> f_192(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v183, v111, v112, v113, v114, 0, 3, 2, 4) :|: TRUE
f_192(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v183, v111, v112, v113, v114, 0, 3, 2, 4) -> f_193(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v183, v111, v112, v113, v114, 0, 3, 2, 4) :|: TRUE
f_193(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v183, v111, v112, v113, v114, 0, 3, 2, 4) -> f_173(v100, v101, v102, v103, v104, v105, 1, v107, v110, v182, v183, v111, v112, v113, v114, 0, 3, 2, 4) :|: TRUE
f_173(v100, v101, v102, v103, v104, v105, 1, v107, v108, v109, v110, v111, v112, v113, v114, 0, 3, 2, 4) -> f_174(v100, v101, v102, v103, v104, v105, 1, v107, v110, v108, v109, v111, v112, v113, v114, 0, 3, 2, 4) :|: 0 = 0
f_105 -> f_106(v1, v2, 3, 1, 4) :|: 1 <= v1 && v2 = 3 + v1 && 4 <= v2
f_106(v1, v2, 3, 1, 4) -> f_107(v1, v3, v2, v4, 3, 1, 4) :|: 1 <= v3 && v4 = 3 + v3 && 4 <= v4
f_107(v1, v3, v2, v4, 3, 1, 4) -> f_108(v1, v3, v5, v2, v4, v6, 3, 1, 4) :|: 1 <= v5 && v6 = 3 + v5 && 4 <= v6
f_108(v1, v3, v5, v2, v4, v6, 3, 1, 4) -> f_109(v1, v3, v5, v7, v2, v4, v6, v8, 3, 1, 4) :|: 1 <= v7 && v8 = 3 + v7 && 4 <= v8
f_109(v1, v3, v5, v7, v2, v4, v6, v8, 3, 1, 4) -> f_110(v1, v3, v5, v7, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_110(v1, v3, v5, v7, v2, v4, v6, v8, 0, 3, 1, 4) -> f_111(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_111(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) -> f_112(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_112(v1, v3, v5, v7, v9, v2, v4, v6, v8, 0, 3, 1, 4) -> f_113(v1, v3, v5, v7, v9, v11, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_113(v1, v3, v5, v7, v9, v11, v2, v4, v6, v8, 0, 3, 1, 4) -> f_114(v1, v3, v5, v7, v9, v11, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_114(v1, v3, v5, v7, v9, v11, v2, v4, v6, v8, 0, 3, 1, 4) -> f_115(v1, v3, v5, v7, v9, v11, v13, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_115(v1, v3, v5, v7, v9, v11, v13, v2, v4, v6, v8, 0, 3, 1, 4) -> f_116(v1, v3, v5, v7, v9, v11, v13, v2, v4, v6, v8, 0, 3, 1, 4) :|: TRUE
f_116(v1, v3, v5, v7, v9, v11, v13, v2, v4, v6, v8, 0, 3, 1, 4) -> f_117(v1, v3, v5, v7, v9, v11, v13, v2, v4, v6, v8, 0, 3, 1, 4) :|: 0 = 0
f_117(v1, v3, v5, v7, v9, v11, v13, v2, v4, v6, v8, 0, 3, 1, 4) -> f_118(v1, v3, v5, v7, v9, v11, v13, v15, v2, v4, v6, v8, 0, 3, 2, 1, 4) :|: v15 = 2 * v11
f_118(v1, v3, v5, v7, v9, v11, v13, v15, v2, v4, v6, v8, 0, 3, 2, 1, 4) -> f_119(v1, v3, v5, v7, v9, v11, v13, v15, v2, v4, v6, v8, 0, 3, 2, 1, 4) :|: 0 = 0
f_119(v1, v3, v5, v7, v9, v11, v13, v15, v2, v4, v6, v8, 0, 3, 2, 1, 4) -> f_120(v1, v3, v5, v7, v9, v11, v13, v15, v2, v4, v6, v8, 0, 3, 2, 1, 4) :|: v13 <= v15
f_120(v1, v3, v5, v7, v9, v11, v13, v15, v2, v4, v6, v8, 0, 3, 2, 1, 4) -> f_122(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 = 0
f_122(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) -> f_124(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) :|: TRUE
f_124(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) -> f_126(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) :|: TRUE
f_126(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) -> f_127(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 = 0
f_127(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) -> f_128(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 <= v9
f_128(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) -> f_130(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 = 0
f_130(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) -> f_132(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) :|: TRUE
f_132(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) -> f_134(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 = 0
f_134(v1, v3, v5, v7, v9, v11, v13, v15, 1, v2, v4, v6, v8, 0, 3, 2, 4) -> f_136(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) :|: v13 = 1 && 2 <= v15 && 1 <= v11
f_136(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) -> f_139(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 = 0
f_139(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) -> f_141(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 = 0
f_141(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) -> f_143(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) :|: TRUE
f_143(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) -> f_145(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 = 0
f_145(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) -> f_147(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) :|: 0 = 0
f_147(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) -> f_148(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) :|: v15 = 2 * v11
f_148(v1, v3, v5, v7, v9, v11, 1, v15, v2, v4, v6, v8, 0, 3, 2, 4) -> f_149(v1, v3, v5, v7, v9, v11, 1, v15, v25, v2, v4, v6, v8, 0, 3, 2, 4) :|: v25 + v15 = v9
f_149(v1, v3, v5, v7, v9, v11, 1, v15, v25, v2, v4, v6, v8, 0, 3, 2, 4) -> f_150(v1, v3, v5, v7, v9, v11, 1, v15, v25, v26, v2, v4, v6, v8, 0, 3, 2, 4) :|: v26 = 1 + v25
f_150(v1, v3, v5, v7, v9, v11, 1, v15, v25, v26, v2, v4, v6, v8, 0, 3, 2, 4) -> f_151(v1, v3, v5, v7, v9, v11, 1, v15, v25, v26, v2, v4, v6, v8, 0, 3, 2, 4) :|: TRUE
f_151(v1, v3, v5, v7, v9, v11, 1, v15, v25, v26, v2, v4, v6, v8, 0, 3, 2, 4) -> f_152(v1, v3, v5, v7, v9, v11, 1, v15, v25, v26, v2, v4, v6, v8, 0, 3, 2, 4) :|: TRUE
f_152(v1, v3, v5, v7, v9, v11, 1, v15, v25, v26, v2, v4, v6, v8, 0, 3, 2, 4) -> f_173(v1, v3, v5, v7, v9, v11, 1, v15, v9, v25, v26, v2, v4, v6, v8, 0, 3, 2, 4) :|: TRUE
Combined rules. Obtained 2 rulesP rules:
f_105 -> f_174(v1:0, v3:0, v5:0, v7:0, v25:0 + 2 * v11:0, v11:0, 1, 2 * v11:0, 1 + v25:0, v25:0 + 2 * v11:0, v25:0, 3 + v1:0, 3 + v3:0, 3 + v5:0, 3 + v7:0, 0, 3, 2, 4) :|: 2 * v11:0 > 1 && v3:0 > 0 && v1:0 > 0 && v5:0 > 0 && v7:0 > 0 && v11:0 > 0 && v25:0 + 2 * v11:0 > -1
f_174(v100:0, v101:0, v102:0, v103:0, v104:0, v105:0, 1, 2 * v105:0, v182:0 + 2 * v105:0, v108:0, v109:0, v111:0, v112:0, v113:0, v114:0, 0, 3, 2, 4) -> f_174(v100:0, v101:0, v102:0, v103:0, v104:0, v105:0, 1, 2 * v105:0, 1 + v182:0, v182:0 + 2 * v105:0, v182:0, v111:0, v112:0, v113:0, v114:0, 0, 3, 2, 4) :|: v109:0 > -2 && v108:0 > 0 && v182:0 + 2 * v105:0 > -1
Filtered unneeded arguments:
   f_174(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_174(x6, x8, x9, x10, x11)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_105 -> f_174(v11:0, 2 * v11:0, 1 + v25:0, v25:0 + 2 * v11:0, v25:0) :|: v11:0 > 0 && v25:0 + 2 * v11:0 > -1 && 2 * v11:0 > 1
f_174(v105:0, times~cons_2~v105:0, sum~v182:0~times~cons_2~v105:0, v108:0, v109:0) -> f_174(v105:0, 2 * v105:0, 1 + v182:0, v182:0 + 2 * v105:0, v182:0) :|: v108:0 > 0 && v182:0 + 2 * v105:0 > -1 && v109:0 > -2 && times~cons_2~v105:0 = 2 * v105:0 && sum~v182:0~times~cons_2~v105:0 = v182:0 + 2 * v105:0

