15.72/4.94 YES 15.72/4.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 15.72/4.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.72/4.95 15.72/4.95 15.72/4.95 Termination of the given C Problem could be proven: 15.72/4.95 15.72/4.95 (0) C Problem 15.72/4.95 (1) CToLLVMProof [EQUIVALENT, 173 ms] 15.72/4.95 (2) LLVM problem 15.72/4.95 (3) LLVMToTerminationGraphProof [EQUIVALENT, 685 ms] 15.72/4.95 (4) LLVM Symbolic Execution Graph 15.72/4.95 (5) SymbolicExecutionGraphToLassoProof [EQUIVALENT, 0 ms] 15.72/4.95 (6) LLVM Symbolic Execution Lasso 15.72/4.95 (7) Lasso2IRS [EQUIVALENT, 44 ms] 15.72/4.95 (8) IntTRS 15.72/4.95 (9) IRS2T2 [EQUIVALENT, 0 ms] 15.72/4.95 (10) T2IntSys 15.72/4.95 (11) T2 [EQUIVALENT, 1283 ms] 15.72/4.95 (12) YES 15.72/4.95 15.72/4.95 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (0) 15.72/4.95 Obligation: 15.72/4.95 c file /export/starexec/sandbox/benchmark/theBenchmark.c 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (1) CToLLVMProof (EQUIVALENT) 15.72/4.95 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (2) 15.72/4.95 Obligation: 15.72/4.95 LLVM Problem 15.72/4.95 15.72/4.95 Aliases: 15.72/4.95 15.72/4.95 Data layout: 15.72/4.95 15.72/4.95 "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" 15.72/4.95 15.72/4.95 Machine: 15.72/4.95 15.72/4.95 "x86_64-pc-linux-gnu" 15.72/4.95 15.72/4.95 Type definitions: 15.72/4.95 15.72/4.95 Global variables: 15.72/4.95 15.72/4.95 Function declarations and definitions: 15.72/4.95 15.72/4.95 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 15.72/4.95 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 15.72/4.95 0: 15.72/4.95 %1 = alloca i32, align 4 15.72/4.95 %x = alloca i32, align 4 15.72/4.95 %y = alloca i32, align 4 15.72/4.95 store 0, %1 15.72/4.95 %2 = call i32 @__VERIFIER_nondet_int() 15.72/4.95 store %2, %x 15.72/4.95 %3 = call i32 @__VERIFIER_nondet_int() 15.72/4.95 store %3, %y 15.72/4.95 %4 = load %y 15.72/4.95 %5 = icmp slt %4 1 15.72/4.95 br %5, %6, %7 15.72/4.95 6: 15.72/4.95 store 0, %1 15.72/4.95 br %21 15.72/4.95 7: 15.72/4.95 br %8 15.72/4.95 8: 15.72/4.95 %9 = load %x 15.72/4.95 %10 = icmp sge %9 0 15.72/4.95 br %10, %11, %20 15.72/4.95 11: 15.72/4.95 %12 = load %x 15.72/4.95 %13 = load %y 15.72/4.95 %14 = sub %12 %13 15.72/4.95 store %14, %x 15.72/4.95 %15 = call i32 @__VERIFIER_nondet_int() 15.72/4.95 store %15, %y 15.72/4.95 %16 = load %y 15.72/4.95 %17 = icmp slt %16 1 15.72/4.95 br %17, %18, %19 15.72/4.95 18: 15.72/4.95 br %20 15.72/4.95 19: 15.72/4.95 br %8 15.72/4.95 20: 15.72/4.95 store 0, %1 15.72/4.95 br %21 15.72/4.95 21: 15.72/4.95 %22 = load %1 15.72/4.95 ret %22 15.72/4.95 15.72/4.95 15.72/4.95 Analyze Termination of all function calls matching the pattern: 15.72/4.95 main() 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (3) LLVMToTerminationGraphProof (EQUIVALENT) 15.72/4.95 Constructed symbolic execution graph for LLVM program and proved memory safety. 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (4) 15.72/4.95 Obligation: 15.72/4.95 SE Graph 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (5) SymbolicExecutionGraphToLassoProof (EQUIVALENT) 15.72/4.95 Converted SEGraph to 1 independent lasso. 