26.48/8.11 YES 26.48/8.12 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 26.48/8.12 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 26.48/8.12 26.48/8.12 26.48/8.12 Termination of the given C Problem could be proven: 26.48/8.12 26.48/8.12 (0) C Problem 26.48/8.12 (1) CToLLVMProof [EQUIVALENT, 175 ms] 26.48/8.12 (2) LLVM problem 26.48/8.12 (3) LLVMToTerminationGraphProof [EQUIVALENT, 2681 ms] 26.48/8.12 (4) LLVM Symbolic Execution Graph 26.48/8.12 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 26.48/8.12 (6) AND 26.48/8.12 (7) LLVM Symbolic Execution SCC 26.48/8.12 (8) SCC2IRS [SOUND, 86 ms] 26.48/8.12 (9) IntTRS 26.48/8.12 (10) IRS2T2 [EQUIVALENT, 0 ms] 26.48/8.12 (11) T2IntSys 26.48/8.12 (12) T2 [EQUIVALENT, 425 ms] 26.48/8.12 (13) YES 26.48/8.12 (14) LLVM Symbolic Execution SCC 26.48/8.12 (15) SCC2IRS [SOUND, 42 ms] 26.48/8.12 (16) IntTRS 26.48/8.12 (17) IntTRSCompressionProof [EQUIVALENT, 2 ms] 26.48/8.12 (18) IntTRS 26.48/8.12 (19) RankingReductionPairProof [EQUIVALENT, 0 ms] 26.48/8.12 (20) YES 26.48/8.12 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (0) 26.48/8.12 Obligation: 26.48/8.12 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (1) CToLLVMProof (EQUIVALENT) 26.48/8.12 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (2) 26.48/8.12 Obligation: 26.48/8.12 LLVM Problem 26.48/8.12 26.48/8.12 Aliases: 26.48/8.12 26.48/8.12 Data layout: 26.48/8.12 26.48/8.12 "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" 26.48/8.12 26.48/8.12 Machine: 26.48/8.12 26.48/8.12 "x86_64-pc-linux-gnu" 26.48/8.12 26.48/8.12 Type definitions: 26.48/8.12 26.48/8.12 Global variables: 26.48/8.12 26.48/8.12 Function declarations and definitions: 26.48/8.12 26.48/8.12 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 26.48/8.12 *BasicFunctionTypename: "rec" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (a i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 26.48/8.12 0: 26.48/8.12 %1 = alloca i32, align 4 26.48/8.12 %2 = alloca i32, align 4 26.48/8.12 %res = alloca i32, align 4 26.48/8.12 %rescopy = alloca i32, align 4 26.48/8.12 store %a, %2 26.48/8.12 %3 = load %2 26.48/8.12 %4 = icmp eq %3 0 26.48/8.12 br %4, %5, %6 26.48/8.12 5: 26.48/8.12 store 0, %1 26.48/8.12 br %20 26.48/8.12 6: 26.48/8.12 %7 = load %2 26.48/8.12 %8 = sub %7 1 26.48/8.12 %9 = call i32 @rec(i32 %8) 26.48/8.12 store %9, %res 26.48/8.12 %10 = load %res 26.48/8.12 store %10, %rescopy 26.48/8.12 br %11 26.48/8.12 11: 26.48/8.12 %12 = load %rescopy 26.48/8.12 %13 = icmp sgt %12 0 26.48/8.12 br %13, %14, %17 26.48/8.12 14: 26.48/8.12 %15 = load %rescopy 26.48/8.12 %16 = add %15 -1 26.48/8.12 store %16, %rescopy 26.48/8.12 br %11 26.48/8.12 17: 26.48/8.12 %18 = load %res 26.48/8.12 %19 = add 1 %18 26.48/8.12 store %19, %1 26.48/8.12 br %20 26.48/8.12 20: 26.48/8.12 %21 = load %1 26.48/8.12 ret %21 26.48/8.12 26.48/8.12 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 26.48/8.12 0: 26.48/8.12 %1 = alloca i32, align 4 26.48/8.12 %i = alloca i32, align 4 26.48/8.12 %res = alloca i32, align 4 26.48/8.12 store 0, %1 26.48/8.12 %2 = call i32 (...)* @__VERIFIER_nondet_int() 26.48/8.12 store %2, %i 26.48/8.12 %3 = load %i 26.48/8.12 %4 = icmp sle %3 0 26.48/8.12 br %4, %5, %6 26.48/8.12 5: 26.48/8.12 store 0, %1 26.48/8.12 br %13 26.48/8.12 6: 26.48/8.12 %7 = load %i 26.48/8.12 %8 = call i32 @rec(i32 %7) 26.48/8.12 store %8, %res 26.48/8.12 br %9 26.48/8.12 9: 26.48/8.12 %10 = load %res 26.48/8.12 %11 = icmp slt %10 1 26.48/8.12 br %11, %12, %13 26.48/8.12 12: 26.48/8.12 br %9 26.48/8.12 13: 26.48/8.12 %14 = load %1 26.48/8.12 ret %14 26.48/8.12 26.48/8.12 26.48/8.12 Analyze Termination of all function calls matching the pattern: 26.48/8.12 main() 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (3) LLVMToTerminationGraphProof (EQUIVALENT) 26.48/8.12 Constructed symbolic execution graph for LLVM program and proved memory safety. 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (4) 26.48/8.12 Obligation: 26.48/8.12 SE Graph 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (5) SymbolicExecutionGraphToSCCProof (SOUND) 26.48/8.12 Splitted symbolic execution graph to 2 SCCs. 