11.61/4.40 YES 12.57/4.42 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 12.57/4.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.57/4.42 12.57/4.42 12.57/4.42 Termination of the given C Problem could be proven: 12.57/4.42 12.57/4.42 (0) C Problem 12.57/4.42 (1) CToLLVMProof [EQUIVALENT, 174 ms] 12.57/4.42 (2) LLVM problem 12.57/4.42 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1994 ms] 12.57/4.42 (4) LLVM Symbolic Execution Graph 12.57/4.42 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 12.57/4.42 (6) LLVM Symbolic Execution SCC 12.57/4.42 (7) SCC2IRS [SOUND, 87 ms] 12.57/4.42 (8) IntTRS 12.57/4.42 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 12.57/4.42 (10) IntTRS 12.57/4.42 (11) PolynomialOrderProcessor [EQUIVALENT, 18 ms] 12.57/4.42 (12) YES 12.57/4.42 12.57/4.42 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (0) 12.57/4.42 Obligation: 12.57/4.42 c file /export/starexec/sandbox/benchmark/theBenchmark.c 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (1) CToLLVMProof (EQUIVALENT) 12.57/4.42 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (2) 12.57/4.42 Obligation: 12.57/4.42 LLVM Problem 12.57/4.42 12.57/4.42 Aliases: 12.57/4.42 12.57/4.42 Data layout: 12.57/4.42 12.57/4.42 "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" 12.57/4.42 12.57/4.42 Machine: 12.57/4.42 12.57/4.42 "x86_64-pc-linux-gnu" 12.57/4.42 12.57/4.42 Type definitions: 12.57/4.42 12.57/4.42 Global variables: 12.57/4.42 12.57/4.42 Function declarations and definitions: 12.57/4.42 12.57/4.42 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 12.57/4.42 *BasicFunctionTypename: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 12.57/4.42 0: 12.57/4.42 %1 = alloca i32, align 4 12.57/4.42 %2 = alloca i32, align 4 12.57/4.42 %c = alloca i32, align 4 12.57/4.42 store %x, %1 12.57/4.42 store %y, %2 12.57/4.42 store 0, %c 12.57/4.42 br %3 12.57/4.42 3: 12.57/4.42 %4 = load %1 12.57/4.42 %5 = icmp sgt %4 0 12.57/4.42 br %5, %6, %9 12.57/4.42 6: 12.57/4.42 %7 = load %2 12.57/4.42 %8 = icmp sgt %7 0 12.57/4.42 br %9 12.57/4.42 9: 12.57/4.42 %10 = phi [0, %3], [%8, %6] 12.57/4.42 br %10, %11, %18 12.57/4.42 11: 12.57/4.42 %12 = load %1 12.57/4.42 %13 = sub %12 1 12.57/4.42 store %13, %1 12.57/4.42 %14 = load %2 12.57/4.42 %15 = sub %14 1 12.57/4.42 store %15, %2 12.57/4.42 %16 = load %c 12.57/4.42 %17 = add %16 1 12.57/4.42 store %17, %c 12.57/4.42 br %3 12.57/4.42 18: 12.57/4.42 %19 = load %c 12.57/4.42 ret %19 12.57/4.42 12.57/4.42 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 12.57/4.42 0: 12.57/4.42 %1 = alloca i32, align 4 12.57/4.42 store 0, %1 12.57/4.42 %2 = call i32 @__VERIFIER_nondet_int() 12.57/4.42 %3 = call i32 @__VERIFIER_nondet_int() 12.57/4.42 %4 = call i32 @test_fun(i32 %2, i32 %3) 12.57/4.42 ret %4 12.57/4.42 12.57/4.42 12.57/4.42 Analyze Termination of all function calls matching the pattern: 12.57/4.42 main() 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (3) LLVMToTerminationGraphProof (EQUIVALENT) 12.57/4.42 Constructed symbolic execution graph for LLVM program and proved memory safety. 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (4) 12.57/4.42 Obligation: 12.57/4.42 SE Graph 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (5) SymbolicExecutionGraphToSCCProof (SOUND) 12.57/4.42 Splitted symbolic execution graph to 1 SCC. 