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

(8)
Obligation:
Rules:
f_105 -> f_174(v11:0, 2 * v11:0, 1 + v25:0, v25:0 + 2 * v11:0, v25:0) :|: v11:0 > 0 && v25:0 + 2 * v11:0 > -1 && 2 * v11:0 > 1
f_174(v105:0, times~cons_2~v105:0, sum~v182:0~times~cons_2~v105:0, v108:0, v109:0) -> f_174(v105:0, 2 * v105:0, 1 + v182:0, v182:0 + 2 * v105:0, v182:0) :|: v108:0 > 0 && v182:0 + 2 * v105:0 > -1 && v109:0 > -2 && times~cons_2~v105:0 = 2 * v105:0 && sum~v182:0~times~cons_2~v105:0 = v182:0 + 2 * v105:0
Start term: f_105

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

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

   (f_105_5,1)
   (f_174_5,2)

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

(10)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
oldX6 := nondet();
assume(oldX5 > 0 && oldX6 + 2 * oldX5 > -1 && 2 * oldX5 > 1);
x0 := oldX5;
x1 := 2 * oldX5;
x2 := 1 + oldX6;
x3 := oldX6 + 2 * oldX5;
x4 := oldX6;
TO: 2;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(oldX3 > 0 && oldX5 + 2 * oldX0 > -1 && oldX4 > -2 && oldX1 = 2 * oldX0 && oldX2 = oldX5 + 2 * oldX0);
x0 := oldX0;
x1 := 2 * oldX0;
x2 := 1 + oldX5;
x3 := oldX5 + 2 * oldX0;
x4 := oldX5;
TO: 2;


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

(11) T2 (EQUIVALENT)
Used the following cutpoint-specific lexicographic rank functions:
 * For cutpoint 5, used the following rank functions/bounds (in descending priority order):
    - RF x2, bound 0

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(12)
YES