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (6) 15.72/4.95 Obligation: 15.72/4.95 Lasso 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (7) Lasso2IRS (EQUIVALENT) 15.72/4.95 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 15.72/4.95 Generated rules. Obtained 45 rulesP rules: 15.72/4.95 f_173(v50, v51, v52, v53, v54, 0, v59, 1, v56, v58, v60, v61, v62, v63, 3, 4) -> f_174(v50, v51, v52, v53, v54, 0, v59, 1, v56, v58, v60, v61, v62, v63, 3, 4) :|: 0 <= v59 && 1 <= v56 15.72/4.95 f_174(v50, v51, v52, v53, v54, 0, v59, 1, v56, v58, v60, v61, v62, v63, 3, 4) -> f_176(v50, v51, v52, v53, v54, 0, v59, 1, v56, v58, v60, v61, v62, v63, 3, 4) :|: 0 = 0 15.72/4.95 f_176(v50, v51, v52, v53, v54, 0, v59, 1, v56, v58, v60, v61, v62, v63, 3, 4) -> f_178(v50, v51, v52, v53, v54, 0, v59, 1, v56, v58, v60, v61, v62, v63, 3, 4) :|: TRUE 15.72/4.95 f_178(v50, v51, v52, v53, v54, 0, v59, 1, v56, v58, v60, v61, v62, v63, 3, 4) -> f_180(v50, v51, v52, v53, v54, 0, v59, 1, v58, v60, v61, v62, v63, 3, 4) :|: 0 = 0 15.72/4.95 f_180(v50, v51, v52, v53, v54, 0, v59, 1, v58, v60, v61, v62, v63, 3, 4) -> f_182(v50, v51, v52, v53, v54, 0, v59, 1, v60, v61, v62, v63, 3, 4) :|: 0 = 0 15.72/4.95 f_182(v50, v51, v52, v53, v54, 0, v59, 1, v60, v61, v62, v63, 3, 4) -> f_184(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v61, v62, v63, 3, 4) :|: v79 + v60 = v59 15.72/4.95 f_184(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v61, v62, v63, 3, 4) -> f_186(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v61, v62, v63, 3, 4) :|: TRUE 15.72/4.95 f_186(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v61, v62, v63, 3, 4) -> f_187(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) :|: TRUE 15.72/4.95 f_187(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) -> f_188(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) :|: TRUE 15.72/4.95 f_188(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) -> f_189(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) :|: 0 = 0 15.72/4.95 f_189(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) -> f_191(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) :|: 1 <= v81 15.72/4.95 f_191(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) -> f_193(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) :|: 0 = 0 15.72/4.95 f_193(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) -> f_195(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) :|: TRUE 15.72/4.95 f_195(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) -> f_197(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) :|: TRUE 15.72/4.95 f_197(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) -> f_172(v50, v51, v52, v53, v54, 0, v59, 1, v60, v79, v81, v61, v62, v63, 3, 4) :|: TRUE 15.72/4.95 f_172(v50, v51, v52, v53, v54, 0, v56, 1, v58, v59, v60, v61, v62, v63, 3, 4) -> f_173(v50, v51, v52, v53, v54, 0, v59, 1, v56, v58, v60, v61, v62, v63, 3, 4) :|: 0 = 0 15.72/4.95 f_99 -> f_100(v1, v2, 3, 1, 4) :|: 1 <= v1 && v2 = 3 + v1 && 4 <= v2 15.72/4.95 f_100(v1, v2, 3, 1, 4) -> f_101(v1, v3, v2, v4, 3, 1, 4) :|: 1 <= v3 && v4 = 3 + v3 && 4 <= v4 15.72/4.95 f_101(v1, v3, v2, v4, 3, 1, 4) -> f_102(v1, v3, v5, v2, v4, v6, 3, 1, 4) :|: 1 <= v5 && v6 = 3 + v5 && 4 <= v6 15.72/4.95 