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (6) 12.57/4.42 Obligation: 12.57/4.42 SCC 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (7) SCC2IRS (SOUND) 12.57/4.42 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 12.57/4.42 Generated rules. Obtained 20 rulesP rules: 12.57/4.42 f_307(v322, v323, v324, v325, v326, v330, 1, v329, v327, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 4) -> f_308(v322, v323, v324, v325, v326, v330, 1, v329, v327, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 < v330 && 2 <= v327 && 2 <= v322 12.57/4.42 f_308(v322, v323, v324, v325, v326, v330, 1, v329, v327, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_310(v322, v323, v324, v325, v326, v330, 1, v329, v327, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 = 0 12.57/4.42 f_310(v322, v323, v324, v325, v326, v330, 1, v329, v327, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_312(v322, v323, v324, v325, v326, v330, 1, v329, v327, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: TRUE 12.57/4.42 f_312(v322, v323, v324, v325, v326, v330, 1, v329, v327, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_314(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 = 0 12.57/4.42 f_314(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_316(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 < v331 && 2 <= v329 && 2 <= v323 12.57/4.42 f_316(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_319(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 = 0 12.57/4.42 f_319(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_322(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 = 0 12.57/4.42 f_322(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_324(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: TRUE 12.57/4.42 f_324(v322, v323, v324, v325, v326, v330, 1, v331, v327, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_326(v322, v323, v324, v325, v326, v330, 1, v331, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 = 0 12.57/4.42 f_326(v322, v323, v324, v325, v326, v330, 1, v331, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_328(v322, v323, v324, v325, v326, v330, 1, v331, v378, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 1 + v378 = v330 && 0 <= v378 12.57/4.42 f_328(v322, v323, v324, v325, v326, v330, 1, v331, v378, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_330(v322, v323, v324, v325, v326, v330, 1, v331, v378, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: TRUE 12.57/4.42 f_330(v322, v323, v324, v325, v326, v330, 1, v331, v378, v329, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_331(v322, v323, v324, v325, v326, v330, 1, v331, v378, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 = 0 12.57/4.42 f_331(v322, v323, v324, v325, v326, v330, 1, v331, v378, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_332(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 1 + v380 = v331 && 0 <= v380 12.57/4.42 f_332(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_333(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: TRUE 12.57/4.42 f_333(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v332, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_334(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: 0 = 0 12.57/4.42 f_334(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_335(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v382, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: v382 = 1 + v333 && 2 <= v382 12.57/4.42 f_335(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v382, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_336(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v382, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: TRUE 12.57/4.42 f_336(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v382, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_337(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v382, v334, v335, v336, v337, v338, 0, 3, 2, 4) :|: TRUE 12.57/4.42 f_337(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v382, v334, v335, v336, v337, v338, 