10.71/4.00 YES 10.71/4.01 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 10.71/4.01 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.71/4.01 10.71/4.01 10.71/4.01 Termination of the given C Problem could be proven: 10.71/4.01 10.71/4.01 (0) C Problem 10.71/4.01 (1) CToLLVMProof [EQUIVALENT, 165 ms] 10.71/4.01 (2) LLVM problem 10.71/4.01 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1455 ms] 10.71/4.01 (4) LLVM Symbolic Execution Graph 10.71/4.01 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 10.71/4.01 (6) LLVM Symbolic Execution SCC 10.71/4.01 (7) SCC2IRS [SOUND, 72 ms] 10.71/4.01 (8) IntTRS 10.71/4.01 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 10.71/4.01 (10) IntTRS 10.71/4.01 (11) RankingReductionPairProof [EQUIVALENT, 0 ms] 10.71/4.01 (12) YES 10.71/4.01 10.71/4.01 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (0) 10.71/4.01 Obligation: 10.71/4.01 c file /export/starexec/sandbox/benchmark/theBenchmark.c 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (1) CToLLVMProof (EQUIVALENT) 10.71/4.01 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (2) 10.71/4.01 Obligation: 10.71/4.01 LLVM Problem 10.71/4.01 10.71/4.01 Aliases: 10.71/4.01 10.71/4.01 Data layout: 10.71/4.01 10.71/4.01 "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" 10.71/4.01 10.71/4.01 Machine: 10.71/4.01 10.71/4.01 "x86_64-pc-linux-gnu" 10.71/4.01 10.71/4.01 Type definitions: 10.71/4.01 10.71/4.01 Global variables: 10.71/4.01 10.71/4.01 Function declarations and definitions: 10.71/4.01 10.71/4.01 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 10.71/4.01 *BasicFunctionTypename: "rec1" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (i i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 10.71/4.01 0: 10.71/4.01 %1 = alloca i32, align 4 10.71/4.01 %2 = alloca i32, align 4 10.71/4.01 store %i, %2 10.71/4.01 %3 = load %2 10.71/4.01 %4 = icmp sle %3 0 10.71/4.01 br %4, %5, %6 10.71/4.01 5: 10.71/4.01 store 0, %1 10.71/4.01 br %11 10.71/4.01 6: 10.71/4.01 %7 = load %2 10.71/4.01 %8 = add %7 1 10.71/4.01 %9 = call i32 @rec1(i32 %8) 10.71/4.01 %10 = call i32 @rec2(i32 %9) 10.71/4.01 store %10, %1 10.71/4.01 br %11 10.71/4.01 11: 10.71/4.01 %12 = load %1 10.71/4.01 ret %12 10.71/4.01 10.71/4.01 *BasicFunctionTypename: "rec2" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (j i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 10.71/4.01 0: 10.71/4.01 %1 = alloca i32, align 4 10.71/4.01 %2 = alloca i32, align 4 10.71/4.01 store %j, %2 10.71/4.01 %3 = load %2 10.71/4.01 %4 = icmp sle %3 0 10.71/4.01 br %4, %5, %6 10.71/4.01 5: 10.71/4.01 store 0, %1 10.71/4.01 br %11 10.71/4.01 6: 10.71/4.01 %7 = load %2 10.71/4.01 %8 = sub %7 1 10.71/4.01 %9 = call i32 @rec2(i32 %8) 10.71/4.01 %10 = call i32 @rec1(i32 %9) 10.71/4.01 store %10, %1 10.71/4.01 br %11 10.71/4.01 11: 10.71/4.01 %12 = load %1 10.71/4.01 ret %12 10.71/4.01 10.71/4.01 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 10.71/4.01 0: 10.71/4.01 %1 = alloca i32, align 4 10.71/4.01 %x = alloca i32, align 4 10.71/4.01 store 0, %1 10.71/4.01 %2 = call i32 (...)* @__VERIFIER_nondet_int() 10.71/4.01 store %2, %x 10.71/4.01 %3 = load %x 10.71/4.01 %4 = call i32 @rec2(i32 %3) 10.71/4.01 %5 = load %1 10.71/4.01 ret %5 10.71/4.01 10.71/4.01 10.71/4.01 Analyze Termination of all function calls matching the pattern: 10.71/4.01 main() 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (3) LLVMToTerminationGraphProof (EQUIVALENT) 10.71/4.01 Constructed symbolic execution graph for LLVM program and proved memory safety. 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (4) 10.71/4.01 Obligation: 10.71/4.01 SE Graph 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (5) SymbolicExecutionGraphToSCCProof (SOUND) 10.71/4.01 Splitted symbolic execution graph to 1 SCC. 