23.62/7.05 YES 23.62/7.06 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 23.62/7.06 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 23.62/7.06 23.62/7.06 23.62/7.06 Termination of the given C Problem could be proven: 23.62/7.06 23.62/7.06 (0) C Problem 23.62/7.06 (1) CToLLVMProof [EQUIVALENT, 174 ms] 23.62/7.06 (2) LLVM problem 23.62/7.06 (3) LLVMToTerminationGraphProof [EQUIVALENT, 981 ms] 23.62/7.06 (4) LLVM Symbolic Execution Graph 23.62/7.06 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 23.62/7.06 (6) AND 23.62/7.06 (7) LLVM Symbolic Execution SCC 23.62/7.06 (8) SCC2IRS [SOUND, 48 ms] 23.62/7.06 (9) IntTRS 23.62/7.06 (10) IRS2T2 [EQUIVALENT, 0 ms] 23.62/7.06 (11) T2IntSys 23.62/7.06 (12) T2 [EQUIVALENT, 944 ms] 23.62/7.06 (13) YES 23.62/7.06 (14) LLVM Symbolic Execution SCC 23.62/7.06 (15) SCC2IRS [SOUND, 41 ms] 23.62/7.06 (16) IntTRS 23.62/7.06 (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] 23.62/7.06 (18) IntTRS 23.62/7.06 (19) PolynomialOrderProcessor [EQUIVALENT, 12 ms] 23.62/7.06 (20) YES 23.62/7.06 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (0) 23.62/7.06 Obligation: 23.62/7.06 c file /export/starexec/sandbox/benchmark/theBenchmark.c 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (1) CToLLVMProof (EQUIVALENT) 23.62/7.06 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (2) 23.62/7.06 Obligation: 23.62/7.06 LLVM Problem 23.62/7.06 23.62/7.06 Aliases: 23.62/7.06 23.62/7.06 Data layout: 23.62/7.06 23.62/7.06 "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" 23.62/7.06 23.62/7.06 Machine: 23.62/7.06 23.62/7.06 "x86_64-pc-linux-gnu" 23.62/7.06 23.62/7.06 Type definitions: 23.62/7.06 23.62/7.06 Global variables: 23.62/7.06 23.62/7.06 Function declarations and definitions: 23.62/7.06 23.62/7.06 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 23.62/7.06 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 23.62/7.06 0: 23.62/7.06 %1 = alloca i32, align 4 23.62/7.06 %x = alloca i32, align 4 23.62/7.06 %y = alloca i32, align 4 23.62/7.06 store 0, %1 23.62/7.06 br %2 23.62/7.06 2: 23.62/7.06 %3 = load %x 23.62/7.06 %4 = icmp sge %3 0 23.62/7.06 br %4, %5, %19 23.62/7.06 5: 23.62/7.06 %6 = load %y 23.62/7.06 %7 = sub %6 1 23.62/7.06 store %7, %y 23.62/7.06 %8 = load %y 23.62/7.06 %9 = icmp slt %8 0 23.62/7.06 br %9, %10, %14 23.62/7.06 10: 23.62/7.06 %11 = load %x 23.62/7.06 %12 = sub %11 1 23.62/7.06 store %12, %x 23.62/7.06 %13 = call i32 @__VERIFIER_nondet_int() 23.62/7.06 store %13, %y 23.62/7.06 br %14 23.62/7.06 14: 23.62/7.06 %15 = load %y 23.62/7.06 %16 = icmp slt %15 0 23.62/7.06 br %16, %17, %18 23.62/7.06 17: 23.62/7.06 br %19 23.62/7.06 18: 23.62/7.06 br %2 23.62/7.06 19: 23.62/7.06 %20 = load %1 23.62/7.06 ret %20 23.62/7.06 23.62/7.06 23.62/7.06 Analyze Termination of all function calls matching the pattern: 23.62/7.06 main() 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (3) LLVMToTerminationGraphProof (EQUIVALENT) 23.62/7.06 Constructed symbolic execution graph for LLVM program and proved memory safety. 