12.73/4.41 YES 12.73/4.42 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 12.73/4.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.73/4.42 12.73/4.42 12.73/4.42 Termination of the given C Problem could be proven: 12.73/4.42 12.73/4.42 (0) C Problem 12.73/4.42 (1) CToLLVMProof [EQUIVALENT, 173 ms] 12.73/4.42 (2) LLVM problem 12.73/4.42 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1921 ms] 12.73/4.42 (4) LLVM Symbolic Execution Graph 12.73/4.42 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 12.73/4.42 (6) LLVM Symbolic Execution SCC 12.73/4.42 (7) SCC2IRS [SOUND, 72 ms] 12.73/4.42 (8) IntTRS 12.73/4.42 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 12.73/4.42 (10) IntTRS 12.73/4.42 (11) PolynomialOrderProcessor [EQUIVALENT, 11 ms] 12.73/4.42 (12) YES 12.73/4.42 12.73/4.42 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (0) 12.73/4.42 Obligation: 12.73/4.42 c file /export/starexec/sandbox/benchmark/theBenchmark.c 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (1) CToLLVMProof (EQUIVALENT) 12.73/4.42 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (2) 12.73/4.42 Obligation: 12.73/4.42 LLVM Problem 12.73/4.42 12.73/4.42 Aliases: 12.73/4.42 12.73/4.42 Data layout: 12.73/4.42 12.73/4.42 "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" 12.73/4.42 12.73/4.42 Machine: 12.73/4.42 12.73/4.42 "x86_64-pc-linux-gnu" 12.73/4.42 12.73/4.42 Type definitions: 12.73/4.42 12.73/4.42 Global variables: 12.73/4.42 12.73/4.42 Function declarations and definitions: 12.73/4.42 12.73/4.42 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 12.73/4.42 *BasicFunctionTypename: "fact" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 12.73/4.42 0: 12.73/4.42 %1 = alloca i32, align 4 12.73/4.42 %2 = alloca i32, align 4 12.73/4.42 %y = alloca i32, align 4 12.73/4.42 store %x, %2 12.73/4.42 %3 = load %2 12.73/4.42 %4 = icmp sgt %3 1 12.73/4.42 br %4, %5, %12 12.73/4.42 5: 12.73/4.42 %6 = load %2 12.73/4.42 %7 = sub %6 1 12.73/4.42 %8 = call i32 @fact(i32 %7) 12.73/4.42 store %8, %y 12.73/4.42 %9 = load %y 12.73/4.42 %10 = load %2 12.73/4.42 %11 = mul %9 %10 12.73/4.42 store %11, %1 12.73/4.42 br %13 12.73/4.42 12: 12.73/4.42 store 1, %1 12.73/4.42 br %13 12.73/4.42 13: 12.73/4.42 %14 = load %1 12.73/4.42 ret %14 12.73/4.42 12.73/4.42 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 12.73/4.42 0: 12.73/4.42 %1 = alloca i32, align 4 12.73/4.42 %x = alloca i32, align 4 12.73/4.42 %y = alloca i32, align 4 12.73/4.42 %z = alloca i32, align 4 12.73/4.42 store 0, %1 12.73/4.42 %2 = call i32 @__VERIFIER_nondet_int() 12.73/4.42 store %2, %x 12.73/4.42 %3 = load %x 12.73/4.42 %4 = icmp slt %3 0 12.73/4.42 br %4, %5, %6 12.73/4.42 5: 12.73/4.42 store 0, %1 12.73/4.42 br %15 12.73/4.42 6: 12.73/4.42 %7 = call i32 @__VERIFIER_nondet_int() 12.73/4.42 store %7, %y 12.73/4.42 %8 = load %y 12.73/4.42 %9 = icmp slt %8 0 12.73/4.42 br %9, %10, %11 12.73/4.42 10: 12.73/4.42 store 0, %1 12.73/4.42 br %15 12.73/4.42 11: 12.73/4.42 %12 = call i32 @__VERIFIER_nondet_int() 12.73/4.42 store %12, %z 12.73/4.42 %13 = load %x 12.73/4.42 %14 = call i32 @fact(i32 %13) 12.73/4.42 br %15 12.73/4.42 15: 12.73/4.42 %16 = load %1 12.73/4.42 ret %16 12.73/4.42 12.73/4.42 12.73/4.42 Analyze Termination of all function calls matching the pattern: 12.73/4.42 main() 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (3) LLVMToTerminationGraphProof (EQUIVALENT) 12.73/4.42 Constructed symbolic execution graph for LLVM program and proved memory safety. 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (4) 12.73/4.42 Obligation: 12.73/4.42 SE Graph 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (5) SymbolicExecutionGraphToSCCProof (SOUND) 12.73/4.42 Splitted symbolic execution graph to 1 SCC. 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (6) 12.73/4.42 Obligation: 12.73/4.42 SCC 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (7) SCC2IRS (SOUND) 12.73/4.42 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 12.73/4.42 Generated rules. Obtained 13 rulesP rules: 12.73/4.42 f_220(v85, v98, v86, v87, v88, v89, v90, v91, v92, v93, v99, 0, v95, v96, v97, 3, 1, 4) -> f_222(v85, v98, v106, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, 0, v95, v96, v97, 3, 1, 4) :|: 1 <= v106 && v107 = 3 + v106 && 4 <= v107 12.73/4.42 f_222(v85, v98, v106, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, 0, v95, v96, v97, 3, 1, 4) -> f_223(v85, v98, v106, v108, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 