24.07/7.93 YES 24.07/7.94 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 24.07/7.94 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 24.07/7.94 24.07/7.94 24.07/7.94 Termination of the given C Problem could be proven: 24.07/7.94 24.07/7.94 (0) C Problem 24.07/7.94 (1) CToLLVMProof [EQUIVALENT, 174 ms] 24.07/7.94 (2) LLVM problem 24.07/7.94 (3) LLVMToTerminationGraphProof [EQUIVALENT, 4605 ms] 24.07/7.94 (4) LLVM Symbolic Execution Graph 24.07/7.94 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 24.07/7.94 (6) LLVM Symbolic Execution SCC 24.07/7.94 (7) SCC2IRS [SOUND, 79 ms] 24.07/7.94 (8) IntTRS 24.07/7.94 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 24.07/7.94 (10) IntTRS 24.07/7.94 (11) PolynomialOrderProcessor [EQUIVALENT, 16 ms] 24.07/7.94 (12) YES 24.07/7.94 24.07/7.94 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (0) 24.07/7.94 Obligation: 24.07/7.94 c file /export/starexec/sandbox/benchmark/theBenchmark.c 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (1) CToLLVMProof (EQUIVALENT) 24.07/7.94 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (2) 24.07/7.94 Obligation: 24.07/7.94 LLVM Problem 24.07/7.94 24.07/7.94 Aliases: 24.07/7.94 24.07/7.94 Data layout: 24.07/7.94 24.07/7.94 "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" 24.07/7.94 24.07/7.94 Machine: 24.07/7.94 24.07/7.94 "x86_64-pc-linux-gnu" 24.07/7.94 24.07/7.94 Type definitions: 24.07/7.94 24.07/7.94 Global variables: 24.07/7.94 24.07/7.94 Function declarations and definitions: 24.07/7.94 24.07/7.94 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 24.07/7.94 *BasicFunctionTypename: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 24.07/7.94 0: 24.07/7.94 %1 = alloca i32, align 4 24.07/7.94 %2 = alloca i32, align 4 24.07/7.94 %x_ref = alloca *i32, align 8 24.07/7.94 %y_ref = alloca *i32, align 8 24.07/7.94 %c = alloca *i32, align 8 24.07/7.94 store %x, %1 24.07/7.94 store %y, %2 24.07/7.94 %3 = alloca i8, numElementsLit: 4 24.07/7.94 %4 = bitcast *i8 %3 to *i32 24.07/7.94 store %4, %x_ref 24.07/7.94 %5 = alloca i8, numElementsLit: 4 24.07/7.94 %6 = bitcast *i8 %5 to *i32 24.07/7.94 store %6, %y_ref 24.07/7.94 %7 = alloca i8, numElementsLit: 4 24.07/7.94 %8 = bitcast *i8 %7 to *i32 24.07/7.94 store %8, %c 24.07/7.94 %9 = load %1 24.07/7.94 %10 = load %x_ref 24.07/7.94 store %9, %10 24.07/7.94 %11 = load %2 24.07/7.94 %12 = load %y_ref 24.07/7.94 store %11, %12 24.07/7.94 %13 = load %c 24.07/7.94 store 0, %13 24.07/7.94 br %14 24.07/7.94 14: 24.07/7.94 %15 = load %x_ref 24.07/7.94 %16 = load %15 24.07/7.94 %17 = load %y_ref 24.07/7.94 %18 = load %17 24.07/7.94 %19 = icmp eq %16 %18 24.07/7.94 br %19, %20, %24 24.07/7.94 20: 24.07/7.94 %21 = load %x_ref 24.07/7.94 %22 = load %21 24.07/7.94 %23 = icmp sgt %22 0 24.07/7.94 br %24 24.07/7.94 24: 24.07/7.94 %25 = phi [0, %14], [%23, %20] 24.07/7.94 br %25, %26, %45 24.07/7.94 26: 24.07/7.94 br %27 24.07/7.94 27: 24.07/7.94 %28 = load %y_ref 24.07/7.94 %29 = load %28 24.07/7.94 %30 = icmp sgt %29 0 24.07/7.94 br %30, %31, %44 24.07/7.94 31: 24.07/7.94 %32 = load %x_ref 24.07/7.94 %33 = load %32 24.07/7.94 %34 = sub %33 1 24.07/7.94 %35 = load %x_ref 24.07/7.94 store %34, %35 24.07/7.94 %36 = load %y_ref 24.07/7.94 %37 = load %36 24.07/7.94 %38 = sub %37 1 24.07/7.94 %39 = load %y_ref 24.07/7.94 store %38, %39 24.07/7.94 %40 = load %c 24.07/7.94 %41 = load %40 24.07/7.94 %42 = add %41 1 24.07/7.94 %43 = load %c 24.07/7.94 store %42, %43 24.07/7.94 br %27 24.07/7.94 44: 24.07/7.94 br %14 24.07/7.94 45: 24.07/7.94 %46 = load %c 24.07/7.94 %47 = load %46 24.07/7.94 ret %47 24.07/7.94 24.07/7.94 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 24.07/7.94 0: 24.07/7.94 %1 = alloca i32, align 4 24.07/7.94 store 0, %1 24.07/7.94 %2 = call i32 @__VERIFIER_nondet_int() 24.07/7.94 %3 = call i32 @__VERIFIER_nondet_int() 24.07/7.94 %4 = call i32 @test_fun(i32 %2, i32 %3) 24.07/7.94 ret %4 24.07/7.94 24.07/7.94 24.07/7.94 Analyze Termination of all function calls matching the pattern: 24.07/7.94 main() 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (3) LLVMToTerminationGraphProof (EQUIVALENT) 24.07/7.94 Constructed symbolic execution graph for LLVM program and proved memory safety. 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (4) 24.07/7.94 Obligation: 24.07/7.94 SE Graph 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (5) SymbolicExecutionGraphToSCCProof (SOUND) 24.07/7.94 Splitted symbolic execution graph to 1 SCC. 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (6) 24.07/7.94 Obligation: 24.07/7.94 SCC 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (7) SCC2IRS (SOUND) 24.07/7.94 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 24.07/7.94 Generated rules. Obtained 22 rulesP rules: 24.07/7.94 f_527(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v262, v263, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 4, 8) -> f_528(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 4, 8) :|: 0 = 0 24.07/7.94 f_528(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 4, 8) -> f_529(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 < v263 && 2 <= v262 && 2 <= v252 24.07/7.94 f_529(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_531(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_531(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_533(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: TRUE 24.07/7.94 f_533(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_535(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_535(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_537(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_537(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_539(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 1 + v277 = v263 && 0 <= v277 24.07/7.94 f_539(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_541(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_541(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_543(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: TRUE 24.07/7.94 f_543(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_545(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_545(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v262, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_547(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_547(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_549(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 1 + v277 = v263 24.07/7.94 f_549(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_551(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_551(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_553(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: TRUE 24.07/7.94 f_553(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_555(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_555(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_557(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_557(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_559(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: v289 = 1 + v265 && 2 <= v289 24.07/7.94 