24.09/7.73 YES 24.09/7.74 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 24.09/7.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 24.09/7.74 24.09/7.74 24.09/7.74 Termination of the given C Problem could be proven: 24.09/7.74 24.09/7.74 (0) C Problem 24.09/7.74 (1) CToLLVMProof [EQUIVALENT, 173 ms] 24.09/7.74 (2) LLVM problem 24.09/7.74 (3) LLVMToTerminationGraphProof [EQUIVALENT, 2883 ms] 24.09/7.74 (4) LLVM Symbolic Execution Graph 24.09/7.74 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 24.09/7.74 (6) AND 24.09/7.74 (7) LLVM Symbolic Execution SCC 24.09/7.74 (8) SCC2IRS [SOUND, 52 ms] 24.09/7.74 (9) IntTRS 24.09/7.74 (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] 24.09/7.74 (11) IntTRS 24.09/7.74 (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 24.09/7.74 (13) YES 24.09/7.74 (14) LLVM Symbolic Execution SCC 24.09/7.74 (15) SCC2IRS [SOUND, 40 ms] 24.09/7.74 (16) IntTRS 24.09/7.74 (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] 24.09/7.74 (18) IntTRS 24.09/7.74 (19) RankingReductionPairProof [EQUIVALENT, 0 ms] 24.09/7.74 (20) YES 24.09/7.74 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (0) 24.09/7.74 Obligation: 24.09/7.74 c file /export/starexec/sandbox/benchmark/theBenchmark.c 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (1) CToLLVMProof (EQUIVALENT) 24.09/7.74 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (2) 24.09/7.74 Obligation: 24.09/7.74 LLVM Problem 24.09/7.74 24.09/7.74 Aliases: 24.09/7.74 24.09/7.74 Data layout: 24.09/7.74 24.09/7.74 "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" 24.09/7.74 24.09/7.74 Machine: 24.09/7.74 24.09/7.74 "x86_64-pc-linux-gnu" 24.09/7.74 24.09/7.74 Type definitions: 24.09/7.74 24.09/7.74 Global variables: 24.09/7.74 24.09/7.74 Function declarations and definitions: 24.09/7.74 24.09/7.74 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 24.09/7.74 *BasicFunctionTypename: "rec" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (a i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 24.09/7.74 0: 24.09/7.74 %1 = alloca i32, align 4 24.09/7.74 %2 = alloca i32, align 4 24.09/7.74 %res = alloca i32, align 4 24.09/7.74 %rescopy = alloca i32, align 4 24.09/7.74 store %a, %2 24.09/7.74 %3 = load %2 24.09/7.74 %4 = icmp eq %3 0 24.09/7.74 br %4, %5, %6 24.09/7.74 5: 24.09/7.74 store 0, %1 24.09/7.74 br %20 24.09/7.74 6: 24.09/7.74 %7 = load %2 24.09/7.74 %8 = sub %7 1 24.09/7.74 %9 = call i32 @rec(i32 %8) 24.09/7.74 store %9, %res 24.09/7.74 %10 = load %res 24.09/7.74 store %10, %rescopy 24.09/7.74 br %11 24.09/7.74 11: 24.09/7.74 %12 = load %rescopy 24.09/7.74 %13 = icmp sgt %12 0 24.09/7.74 br %13, %14, %17 24.09/7.74 14: 24.09/7.74 %15 = load %rescopy 24.09/7.74 %16 = add %15 -1 24.09/7.74 store %16, %rescopy 24.09/7.74 br %11 24.09/7.74 17: 24.09/7.74 %18 = load %res 24.09/7.74 %19 = add 1 %18 24.09/7.74 store %19, %1 24.09/7.74 br %20 24.09/7.74 20: 24.09/7.74 %21 = load %1 24.09/7.74 ret %21 24.09/7.74 24.09/7.74 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 24.09/7.74 0: 24.09/7.74 %1 = alloca i32, align 4 24.09/7.74 %i = alloca i32, align 4 24.09/7.74 %res = alloca i32, align 4 24.09/7.74 store 0, %1 24.09/7.74 %2 = call i32 (...)* @__VERIFIER_nondet_int() 24.09/7.74 store %2, %i 24.09/7.74 %3 = load %i 24.09/7.74 %4 = icmp sle %3 0 24.09/7.74 br %4, %5, %6 24.09/7.74 5: 24.09/7.74 store 0, %1 24.09/7.74 br %9 24.09/7.74 6: 24.09/7.74 %7 = load %i 24.09/7.74 %8 = call i32 @rec(i32 %7) 24.09/7.74 store %8, %res 24.09/7.74 br %9 24.09/7.74 9: 24.09/7.74 %10 = load %1 24.09/7.74 ret %10 24.09/7.74 24.09/7.74 24.09/7.74 Analyze Termination of all function calls matching the pattern: 24.09/7.74 main() 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (3) LLVMToTerminationGraphProof (EQUIVALENT) 24.09/7.74 Constructed symbolic execution graph for LLVM program and proved memory safety. 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (4) 24.09/7.74 Obligation: 24.09/7.74 SE Graph 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (5) SymbolicExecutionGraphToSCCProof (SOUND) 24.09/7.74 Splitted symbolic execution graph to 2 SCCs. 