8.68/3.52 YES 8.68/3.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 8.68/3.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.68/3.54 8.68/3.54 8.68/3.54 Termination of the given C Problem could be proven: 8.68/3.54 8.68/3.54 (0) C Problem 8.68/3.54 (1) CToLLVMProof [EQUIVALENT, 171 ms] 8.68/3.54 (2) LLVM problem 8.68/3.54 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1182 ms] 8.68/3.54 (4) LLVM Symbolic Execution Graph 8.68/3.54 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 8.68/3.54 (6) LLVM Symbolic Execution SCC 8.68/3.54 (7) SCC2IRS [SOUND, 42 ms] 8.68/3.54 (8) IntTRS 8.68/3.54 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 8.68/3.54 (10) IntTRS 8.68/3.54 (11) PolynomialOrderProcessor [EQUIVALENT, 12 ms] 8.68/3.54 (12) YES 8.68/3.54 8.68/3.54 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (0) 8.68/3.54 Obligation: 8.68/3.54 c file /export/starexec/sandbox/benchmark/theBenchmark.c 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (1) CToLLVMProof (EQUIVALENT) 8.68/3.54 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (2) 8.68/3.54 Obligation: 8.68/3.54 LLVM Problem 8.68/3.54 8.68/3.54 Aliases: 8.68/3.54 8.68/3.54 Data layout: 8.68/3.54 8.68/3.54 "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" 8.68/3.54 8.68/3.54 Machine: 8.68/3.54 8.68/3.54 "x86_64-pc-linux-gnu" 8.68/3.54 8.68/3.54 Type definitions: 8.68/3.54 8.68/3.54 Global variables: 8.68/3.54 8.68/3.54 Function declarations and definitions: 8.68/3.54 8.68/3.54 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.68/3.54 *BasicFunctionTypename: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.68/3.54 0: 8.68/3.54 %1 = alloca i32, align 4 8.68/3.54 %2 = alloca i32, align 4 8.68/3.54 %c = alloca i32, align 4 8.68/3.54 store %x, %1 8.68/3.54 store %y, %2 8.68/3.54 store 0, %c 8.68/3.54 br %3 8.68/3.54 3: 8.68/3.54 %4 = load %1 8.68/3.54 %5 = load %2 8.68/3.54 %6 = icmp sgt %4 %5 8.68/3.54 br %6, %7, %12 8.68/3.54 7: 8.68/3.54 %8 = load %1 8.68/3.54 %9 = sub %8 1 8.68/3.54 store %9, %1 8.68/3.54 %10 = load %c 8.68/3.54 %11 = add %10 1 8.68/3.54 store %11, %c 8.68/3.54 br %3 8.68/3.54 12: 8.68/3.54 %13 = load %c 8.68/3.54 ret %13 8.68/3.54 8.68/3.54 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.68/3.54 0: 8.68/3.54 %1 = alloca i32, align 4 8.68/3.54 store 0, %1 8.68/3.54 %2 = call i32 @__VERIFIER_nondet_int() 8.68/3.54 %3 = call i32 @__VERIFIER_nondet_int() 8.68/3.54 %4 = call i32 @test_fun(i32 %2, i32 %3) 8.68/3.54 ret %4 8.68/3.54 8.68/3.54 8.68/3.54 Analyze Termination of all function calls matching the pattern: 8.68/3.54 main() 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (3) LLVMToTerminationGraphProof (EQUIVALENT) 8.68/3.54 Constructed symbolic execution graph for LLVM program and proved memory safety. 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (4) 8.68/3.54 Obligation: 8.68/3.54 SE Graph 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (5) SymbolicExecutionGraphToSCCProof (SOUND) 8.68/3.54 Splitted symbolic execution graph to 1 SCC. 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (6) 8.68/3.54 Obligation: 8.68/3.54 SCC 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (7) SCC2IRS (SOUND) 8.68/3.54 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 8.68/3.54 Generated rules. Obtained 13 rulesP rules: 8.68/3.54 f_202(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_203(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: 0 = 0 8.68/3.54 f_203(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_204(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: v98 < v104 8.68/3.54 f_204(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_206(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: 0 = 0 8.68/3.54 f_206(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_208(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: TRUE 8.68/3.54 f_208(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_210(v97, v98, v99, v100, v101, v104, 1, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: 0 = 0 8.68/3.54 f_210(v97, v98, v99, v100, v101, v104, 1, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_212(v97, v98, v99, v100, v101, v104, 1, v113, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: 1 + v113 = v104 8.68/3.54 f_212(v97, v98, v99, v100, v101, v104, 1, v113, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_214(v97, v98, v99, v100, v101, v104, 1, v113, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: TRUE 8.68/3.54 f_214(v97, v98, v99, v100, v101, v104, 1, v113, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_215(v97, v98, v99, v100, v101, v104, 1, v113, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: 0 = 0 8.68/3.54 f_215(v97, v98, v99, v100, v101, v104, 1, v113, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_216(v97, v98, v99, v100, v101, v104, 1, v113, v106, v115, v107, v108, v109, v110, v111, 0, 3, 4, 2) :|: v115 = 1 + v106 && 2 <= v115 8.68/3.54 f_216(v97, v98, v99, v100, v101, v104, 1, v113, v106, v115, v107, v108, v109, v110, v111, 0, 3, 4, 2) -> f_217(v97, v98, v99, v100, v101, v104, 1, v113, v106, v115, v107, v108, v109, v110, v111, 0, 3, 4, 2) :|: TRUE 8.68/3.54 f_217(v97, v98, v99, v100, v101, v104, 1, v113, v106, v115, v107, v108, v109, v110, v111, 0, 3, 4, 2) -> f_218(v97, v98, v99, v100, v101, v104, 1, v113, v106, v115, v107, v108, v109, v110, v111, 0, 3, 4, 2) :|: TRUE 8.68/3.54 f_218(v97, v98, v99, v100, v101, v104, 1, v113, v106, v115, v107, v108, v109, v110, v111, 0, 3, 4, 2) -> f_201(v97, v98, v99, v100, v101, v104, 1, v113, v106, v115, v107, v108, v109, v110, v111, 0, 3, 4) :|: TRUE 8.68/3.54 f_201(v97, v98, v99, v100, v101, v102, 1, v104, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) -> f_202(v97, v98, v99, v100, v101, v104, 1, v102, v105, v106, v107, v108, v109, v110, v111, 0, 3, 4) :|: 0 = 0 8.68/3.54 Combined rules. Obtained 1 rulesP rules: 8.68/3.54 f_202(v97:0, v98:0, v99:0, v100:0, v101:0, 1 + v113:0, 1, v102:0, v105:0, v106:0, v107:0, v108:0, v109:0, v110:0, v111:0, 0, 3, 4) -> f_202(v97:0, v98:0, v99:0, v100:0, v101:0, v113:0, 1, 1 + v113:0, v106:0, 1 + v106:0, v107:0, v108:0, v109:0, v110:0, v111:0, 0, 3, 4) :|: v106:0 > 0 && v98:0 < 1 + v113:0 8.68/3.54 Filtered unneeded arguments: 8.68/3.54 f_202(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_202(x2, x6, x10) 8.68/3.54 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 8.68/3.54 f_202(v98:0, sum~cons_1~v113:0, v106:0) -> f_202(v98:0, v113:0, 1 + v106:0) :|: v106:0 > 0 && v98:0 < 1 + v113:0 && sum~cons_1~v113:0 = 1 + v113:0 8.68/3.54 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (8) 8.68/3.54 Obligation: 8.68/3.54 Rules: 8.68/3.54 f_202(v98:0, sum~cons_1~v113:0, v106:0) -> f_202(v98:0, v113:0, 1 + v106:0) :|: v106:0 > 0 && v98:0 < 1 + v113:0 && sum~cons_1~v113:0 = 1 + v113:0 8.68/3.54 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (9) IntTRSCompressionProof (EQUIVALENT) 8.68/3.54 Compressed rules. 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (10) 8.68/3.54 Obligation: 8.68/3.54 Rules: 8.68/3.54 f_202(v98:0:0, sum~cons_1~v113:0:0, v106:0:0) -> f_202(v98:0:0, v113:0:0, 1 + v106:0:0) :|: v106:0:0 > 0 && v98:0:0 < 1 + v113:0:0 && sum~cons_1~v113:0:0 = 1 + v113:0:0 8.68/3.54 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (11) PolynomialOrderProcessor (EQUIVALENT) 8.68/3.54 Found the following polynomial interpretation: 8.68/3.54 [f_202(x, x1, x2)] = -x + x1 8.68/3.54 8.68/3.54 The following rules are decreasing: 8.68/3.54 f_202(v98:0:0, sum~cons_1~v113:0:0, v106:0:0) -> f_202(v98:0:0, v113:0:0, 1 + v106:0:0) :|: v106:0:0 > 0 && v98:0:0 < 1 + v113:0:0 && sum~cons_1~v113:0:0 = 1 + v113:0:0 8.68/3.54 The following rules are bounded: 8.68/3.54 f_202(v98:0:0, sum~cons_1~v113:0:0, v106:0:0) -> f_202(v98:0:0, v113:0:0, 1 + v106:0:0) :|: v106:0:0 > 0 && v98:0:0 < 1 + v113:0:0 && sum~cons_1~v113:0:0 = 1 + v113:0:0 8.68/3.54 8.68/3.54 ---------------------------------------- 8.68/3.54 8.68/3.54 (12) 8.68/3.54 YES 8.68/3.59 EOF