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (6) 26.48/8.12 Complex Obligation (AND) 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (7) 26.48/8.12 Obligation: 26.48/8.12 SCC 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (8) SCC2IRS (SOUND) 26.48/8.12 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 26.48/8.12 Generated rules. Obtained 9 rulesP rules: 26.48/8.12 f_425(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 4) -> f_426(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 26.48/8.12 f_426(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_428(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) :|: 0 = 0 26.48/8.12 f_428(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_430(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) :|: TRUE 26.48/8.12 f_430(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 2, 4) -> f_432(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v618, v619, v620, v621, 3, 2, 4) :|: 0 = 0 26.48/8.12 f_432(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v618, v619, v620, v621, 3, 2, 4) -> f_434(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: 1 + v630 = v617 && 0 <= v630 26.48/8.12 f_434(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_436(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: TRUE 26.48/8.12 f_436(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_438(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) :|: TRUE 26.48/8.12 f_438(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 2, 4) -> f_424(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v630, v618, v619, v620, v621, 3, 4) :|: TRUE 26.48/8.12 f_424(v607, v608, v609, v610, v611, 0, v613, v614, v615, 1, v617, v618, v619, v620, v621, 3, 4) -> f_425(v607, v608, v609, v610, v611, 0, v613, v614, v617, 1, v615, v618, v619, v620, v621, 3, 4) :|: 0 = 0 26.48/8.12 Combined rules. Obtained 1 rulesP rules: 26.48/8.12 f_425(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_425(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 26.48/8.12 Filtered unneeded arguments: 26.48/8.12 f_425(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_425(x1, x7, x8, x9, x11) 26.48/8.12 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 26.48/8.12 f_425(v607:0, v613:0, v614:0, sum~cons_1~v630:0, v615:0) -> f_425(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 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (9) 26.48/8.12 Obligation: 26.48/8.12 Rules: 26.48/8.12 f_425(v607:0, v613:0, v614:0, sum~cons_1~v630:0, v615:0) -> f_425(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 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (10) IRS2T2 (EQUIVALENT) 26.48/8.12 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 26.48/8.12 26.48/8.12 (f_425_5,1) 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (11) 26.48/8.12 Obligation: 26.48/8.12 START: 0; 26.48/8.12 26.48/8.12 FROM: 0; 26.48/8.12 TO: 1; 26.48/8.12 26.48/8.12 FROM: 1; 26.48/8.12 oldX0 := x0; 26.48/8.12 oldX1 := x1; 26.48/8.12 oldX2 := x2; 26.48/8.12 oldX3 := x3; 26.48/8.12 oldX4 := x4; 26.48/8.12 oldX5 := oldX3 - 1; 26.48/8.12 assume(oldX5 > -1 && oldX4 > 1 && oldX2 > 1 && oldX1 > 0 && oldX0 > 1 && oldX3 = 1 + oldX5); 26.48/8.12 x0 := oldX0; 26.48/8.12 x1 := oldX1; 26.48/8.12 x2 := oldX2; 26.48/8.12 x3 := oldX3 - 1; 26.48/8.12 x4 := 1 + oldX5; 26.48/8.12 TO: 1; 26.48/8.12 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (12) T2 (EQUIVALENT) 26.48/8.12 Initially, performed program simplifications using lexicographic rank functions: 26.48/8.12 * Removed transitions 1, 3, 4 using the following rank functions: 26.48/8.12 - Rank function 1: 26.48/8.12 RF for loc. 5: 1+2*x3 26.48/8.12 RF for loc. 6: 2*x3 26.48/8.12 Bound for (chained) transitions 3: 2 26.48/8.12 Bound for (chained) transitions 4: 2 26.48/8.12 - Rank function 2: 26.48/8.12 RF for loc. 5: 0 26.48/8.12 RF for loc. 6: -1 26.48/8.12 Bound for (chained) transitions 1: 0 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (13) 26.48/8.12 