f_102(v1, v3, v5, v2, v4, v6, 3, 1, 4) -> f_103(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 15.72/4.95 f_103(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) -> f_104(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 15.72/4.95 f_104(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_105(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 15.72/4.95 f_105(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_106(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 15.72/4.95 f_106(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_107(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 15.72/4.95 f_107(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_108(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 = 0 15.72/4.95 f_108(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_110(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 1 <= v9 15.72/4.95 f_110(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_112(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) :|: 0 = 0 15.72/4.95 f_112(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) -> f_114(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) :|: TRUE 15.72/4.95 f_114(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) -> f_116(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) :|: TRUE 15.72/4.95 f_116(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) -> f_118(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) :|: 0 = 0 15.72/4.95 f_118(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) -> f_120(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) :|: 0 <= v7 15.72/4.95 f_120(v1, v3, v5, v7, v9, 0, v2, v4, v6, 3, 1, 4) -> f_122(v1, v3, v5, v7, v9, 0, 1, v2, v4, v6, 3, 4) :|: 0 = 0 15.72/4.95 f_122(v1, v3, v5, v7, v9, 0, 1, v2, v4, v6, 3, 4) -> f_124(v1, v3, v5, v7, v9, 0, 1, v2, v4, v6, 3, 4) :|: TRUE 15.72/4.95 f_124(v1, v3, v5, v7, v9, 0, 1, v2, v4, v6, 3, 4) -> f_126(v1, v3, v5, v7, v9, 0, 1, v2, v4, v6, 3, 4) :|: 0 = 0 15.72/4.95 f_126(v1, v3, v5, v7, v9, 0, 1, v2, v4, v6, 3, 4) -> f_128(v1, v3, v5, v7, v9, 0, 1, v2, v4, v6, 3, 4) :|: 0 = 0 15.72/4.95 f_128(v1, v3, v5, v7, v9, 0, 1, v2, v4, v6, 3, 4) -> f_130(v1, v3, v5, v7, v9, 0, 1, v11, v2, v4, v6, 3, 4) :|: v11 + v9 = v7 15.72/4.95 f_130(v1, v3, v5, v7, v9, 0, 1, v11, v2, v4, v6, 3, 4) -> f_132(v1, v3, v5, v7, v9, 0, 1, v11, v2, v4, v6, 3, 4) :|: TRUE 15.72/4.95 f_132(v1, v3, v5, v7, v9, 0, 1, v11, v2, v4, v6, 3, 4) -> f_133(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) :|: TRUE 15.72/4.95 f_133(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) -> f_134(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) :|: TRUE 15.72/4.95 f_134(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) -> f_135(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) :|: 0 = 0 15.72/4.95 f_135(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) -> f_137(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) :|: 1 <= v13 15.72/4.95 f_137(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) -> f_139(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) :|: 0 = 0 15.72/4.95 f_139(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) -> f_141(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) :|: TRUE 15.72/4.95 f_141(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) -> f_143(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) :|: TRUE 15.72/4.95 f_143(v1, v3, v5, v7, v9, 0, 1, v11, v13, v2, v4, v6, 3, 4) -> f_172(v1, v3, v5, v7, v9, 0, v7, 1, v9, v11, v13, v2, v4, v6, 3, 4) :|: TRUE 15.72/4.95 Combined rules. Obtained 2 rulesP rules: 15.72/4.95 f_173(v50:0, v51:0, v52:0, v53:0, v54:0, 0, v79:0 + v60:0, 1, v56:0, v58:0, v60:0, v61:0, v62:0, v63:0, 3, 4) -> f_173(v50:0, v51:0, v52:0, v53:0, v54:0, 0, v79:0, 1, v79:0 + v60:0, v60:0, v81:0, v61:0, v62:0, v63:0, 3, 4) :|: v56:0 > 0 && v81:0 > 0 && v79:0 + v60:0 > -1 15.72/4.95 f_99 -> f_173(v1:0, v3:0, v5:0, v11:0 + v9:0, v9:0, 0, v11:0, 1, v11:0 + v9:0, v9:0, v13:0, 3 + v1:0, 3 + v3:0, 3 + v5:0, 3, 4) :|: v3:0 > 0 && v1:0 > 0 && v5:0 > 0 && v9:0 > 0 && v13:0 > 0 && v11:0 + v9:0 > -1 15.72/4.95 Filtered unneeded arguments: 15.72/4.95 f_173(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_173(x7, x9, x11) 15.72/4.95 Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules: 15.72/4.95 f_173(sum~v79:0~v60:0, v56:0, v60:0) -> f_173(v79:0, v79:0 + v60:0, v81:0) :|: v81:0 > 0 && v79:0 + v60:0 > -1 && v56:0 > 0 && sum~v79:0~v60:0 = v79:0 + v60:0 15.72/4.95 f_99 -> f_173(v11:0, v11:0 + v9:0, v13:0) :|: v13:0 > 0 && v11:0 + v9:0 > -1 && v9:0 > 0 15.72/4.95 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (8) 15.72/4.95 Obligation: 15.72/4.95 Rules: 15.72/4.95 f_173(sum~v79:0~v60:0, v56:0, v60:0) -> f_173(v79:0, v79:0 + v60:0, v81:0) :|: v81:0 > 0 && v79:0 + v60:0 > -1 && v56:0 > 0 && sum~v79:0~v60:0 = v79:0 + v60:0 15.72/4.95 f_99 -> f_173(v11:0, v11:0 + v9:0, v13:0) :|: v13:0 > 0 && v11:0 + v9:0 > -1 && v9:0 > 0 15.72/4.95 Start term: f_99 15.72/4.95 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (9) IRS2T2 (EQUIVALENT) 15.72/4.95 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 15.72/4.95 15.72/4.95 (f_173_3,1) 15.72/4.95 (f_99_3,2) 15.72/4.95 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (10) 15.72/4.95 Obligation: 15.72/4.95 START: 2; 15.72/4.95 15.72/4.95 FROM: 1; 15.72/4.95 oldX0 := x0; 15.72/4.95 oldX1 := x1; 15.72/4.95 oldX2 := x2; 15.72/4.95 oldX3 := oldX0 - oldX2; 15.72/4.95 oldX4 := nondet(); 15.72/4.95 assume(oldX4 > 0 && oldX3 + oldX2 > -1 && oldX1 > 0 && oldX0 = oldX3 + oldX2); 15.72/4.95 x0 := oldX0 - oldX2; 15.72/4.95 x1 := oldX3 + oldX2; 15.72/4.95 x2 := oldX4; 15.72/4.95 TO: 1; 15.72/4.95 15.72/4.95 FROM: 2; 15.72/4.95 oldX0 := x0; 15.72/4.95 oldX1 := x1; 15.72/4.95 oldX2 := x2; 15.72/4.95 oldX3 := nondet(); 15.72/4.95 oldX4 := nondet(); 15.72/4.95 oldX5 := nondet(); 15.72/4.95 assume(oldX5 > 0 && oldX3 + oldX4 > -1 && oldX4 > 0); 15.72/4.95 x0 := oldX3; 15.72/4.95 x1 := oldX3 + oldX4; 15.72/4.95 x2 := oldX5; 15.72/4.95 TO: 1; 15.72/4.95 15.72/4.95 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (11) T2 (EQUIVALENT) 15.72/4.95 Used the following cutpoint-specific lexicographic rank functions: 15.72/4.95 * For cutpoint 5, used the following rank functions/bounds (in descending priority order): 15.72/4.95 - RF x0, bound 0 15.72/4.95 15.72/4.95 ---------------------------------------- 15.72/4.95 15.72/4.95 (12) 15.72/4.95 YES 15.80/5.03 EOF