1, 4) :|: 1 <= v108 && v109 = 3 + v108 && 4 <= v109 12.73/4.42 f_223(v85, v98, v106, v108, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 1, 4) -> f_224(v85, v98, v106, v108, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 1, 4) :|: TRUE 12.73/4.42 f_224(v85, v98, v106, v108, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 1, 4) -> f_225(v85, v98, v106, v108, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 1, 4) :|: 0 = 0 12.73/4.42 f_225(v85, v98, v106, v108, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 1, 4) -> f_226(v85, v98, v106, v108, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 1, 4) :|: 1 < v85 && 2 <= v95 12.73/4.42 f_226(v85, v98, v106, v108, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 1, 4) -> f_228(v85, v98, v106, v108, 1, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 4) :|: 0 = 0 12.73/4.42 f_228(v85, v98, v106, v108, 1, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 4) -> f_230(v85, v98, v106, v108, 1, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 4) :|: TRUE 12.73/4.42 f_230(v85, v98, v106, v108, 1, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 4) -> f_232(v85, v98, v106, v108, 1, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 4) :|: 0 = 0 12.73/4.42 f_232(v85, v98, v106, v108, 1, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 4) -> f_234(v85, v98, v106, v108, 1, v111, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 4) :|: 1 + v111 = v85 && 1 <= v111 12.73/4.42 f_234(v85, v98, v106, v108, 1, v111, v86, v87, v88, v89, v90, v91, v92, v93, v99, v107, v109, 0, v95, v96, v97, 3, 2, 4) -> f_236(v111, v86, v87, v88, v89, v90, v91, v92, v93, v98, v99, v106, v107, v108, v109, 0, v95, v96, v97, v85, 1, 3, 2, 4) :|: 0 = 0 12.73/4.42 f_236(v111, v86, v87, v88, v89, v90, v91, v92, v93, v98, v99, v106, v107, v108, v109, 0, v95, v96, v97, v85, 1, 3, 2, 4) -> f_238(v111, v86, v87, v88, v89, v90, v91, v92, v93, v98, v99, v106, v107, v108, v109, 0, v95, v96, v97, v85, 3, 1, 2, 4) :|: TRUE 12.73/4.42 f_238(v111, v86, v87, v88, v89, v90, v91, v92, v93, v98, v99, v106, v107, v108, v109, 0, v95, v96, v97, v85, 3, 1, 2, 4) -> f_218(v111, v86, v87, v88, v89, v90, v91, v92, v93, 0, v95, v96, v97, 3, 1, 4) :|: TRUE 12.73/4.42 f_218(v85, v86, v87, v88, v89, v90, v91, v92, v93, 0, v95, v96, v97, 3, 1, 4) -> f_220(v85, v98, v86, v87, v88, v89, v90, v91, v92, v93, v99, 0, v95, v96, v97, 3, 1, 4) :|: 1 <= v98 && v99 = 3 + v98 && 4 <= v99 12.73/4.42 Combined rules. Obtained 1 rulesP rules: 12.73/4.42 f_220(1 + v111:0, v98:0, v86:0, v87:0, v88:0, v89:0, v90:0, v91:0, v92:0, v93:0, v99:0, 0, v95:0, v96:0, v97:0, 3, 1, 4) -> f_220(v111:0, v98:1, v86:0, v87:0, v88:0, v89:0, v90:0, v91:0, v92:0, v93:0, 3 + v98:1, 0, v95:0, v96:0, v97:0, 3, 1, 4) :|: v108:0 > 0 && v106:0 > 0 && v95:0 > 1 && v111:0 > 0 && v98:1 > 0 12.73/4.42 Filtered unneeded arguments: 12.73/4.42 f_220(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_220(x1, x13) 12.73/4.42 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 12.73/4.42 f_220(sum~cons_1~v111:0, v95:0) -> f_220(v111:0, v95:0) :|: v95:0 > 1 && v111:0 > 0 && sum~cons_1~v111:0 = 1 + v111:0 12.73/4.42 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (8) 12.73/4.42 Obligation: 12.73/4.42 Rules: 12.73/4.42 f_220(sum~cons_1~v111:0, v95:0) -> f_220(v111:0, v95:0) :|: v95:0 > 1 && v111:0 > 0 && sum~cons_1~v111:0 = 1 + v111:0 12.73/4.42 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (9) IntTRSCompressionProof (EQUIVALENT) 12.73/4.42 Compressed rules. 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (10) 12.73/4.42 Obligation: 12.73/4.42 Rules: 12.73/4.42 f_220(sum~cons_1~v111:0:0, v95:0:0) -> f_220(v111:0:0, v95:0:0) :|: v95:0:0 > 1 && v111:0:0 > 0 && sum~cons_1~v111:0:0 = 1 + v111:0:0 12.73/4.42 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (11) PolynomialOrderProcessor (EQUIVALENT) 12.73/4.42 Found the following polynomial interpretation: 12.73/4.42 [f_220(x, x1)] = x 12.73/4.42 12.73/4.42 The following rules are decreasing: 12.73/4.42 f_220(sum~cons_1~v111:0:0, v95:0:0) -> f_220(v111:0:0, v95:0:0) :|: v95:0:0 > 1 && v111:0:0 > 0 && sum~cons_1~v111:0:0 = 1 + v111:0:0 12.73/4.42 The following rules are bounded: 12.73/4.42 f_220(sum~cons_1~v111:0:0, v95:0:0) -> f_220(v111:0:0, v95:0:0) :|: v95:0:0 > 1 && v111:0:0 > 0 && sum~cons_1~v111:0:0 = 1 + v111:0:0 12.73/4.42 12.73/4.42 ---------------------------------------- 12.73/4.42 12.73/4.42 (12) 12.73/4.42 YES 12.96/4.77 EOF