0, 3, 2, 4) -> f_306(v322, v323, v324, v325, v326, v330, 1, v331, v378, v380, v333, v382, v334, v335, v336, v337, v338, 0, 3, 4) :|: TRUE 12.57/4.42 f_306(v322, v323, v324, v325, v326, v327, 1, v329, v330, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 4) -> f_307(v322, v323, v324, v325, v326, v330, 1, v329, v327, v331, v332, v333, v334, v335, v336, v337, v338, 0, 3, 4) :|: 0 = 0 12.57/4.42 Combined rules. Obtained 1 rulesP rules: 12.57/4.42 f_307(v322:0, v323:0, v324:0, v325:0, v326:0, 1 + v378:0, 1, v329:0, v327:0, 1 + v380:0, v332:0, v333:0, v334:0, v335:0, v336:0, v337:0, v338:0, 0, 3, 4) -> f_307(v322:0, v323:0, v324:0, v325:0, v326:0, v378:0, 1, 1 + v380:0, 1 + v378:0, v380:0, v333:0, 1 + v333:0, v334:0, v335:0, v336:0, v337:0, v338:0, 0, 3, 4) :|: v327:0 > 1 && v378:0 > -1 && v322:0 > 1 && v329:0 > 1 && v380:0 > -1 && v323:0 > 1 && v333:0 > 0 12.57/4.42 Filtered unneeded arguments: 12.57/4.42 f_307(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f_307(x1, x2, x6, x8, x9, x10, x12) 12.57/4.42 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 12.57/4.42 f_307(v322:0, v323:0, sum~cons_1~v378:0, v329:0, v327:0, sum~cons_1~v380:0, v333:0) -> f_307(v322:0, v323:0, v378:0, 1 + v380:0, 1 + v378:0, v380:0, 1 + v333:0) :|: v378:0 > -1 && v327:0 > 1 && v322:0 > 1 && v329:0 > 1 && v380:0 > -1 && v333:0 > 0 && v323:0 > 1 && sum~cons_1~v378:0 = 1 + v378:0 && sum~cons_1~v380:0 = 1 + v380:0 12.57/4.42 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (8) 12.57/4.42 Obligation: 12.57/4.42 Rules: 12.57/4.42 f_307(v322:0, v323:0, sum~cons_1~v378:0, v329:0, v327:0, sum~cons_1~v380:0, v333:0) -> f_307(v322:0, v323:0, v378:0, 1 + v380:0, 1 + v378:0, v380:0, 1 + v333:0) :|: v378:0 > -1 && v327:0 > 1 && v322:0 > 1 && v329:0 > 1 && v380:0 > -1 && v333:0 > 0 && v323:0 > 1 && sum~cons_1~v378:0 = 1 + v378:0 && sum~cons_1~v380:0 = 1 + v380:0 12.57/4.42 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (9) IntTRSCompressionProof (EQUIVALENT) 12.57/4.42 Compressed rules. 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (10) 12.57/4.42 Obligation: 12.57/4.42 Rules: 12.57/4.42 f_307(v322:0:0, v323:0:0, sum~cons_1~v378:0:0, v329:0:0, v327:0:0, sum~cons_1~v380:0:0, v333:0:0) -> f_307(v322:0:0, v323:0:0, v378:0:0, 1 + v380:0:0, 1 + v378:0:0, v380:0:0, 1 + v333:0:0) :|: v333:0:0 > 0 && v323:0:0 > 1 && v380:0:0 > -1 && v329:0:0 > 1 && v322:0:0 > 1 && v327:0:0 > 1 && v378:0:0 > -1 && sum~cons_1~v378:0:0 = 1 + v378:0:0 && sum~cons_1~v380:0:0 = 1 + v380:0:0 12.57/4.42 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (11) PolynomialOrderProcessor (EQUIVALENT) 12.57/4.42 Found the following polynomial interpretation: 12.57/4.42 [f_307(x, x1, x2, x3, x4, x5, x6)] = x2 12.57/4.42 12.57/4.42 The following rules are decreasing: 12.57/4.42 f_307(v322:0:0, v323:0:0, sum~cons_1~v378:0:0, v329:0:0, v327:0:0, sum~cons_1~v380:0:0, v333:0:0) -> f_307(v322:0:0, v323:0:0, v378:0:0, 1 + v380:0:0, 1 + v378:0:0, v380:0:0, 1 + v333:0:0) :|: v333:0:0 > 0 && v323:0:0 > 1 && v380:0:0 > -1 && v329:0:0 > 1 && v322:0:0 > 1 && v327:0:0 > 1 && v378:0:0 > -1 && sum~cons_1~v378:0:0 = 1 + v378:0:0 && sum~cons_1~v380:0:0 = 1 + v380:0:0 12.57/4.42 The following rules are bounded: 12.57/4.42 f_307(v322:0:0, v323:0:0, sum~cons_1~v378:0:0, v329:0:0, v327:0:0, sum~cons_1~v380:0:0, v333:0:0) -> f_307(v322:0:0, v323:0:0, v378:0:0, 1 + v380:0:0, 1 + v378:0:0, v380:0:0, 1 + v333:0:0) :|: v333:0:0 > 0 && v323:0:0 > 1 && v380:0:0 > -1 && v329:0:0 > 1 && v322:0:0 > 1 && v327:0:0 > 1 && v378:0:0 > -1 && sum~cons_1~v378:0:0 = 1 + v378:0:0 && sum~cons_1~v380:0:0 = 1 + v380:0:0 12.57/4.42 12.57/4.42 ---------------------------------------- 12.57/4.42 12.57/4.42 (12) 12.57/4.42 YES 12.57/4.46 EOF