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (4) 23.62/7.06 Obligation: 23.62/7.06 SE Graph 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (5) SymbolicExecutionGraphToSCCProof (SOUND) 23.62/7.06 Splitted symbolic execution graph to 2 SCCs. 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (6) 23.62/7.06 Complex Obligation (AND) 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (7) 23.62/7.06 Obligation: 23.62/7.06 SCC 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (8) SCC2IRS (SOUND) 23.62/7.06 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 23.62/7.06 Generated rules. Obtained 55 rulesP rules: 23.62/7.06 f_132(v1, v3, v5, v7, 1, v9, v11, v13, v15, 0, v2, v4, v6, 3, 4) -> f_135(v1, v3, v5, v13, 1, v9, v11, v7, v15, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_135(v1, v3, v5, v13, 1, v9, v11, v7, v15, 0, v2, v4, v6, 3, 4) -> f_138(v1, v3, v5, v13, 1, v9, v11, v7, v15, 0, v2, v4, v6, 3, 4) :|: 0 <= v13 && 1 <= v7 23.62/7.06 f_138(v1, v3, v5, v13, 1, v9, v11, v7, v15, 0, v2, v4, v6, 3, 4) -> f_142(v1, v3, v5, v13, 1, v9, v11, v7, v15, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_142(v1, v3, v5, v13, 1, v9, v11, v7, v15, 0, v2, v4, v6, 3, 4) -> f_146(v1, v3, v5, v13, 1, v9, v11, v7, v15, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_146(v1, v3, v5, v13, 1, v9, v11, v7, v15, 0, v2, v4, v6, 3, 4) -> f_150(v1, v3, v5, v13, 1, v15, v11, v7, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_150(v1, v3, v5, v13, 1, v15, v11, v7, 0, v2, v4, v6, 3, 4) -> f_154(v1, v3, v5, v13, 1, v15, v38, v11, v7, 0, v2, v4, v6, 3, 4) :|: 1 + v38 = v15 && 0 <= 1 + v38 23.62/7.06 f_154(v1, v3, v5, v13, 1, v15, v38, v11, v7, 0, v2, v4, v6, 3, 4) -> f_157(v1, v3, v5, v13, 1, v15, v38, v11, v7, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_157(v1, v3, v5, v13, 1, v15, v38, v11, v7, 0, v2, v4, v6, 3, 4) -> f_160(v1, v3, v5, v13, 1, v15, v38, v7, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_160(v1, v3, v5, v13, 1, v15, v38, v7, 0, v2, v4, v6, 3, 4) -> f_162(v1, v3, v5, v13, 1, 0, -1, v7, v2, v4, v6, 3, 4) :|: v38 < 0 && v15 = 0 && 1 + v38 = 0 && 0 = 0 23.62/7.06 f_160(v1, v3, v5, v13, 1, v15, v38, v7, 0, v2, v4, v6, 3, 4) -> f_163(v1, v3, v5, v13, 1, v15, v38, v7, 0, v2, v4, v6, 3, 4) :|: 0 <= v38 && 1 <= v15 23.62/7.06 f_162(v1, v3, v5, v13, 1, 0, -1, v7, v2, v4, v6, 3, 4) -> f_165(v1, v3, v5, v13, 1, 0, -1, v7, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_165(v1, v3, v5, v13, 1, 0, -1, v7, v2, v4, v6, 3, 4) -> f_168(v1, v3, v5, v13, 1, 0, -1, v7, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_168(v1, v3, v5, v13, 1, 0, -1, v7, v2, v4, v6, 3, 4) -> f_199(v1, v3, v5, v13, 1, 0, -1, v7, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_199(v234, v235, v236, v237, 1, 0, -1, v241, v242, v243, v244, v245, 3, 4) -> f_202(v234, v235, v236, v237, 1, 0, -1, v242, v243, v244, v245, 3, 4) :|: 0 = 0 23.62/7.06 f_202(v234, v235, v236, v237, 1, 0, -1, v242, v243, v244, v245, 3, 4) -> f_204(v234, v235, v236, v237, 