f_559(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_561(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: 0 = 0 24.07/7.94 f_561(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_563(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: TRUE 24.07/7.94 f_563(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_565(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) :|: TRUE 24.07/7.94 f_565(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 2, 4, 8) -> f_526(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v263, v277, v265, v289, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 4, 8) :|: TRUE 24.07/7.94 f_526(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v262, v263, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 4, 8) -> f_527(v252, v253, v254, v255, v256, v257, v258, v259, v260, 1, v262, v263, v264, v265, v266, v267, v268, v269, v270, v271, v272, v273, v274, v275, 0, 3, 7, 4, 8) :|: 0 = 0 24.07/7.94 Combined rules. Obtained 1 rulesP rules: 24.07/7.94 f_527(v252:0, v253:0, v254:0, v255:0, v256:0, v257:0, v258:0, v259:0, v260:0, 1, v262:0, 1 + v277:0, v264:0, v265:0, v266:0, v267:0, v268:0, v269:0, v270:0, v271:0, v272:0, v273:0, v274:0, v275:0, 0, 3, 7, 4, 8) -> f_527(v252:0, v253:0, v254:0, v255:0, v256:0, v257:0, v258:0, v259:0, v260:0, 1, 1 + v277:0, v277:0, v265:0, 1 + v265:0, v266:0, v267:0, v268:0, v269:0, v270:0, v271:0, v272:0, v273:0, v274:0, v275:0, 0, 3, 7, 4, 8) :|: v262:0 > 1 && v277:0 > -1 && v252:0 > 1 && v265:0 > 0 24.07/7.94 Filtered unneeded arguments: 24.07/7.94 f_527(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, x29) -> f_527(x1, x11, x12, x14) 24.07/7.94 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 24.07/7.94 f_527(v252:0, v262:0, sum~cons_1~v277:0, v265:0) -> f_527(v252:0, 1 + v277:0, v277:0, 1 + v265:0) :|: v277:0 > -1 && v262:0 > 1 && v265:0 > 0 && v252:0 > 1 && sum~cons_1~v277:0 = 1 + v277:0 24.07/7.94 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (8) 24.07/7.94 Obligation: 24.07/7.94 Rules: 24.07/7.94 f_527(v252:0, v262:0, sum~cons_1~v277:0, v265:0) -> f_527(v252:0, 1 + v277:0, v277:0, 1 + v265:0) :|: v277:0 > -1 && v262:0 > 1 && v265:0 > 0 && v252:0 > 1 && sum~cons_1~v277:0 = 1 + v277:0 24.07/7.94 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (9) IntTRSCompressionProof (EQUIVALENT) 24.07/7.94 Compressed rules. 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (10) 24.07/7.94 Obligation: 24.07/7.94 Rules: 24.07/7.94 f_527(v252:0:0, v262:0:0, sum~cons_1~v277:0:0, v265:0:0) -> f_527(v252:0:0, 1 + v277:0:0, v277:0:0, 1 + v265:0:0) :|: v265:0:0 > 0 && v252:0:0 > 1 && v262:0:0 > 1 && v277:0:0 > -1 && sum~cons_1~v277:0:0 = 1 + v277:0:0 24.07/7.94 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (11) PolynomialOrderProcessor (EQUIVALENT) 24.07/7.94 Found the following polynomial interpretation: 24.07/7.94 [f_527(x, x1, x2, x3)] = x2 24.07/7.94 24.07/7.94 The following rules are decreasing: 24.07/7.94 f_527(v252:0:0, v262:0:0, sum~cons_1~v277:0:0, v265:0:0) -> f_527(v252:0:0, 1 + v277:0:0, v277:0:0, 1 + v265:0:0) :|: v265:0:0 > 0 && v252:0:0 > 1 && v262:0:0 > 1 && v277:0:0 > -1 && sum~cons_1~v277:0:0 = 1 + v277:0:0 24.07/7.94 The following rules are bounded: 24.07/7.94 f_527(v252:0:0, v262:0:0, sum~cons_1~v277:0:0, v265:0:0) -> f_527(v252:0:0, 1 + v277:0:0, v277:0:0, 1 + v265:0:0) :|: v265:0:0 > 0 && v252:0:0 > 1 && v262:0:0 > 1 && v277:0:0 > -1 && sum~cons_1~v277:0:0 = 1 + v277:0:0 24.07/7.94 24.07/7.94 ---------------------------------------- 24.07/7.94 24.07/7.94 (12) 24.07/7.94 YES 24.56/8.02 EOF