YES 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (14) 26.48/8.12 Obligation: 26.48/8.12 SCC 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (15) SCC2IRS (SOUND) 26.48/8.12 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 26.48/8.12 Generated rules. Obtained 14 rulesP rules: 26.48/8.12 f_211(v52, v61, v53, v54, v55, v56, v57, v58, v62, 0, v60, 3, 1, 4) -> f_212(v52, v61, v63, v53, v54, v55, v56, v57, v58, v62, v64, 0, v60, 3, 1, 4) :|: 1 <= v63 && v64 = 3 + v63 && 4 <= v64 26.48/8.12 f_212(v52, v61, v63, v53, v54, v55, v56, v57, v58, v62, v64, 0, v60, 3, 1, 4) -> f_213(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 26.48/8.12 f_213(v52, v61, v63, v65, v53, v54, v55, v56, v57, v58, v62, v64, v66, 0, v60, 3, 1, 4) -> f_214(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 26.48/8.12 f_214(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_215(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: TRUE 26.48/8.12 f_215(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_216(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: 0 = 0 26.48/8.12 f_216(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_218(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) :|: v52 != 0 26.48/8.12 f_218(v52, v61, v63, v65, v67, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, 0, v60, 3, 1, 4) -> f_220(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: 0 = 0 26.48/8.12 f_220(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_222(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: TRUE 26.48/8.12 f_222(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_224(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) :|: 0 = 0 26.48/8.12 f_224(v52, v61, v63, v65, v67, 0, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_226(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 26.48/8.12 f_226(v52, v61, v63, v65, v67, 0, v70, v53, v54, v55, v56, v57, v58, v62, v64, v66, v68, v60, 3, 1, 4) -> f_228(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) :|: 0 = 0 26.48/8.12 f_228(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) -> f_230(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) :|: TRUE 26.48/8.12 f_230(v70, v53, v54, v55, v56, v57, v58, v61, v62, v63, v64, v65, v66, v67, v68, 0, v60, v52, 3, 1, 4) -> f_210(v70, v53, v54, v55, v56, v57, v58, 0, v60, 3, 1, 4) :|: TRUE 26.48/8.12 f_210(v52, v53, v54, v55, v56, v57, v58, 0, v60, 3, 1, 4) -> f_211(v52, v61, v53, v54, v55, v56, v57, v58, v62, 0, v60, 3, 1, 4) :|: 1 <= v61 && v62 = 3 + v61 && 4 <= v62 26.48/8.12 Combined rules. Obtained 1 rulesP rules: 26.48/8.12 f_211(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_211(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 26.48/8.12 Filtered unneeded arguments: 26.48/8.12 f_211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f_211(x1) 26.48/8.12 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 26.48/8.12 f_211(sum~cons_1~v70:0) -> f_211(v70:0) :|: v70:0 > -1 && sum~cons_1~v70:0 = 1 + v70:0 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (16) 26.48/8.12 Obligation: 26.48/8.12 Rules: 26.48/8.12 f_211(sum~cons_1~v70:0) -> f_211(v70:0) :|: v70:0 > -1 && sum~cons_1~v70:0 = 1 + v70:0 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (17) IntTRSCompressionProof (EQUIVALENT) 26.48/8.12 Compressed rules. 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (18) 26.48/8.12 Obligation: 26.48/8.12 Rules: 26.48/8.12 f_211(sum~cons_1~v70:0:0) -> f_211(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (19) RankingReductionPairProof (EQUIVALENT) 26.48/8.12 Interpretation: 26.48/8.12 [ f_211 ] = f_211_1 26.48/8.12 26.48/8.12 The following rules are decreasing: 26.48/8.12 f_211(sum~cons_1~v70:0:0) -> f_211(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0 26.48/8.12 26.48/8.12 The following rules are bounded: 26.48/8.12 f_211(sum~cons_1~v70:0:0) -> f_211(v70:0:0) :|: v70:0:0 > -1 && sum~cons_1~v70:0:0 = 1 + v70:0:0 26.48/8.12 26.48/8.12 26.48/8.12 ---------------------------------------- 26.48/8.12 26.48/8.12 (20) 26.48/8.12 YES 26.55/8.17 EOF