1, 0, -1, v281, v242, v243, v244, v245, 3, 4) :|: 1 + v281 = v237 && 0 <= 1 + v281 23.62/7.06 f_204(v234, v235, v236, v237, 1, 0, -1, v281, v242, v243, v244, v245, 3, 4) -> f_206(v234, v235, v236, v237, 1, 0, -1, v281, v242, v243, v244, v245, 3, 4) :|: TRUE 23.62/7.06 f_206(v234, v235, v236, v237, 1, 0, -1, v281, v242, v243, v244, v245, 3, 4) -> f_208(v234, v235, v236, v237, 1, 0, -1, v281, v296, v243, v244, v245, 3, 4) :|: TRUE 23.62/7.06 f_208(v234, v235, v236, v237, 1, 0, -1, v281, v296, v243, v244, v245, 3, 4) -> f_210(v234, v235, v236, v237, 1, 0, -1, v281, v296, v243, v244, v245, 3, 4) :|: TRUE 23.62/7.06 f_210(v234, v235, v236, v237, 1, 0, -1, v281, v296, v243, v244, v245, 3, 4) -> f_212(v234, v235, v236, v237, 1, 0, -1, v281, v296, v243, v244, v245, 3, 4) :|: TRUE 23.62/7.06 f_212(v234, v235, v236, v237, 1, 0, -1, v281, v296, v243, v244, v245, 3, 4) -> f_164(v234, v235, v236, v237, 1, 0, -1, v281, v296, v243, v244, v245, 3, 4) :|: TRUE 23.62/7.06 f_164(v1, v3, v5, v7, 1, 0, -1, v37, v46, v2, v4, v6, 3, 4) -> f_167(v1, v3, v5, v7, 1, 0, -1, v46, v37, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_167(v1, v3, v5, v7, 1, 0, -1, v46, v37, v2, v4, v6, 3, 4) -> f_171(v1, v3, v5, v7, 1, 0, -1, v46, v37, v2, v4, v6, 3, 4) :|: 0 <= v46 23.62/7.06 f_171(v1, v3, v5, v7, 1, 0, -1, v46, v37, v2, v4, v6, 3, 4) -> f_175(v1, v3, v5, v7, 1, 0, -1, v46, v37, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_175(v1, v3, v5, v7, 1, 0, -1, v46, v37, v2, v4, v6, 3, 4) -> f_179(v1, v3, v5, v7, 1, 0, -1, v46, v37, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_179(v1, v3, v5, v7, 1, 0, -1, v46, v37, v2, v4, v6, 3, 4) -> f_129(v1, v3, v5, v7, 1, 0, -1, v37, v46, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_129(v1, v3, v5, v7, 1, v9, v11, v13, v15, 0, v2, v4, v6, 3, 4) -> f_132(v1, v3, v5, v7, 1, v9, v11, v13, v15, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_163(v1, v3, v5, v13, 1, v15, v38, v7, 0, v2, v4, v6, 3, 4) -> f_166(v1, v3, v5, v13, 1, v15, v38, 0, v7, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_166(v1, v3, v5, v13, 1, v15, v38, 0, v7, v2, v4, v6, 3, 4) -> f_169(v1, v3, v5, v13, 1, v15, v38, 0, v7, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_169(v1, v3, v5, v13, 1, v15, v38, 0, v7, v2, v4, v6, 3, 4) -> f_201(v1, v3, v5, v13, 1, v15, v38, 0, v7, v15, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_201(v268, v269, v270, v271, 1, v273, v274, 0, v276, v277, v278, v279, v280, 3, 4) -> f_225(v268, v269, v270, v271, 1, v273, v274, 0, v276, v277, v278, v279, v280, 3, 4) :|: TRUE 23.62/7.06 f_225(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_226(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) :|: 0 = 0 23.62/7.06 f_226(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_227(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) :|: 0 = 0 23.62/7.06 