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (6) 24.09/7.74 Complex Obligation (AND) 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (7) 24.09/7.74 Obligation: 24.09/7.74 SCC 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (8) SCC2IRS (SOUND) 24.09/7.74 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 24.09/7.74 Generated rules. Obtained 9 rulesP rules: 24.09/7.74 f_398(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 4) -> f_399(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) :|: 0 < v617 && 2 <= v615 && 2 <= v614 && 2 <= v607 && 1 <= v613 24.09/7.74 f_399(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_401(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) :|: 0 = 0 24.09/7.74 f_401(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_403(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) :|: TRUE 24.09/7.74 f_403(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_405(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v618, v619, v620, v621, 3, 2, 4) :|: 0 = 0 24.09/7.74 f_405(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v618, v619, v620, v621, 3, 2, 4) -> f_407(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: 1 + v630 = v617 && 0 <= v630 24.09/7.74 f_407(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_409(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: TRUE 24.09/7.74 f_409(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_411(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: TRUE 24.09/7.74 f_411(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_397(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 4) :|: TRUE 24.09/7.74 f_397(v607, v608, v609, v610, v611, 0, v613, v614, v615, 1, v617, v618, v619, v620, v621, 3, 4) -> f_398(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 4) :|: 0 = 0 24.09/7.74 Combined rules. Obtained 1 rulesP rules: 24.09/7.74 f_398(v607:0, v608:0, v609:0, v610:0, v611:0, 0, v613:0, v614:0, 1 + v630:0, 1, v615:0, v618:0, v619:0, v620:0, v621:0, 3, 4) -> f_398(v607:0, v608:0, v609:0, v610:0, v611:0, 0, v613:0, v614:0, v630:0, 1, 1 + v630:0, v618:0, v619:0, v620:0, v621:0, 3, 4) :|: v615:0 > 1 && v630:0 > -1 && v614:0 > 1 && v607:0 > 1 && v613:0 > 0 24.09/7.74 Filtered unneeded arguments: 24.09/7.74 f_398(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_398(x1, x7, x8, x9, x11) 24.09/7.74 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 24.09/7.74 f_398(v607:0, v613:0, v614:0, sum~cons_1~v630:0, v615:0) -> f_398(v607:0, v613:0, v614:0, v630:0, 1 + v630:0) :|: v630:0 > -1 && v615:0 > 1 && v614:0 > 1 && v613:0 > 0 && v607:0 > 1 && sum~cons_1~v630:0 = 1 + v630:0 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (9) 24.09/7.74 Obligation: 24.09/7.74 Rules: 24.09/7.74 f_398(v607:0, v613:0, v614:0, sum~cons_1~v630:0, v615:0) -> f_398(v607:0, v613:0, v614:0, v630:0, 1 + v630:0) :|: v630:0 > -1 && v615:0 > 1 && v614:0 > 1 && v613:0 > 0 && v607:0 > 1 && sum~cons_1~v630:0 = 1 + v630:0 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (10) IntTRSCompressionProof (EQUIVALENT) 24.09/7.74 Compressed rules. 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (11) 24.09/7.74 Obligation: 24.09/7.74 Rules: 24.09/7.74 f_398(v607:0:0, v613:0:0, v614:0:0, sum~cons_1~v630:0:0, v615:0:0) -> f_398(v607:0:0, v613:0:0, v614:0:0, v630:0:0, 1 + v630:0:0) :|: v613:0:0 > 0 && v607:0:0 > 1 && v614:0:0 > 1 && v615:0:0 > 1 && v630:0:0 > -1 && sum~cons_1~v630:0:0 = 1 + v630:0:0 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (12) PolynomialOrderProcessor (EQUIVALENT) 24.09/7.74 Found the following polynomial interpretation: 24.09/7.74 [f_398(x, x1, x2, x3, x4)] = x3 24.09/7.74 24.09/7.74 The following rules are decreasing: 24.09/7.74 f_398(v607:0:0, v613:0:0, v614:0:0, sum~cons_1~v630:0:0, v615:0:0) -> f_398(v607:0:0, v613:0:0, v614:0:0, v630:0:0, 1 + v630:0:0) :|: v613:0:0 > 0 && v607:0:0 > 1 && v614:0:0 > 1 && v615:0:0 > 1 && v630:0:0 > -1 && sum~cons_1~v630:0:0 = 1 + v630:0:0 24.09/7.74 The following rules are bounded: 24.09/7.74 f_398(v607:0:0, v613:0:0, v614:0:0, sum~cons_1~v630:0:0, v615:0:0) -> f_398(v607:0:0, v613:0:0, v614:0:0, v630:0:0, 1 + v630:0:0) :|: v613:0:0 > 0 && v607:0:0 > 1 && v614:0:0 > 1 && v615:0:0 > 1 && v630:0:0 > -1 && sum~cons_1~v630:0:0 = 1 + v630:0:0 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (13) 24.09/7.74 