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (6) 10.71/4.01 Obligation: 10.71/4.01 SCC 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (7) SCC2IRS (SOUND) 10.71/4.01 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 10.71/4.01 Generated rules. Obtained 12 rulesP rules: 10.71/4.01 f_179(v45, v52, v46, v47, v48, v49, v53, 0, v51, 3, 1, 4) -> f_180(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 1 <= v54 && v55 = 3 + v54 && 4 <= v55 10.71/4.01 f_180(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_181(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: TRUE 10.71/4.01 f_181(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_182(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 0 = 0 10.71/4.01 f_182(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_184(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) :|: 0 < v45 && 1 <= v51 10.71/4.01 f_184(v45, v52, v54, v46, v47, v48, v49, v53, v55, 0, v51, 3, 1, 4) -> f_186(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: 0 = 0 10.71/4.01 f_186(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_188(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: TRUE 10.71/4.01 f_188(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_190(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: 0 = 0 10.71/4.01 f_190(v45, v52, v54, 0, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_192(v45, v52, v54, 0, v57, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) :|: 1 + v57 = v45 && 0 <= v57 10.71/4.01 f_192(v45, v52, v54, 0, v57, v46, v47, v48, v49, v53, v55, v51, 3, 1, 4) -> f_194(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 4) :|: 0 = 0 10.71/4.01 f_194(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 4) -> f_196(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 4) :|: TRUE 10.71/4.01 f_196(v57, v46, v47, v48, v49, v52, v53, v54, v55, 0, v51, v45, 3, 1, 4) -> f_177(v57, v46, v47, v48, v49, 0, v51, 3, 1, 4) :|: TRUE 10.71/4.01 f_177(v45, v46, v47, v48, v49, 0, v51, 3, 1, 4) -> f_179(v45, v52, v46, v47, v48, v49, v53, 0, v51, 3, 1, 4) :|: 1 <= v52 && v53 = 3 + v52 && 4 <= v53 10.71/4.01 Combined rules. Obtained 1 rulesP rules: 10.71/4.01 f_179(1 + v57:0, v52:0, v46:0, v47:0, v48:0, v49:0, v53:0, 0, v51:0, 3, 1, 4) -> f_179(v57:0, v52:1, v46:0, v47:0, v48:0, v49:0, 3 + v52:1, 0, v51:0, 3, 1, 4) :|: v54:0 > 0 && v51:0 > 0 && v57:0 > -1 && v52:1 > 0 10.71/4.01 Filtered unneeded arguments: 10.71/4.01 f_179(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f_179(x1, x9) 10.71/4.01 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 10.71/4.01 f_179(sum~cons_1~v57:0, v51:0) -> f_179(v57:0, v51:0) :|: v51:0 > 0 && v57:0 > -1 && sum~cons_1~v57:0 = 1 + v57:0 10.71/4.01 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (8) 10.71/4.01 Obligation: 10.71/4.01 Rules: 10.71/4.01 f_179(sum~cons_1~v57:0, v51:0) -> f_179(v57:0, v51:0) :|: v51:0 > 0 && v57:0 > -1 && sum~cons_1~v57:0 = 1 + v57:0 10.71/4.01 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (9) IntTRSCompressionProof (EQUIVALENT) 10.71/4.01 Compressed rules. 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (10) 10.71/4.01 Obligation: 10.71/4.01 Rules: 10.71/4.01 f_179(sum~cons_1~v57:0:0, v51:0:0) -> f_179(v57:0:0, v51:0:0) :|: v51:0:0 > 0 && v57:0:0 > -1 && sum~cons_1~v57:0:0 = 1 + v57:0:0 10.71/4.01 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (11) RankingReductionPairProof (EQUIVALENT) 10.71/4.01 Interpretation: 10.71/4.01 [ f_179 ] = f_179_1 10.71/4.01 10.71/4.01 The following rules are decreasing: 10.71/4.01 f_179(sum~cons_1~v57:0:0, v51:0:0) -> f_179(v57:0:0, v51:0:0) :|: v51:0:0 > 0 && v57:0:0 > -1 && sum~cons_1~v57:0:0 = 1 + v57:0:0 10.71/4.01 10.71/4.01 The following rules are bounded: 10.71/4.01 f_179(sum~cons_1~v57:0:0, v51:0:0) -> f_179(v57:0:0, v51:0:0) :|: v51:0:0 > 0 && v57:0:0 > -1 && sum~cons_1~v57:0:0 = 1 + v57:0:0 10.71/4.01 10.71/4.01 10.71/4.01 ---------------------------------------- 10.71/4.01 10.71/4.01 (12) 10.71/4.01 YES 10.71/4.06 EOF