f_227(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_228(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_228(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_229(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_229(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_230(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) :|: 0 = 0 23.62/7.06 f_230(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_231(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) :|: 0 = 0 23.62/7.06 f_231(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_232(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_232(v394, v395, v396, v397, 1, v399, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_233(v394, v395, v396, v397, 1, v400, 0, v402, v403, v404, v405, v406, 3, 4) :|: 0 = 0 23.62/7.06 f_233(v394, v395, v396, v397, 1, v400, 0, v402, v403, v404, v405, v406, 3, 4) -> f_234(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 4) :|: 1 + v446 = v400 && 0 <= 1 + v446 23.62/7.06 f_234(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 4) -> f_235(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_235(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 4) -> f_236(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 4) :|: 0 = 0 23.62/7.06 f_236(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 4) -> f_237(v394, v395, v396, v397, 1, 0, -1, v402, v403, v404, v405, v406, 3, 4) :|: v446 < 0 && v400 = 0 && 1 + v446 = 0 && 0 = 0 23.62/7.06 f_236(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 4) -> f_238(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 2, 4) :|: 0 <= v446 && 1 <= v400 && 2 <= v403 23.62/7.06 f_237(v394, v395, v396, v397, 1, 0, -1, v402, v403, v404, v405, v406, 3, 4) -> f_239(v394, v395, v396, v397, 1, 0, -1, v402, v403, v404, v405, v406, 3, 4) :|: 0 = 0 23.62/7.06 f_239(v394, v395, v396, v397, 1, 0, -1, v402, v403, v404, v405, v406, 3, 4) -> f_241(v394, v395, v396, v397, 1, 0, -1, v402, v403, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_241(v394, v395, v396, v397, 1, 0, -1, v402, v403, v404, v405, v406, 3, 4) -> f_243(v394, v395, v396, v397, 1, 0, -1, v403, v404, v405, v406, 3, 4) :|: 0 = 0 23.62/7.06 f_243(v394, v395, v396, v397, 1, 0, -1, v403, v404, v405, v406, 3, 4) -> f_244(v394, v395, v396, v397, 1, 0, -1, v498, v403, v404, v405, v406, 3, 4) :|: 1 + v498 = v397 && 0 <= 1 + v498 23.62/7.06 f_244(v394, v395, v396, v397, 1, 0, -1, v498, v403, v404, v405, v406, 3, 4) -> f_245(v394, v395, v396, v397, 1, 0, -1, v498, v403, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_245(v394, v395, v396, v397, 1, 0, -1, v498, v403, v404, v405, v406, 3, 4) -> f_246(v394, v395, v396, v397, 1, 0, -1, v498, v500, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_246(v394, v395, v396, v397, 1, 0, -1, v498, v500, v404, v405, v406, 3, 4) -> f_247(v394, v395, v396, v397, 1, 0, -1, v498, v500, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_247(v394, v395, v396, v397, 1, 0, -1, v498, v500, v404, v405, v406, 3, 4) -> f_248(v394, v395, v396, v397, 1, 0, -1, v498, v500, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_248(v394, v395, v396, v397, 1, 0, -1, v498, v500, v404, v405, v406, 