YES 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (14) 24.09/7.74 Obligation: 24.09/7.74 SCC 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (15) SCC2IRS (SOUND) 24.09/7.74 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 24.09/7.74 Generated rules. Obtained 14 rulesP rules: 24.09/7.74 f_199(v52, v61, v53, v54, v55, v56, v57, v58, v62, 0, v60, 3, 1, 4) -> f_200(v52, v61, v63, v53, v54, v55, v56, v57, v58, v62, v64, 0, v60, 3, 1, 4) :|: 1 <= v63 && v64 = 3 + v63 && 4 <= v64 24.09/7.74 f_200(v52, v61, v63, v53, v54, v55, v56, v57, v58, v62, v64, 0, v60, 3, 1, 4) -> f_201(v52, v61, v63, v65, v53, v54, v55, v56, v57, v58, v62, v64, v66, 0, v60, 3, 1, 4) :|: 1 <= v65 && v66 = 3 + v65 && 4 <= v66 24.09/7.74 f_201(v52, v61, v63, v65, v53, v54, v55, v56, v57, v58, v62, v64, v66, 0, v60, 3, 1, 4) -> f_202(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: 1 <= v67 && v68 = 3 + v67 && 4 <= v68 24.09/7.74 f_202(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_203(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: TRUE 24.09/7.74 f_203(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_204(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: 0 = 0 24.09/7.74 f_204(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_206(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: v52 != 0 24.09/7.74 f_206(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_208(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: 0 = 0 24.09/7.74 f_208(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_210(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: TRUE 24.09/7.74 f_210(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_212(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: 0 = 0 24.09/7.74 f_212(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_214(v52, v61, v63, v65, v67, 0, v70, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: 1 + v70 = v52 && 0 <= v70 24.09/7.74 f_214(v52, v61, v63, v65, v67, 0, v70, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_216(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) :|: 0 = 0 24.09/7.74 f_216(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) -> f_218(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) :|: TRUE 24.09/7.74 f_218(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) -> f_198(v70, v53, v54, v55, v56, v57, v58, 0, v60, 3, 1, 4) :|: TRUE 24.09/7.74 f_198(v52, v53, v54, v55, v56, v57, v58, 0, v60, 3, 1, 4) -> f_199(v52, v61, v53, v54, v55, v56, v57, v58, v62, 0, v60, 3, 1, 4) :|: 1 <= v61 && v62 = 3 + v61 && 4 <= v62 24.09/7.74 Combined rules. Obtained 1 rulesP rules: 24.09/7.74 f_199(1 + v70:0, v61:0, v53:0, v54:0, v55:0, v56:0, v57:0, v58:0, v62:0, 0, v60:0, 3, 1, 4) -> f_199(v70:0, v61:1, v53:0, v54:0, v55:0, v56:0, v57:0, v58:0, 3 + v61:1, 0, v60:0, 3, 1, 4) :|: v65:0 > 0 && v63:0 > 0 && v67:0 > 0 && v70:0 > -1 && v61:1 > 0 24.09/7.74 Filtered unneeded arguments: 24.09/7.74 f_199(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f_199(x1) 24.09/7.74 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 24.09/7.74 f_199(sum~cons_1~v70:0) -> f_199(v70:0) :|: v70:0 > -1 && sum~cons_1~v70:0 = 1 + v70:0 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (16) 24.09/7.74 Obligation: 24.09/7.74 Rules: 24.09/7.74 f_199(sum~cons_1~v70:0) -> f_199(v70:0) :|: v70:0 > -1 && sum~cons_1~v70:0 = 1 + v70:0 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (17) IntTRSCompressionProof (EQUIVALENT) 24.09/7.74 Compressed rules. 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (18) 24.09/7.74 Obligation: 24.09/7.74 Rules: 24.09/7.74 f_199(sum~cons_1~v70:0:0) -> f_199(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (19) RankingReductionPairProof (EQUIVALENT) 24.09/7.74 Interpretation: 24.09/7.74 [ f_199 ] = f_199_1 24.09/7.74 24.09/7.74 The following rules are decreasing: 24.09/7.74 f_199(sum~cons_1~v70:0:0) -> f_199(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0 24.09/7.74 24.09/7.74 The following rules are bounded: 24.09/7.74 f_199(sum~cons_1~v70:0:0) -> f_199(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0 24.09/7.74 24.09/7.74 24.09/7.74 ---------------------------------------- 24.09/7.74 24.09/7.74 (20) 24.09/7.74 YES 24.09/7.78 EOF