3, 4) -> f_164(v394, v395, v396, v397, 1, 0, -1, v498, v500, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 f_238(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 2, 4) -> f_240(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 2, 4) :|: 0 = 0 23.62/7.06 f_240(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 2, 4) -> f_242(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 2, 4) :|: TRUE 23.62/7.06 f_242(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 2, 4) -> f_225(v394, v395, v396, v397, 1, v400, v446, 0, v402, v403, v404, v405, v406, 3, 4) :|: TRUE 23.62/7.06 Combined rules. Obtained 4 rulesP rules: 23.62/7.06 f_236(v394:0, v395:0, v396:0, v397:0, 1, v400:0, 1 + v446:1, 0, v402:0, v403:0, v404:0, v405:0, v406:0, 3, 4) -> f_236(v394:0, v395:0, v396:0, v397:0, 1, 1 + v446:1, v446:1, 0, v402:0, v403:0, v404:0, v405:0, v406:0, 3, 4) :|: v446:1 > -2 && v400:0 > 0 && v403:0 > 1 23.62/7.06 f_132(v1:0, v3:0, v5:0, v7:0, 1, v9:0, v11:0, v13:0, 1 + (1 + v446:0), 0, v2:0, v4:0, v6:0, 3, 4) -> f_236(v1:0, v3:0, v5:0, v13:0, 1, 1 + v446:0, v446:0, 0, v7:0, 1 + (1 + v446:0), v2:0, v4:0, v6:0, 3, 4) :|: v446:0 > -2 && v7:0 > 0 && v13:0 > -1 23.62/7.06 f_132(v1:0, v3:0, v5:0, v7:0, 1, v9:0, v11:0, 1 + v281:0, 0, 0, v2:0, v4:0, v6:0, 3, 4) -> f_132(v1:0, v3:0, v5:0, 1 + v281:0, 1, 0, -1, v281:0, v296:0, 0, v2:0, v4:0, v6:0, 3, 4) :|: v7:0 > 0 && v281:0 > -2 && v296:0 > -1 23.62/7.06 f_236(v394:0, v395:0, v396:0, 1 + v498:0, 1, 0, -1, 0, v402:0, v403:0, v404:0, v405:0, v406:0, 3, 4) -> f_132(v394:0, v395:0, v396:0, 1 + v498:0, 1, 0, -1, v498:0, v500:0, 0, v404:0, v405:0, v406:0, 3, 4) :|: v500:0 > -1 && v498:0 > -2 23.62/7.06 Filtered unneeded arguments: 23.62/7.06 f_236(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_236(x4, x6, x7, x10) 23.62/7.06 f_132(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_132(x4, x8, x9) 23.62/7.06 Removed division, modulo operations, cleaned up constraints. Obtained 4 rules.P rules: 23.62/7.06 f_236(v397:0, v400:0, sum~cons_1~v446:1, v403:0) -> f_236(v397:0, 1 + v446:1, v446:1, v403:0) :|: v400:0 > 0 && v403:0 > 1 && v446:1 > -2 && sum~cons_1~v446:1 = 1 + v446:1 23.62/7.06 f_132(v7:0, v13:0, sum~cons_1~sum~cons_1~v446:0) -> f_236(v13:0, 1 + v446:0, v446:0, 1 + (1 + v446:0)) :|: v7:0 > 0 && v13:0 > -1 && v446:0 > -2 && sum~cons_1~sum~cons_1~v446:0 = 1 + (1 + v446:0) 23.62/7.06 f_132(v7:0, sum~cons_1~v281:0, cons_0) -> f_132(1 + v281:0, v281:0, v296:0) :|: v281:0 > -2 && v296:0 > -1 && v7:0 > 0 && sum~cons_1~v281:0 = 1 + v281:0 && cons_0 = 0 23.62/7.06 f_236(sum~cons_1~v498:0, cons_0, cons_-1, v403:0) -> f_132(1 + v498:0, v498:0, v500:0) :|: v500:0 > -1 && v498:0 > -2 && sum~cons_1~v498:0 = 1 + v498:0 && cons_0 = 0 && cons_-1 = -1 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (9) 23.62/7.06 Obligation: 23.62/7.06 Rules: 23.62/7.06 f_236(v397:0, v400:0, sum~cons_1~v446:1, v403:0) -> f_236(v397:0, 1 + v446:1, v446:1, v403:0) :|: v400:0 > 0 && v403:0 > 1 && v446:1 > -2 && sum~cons_1~v446:1 = 1 + v446:1 23.62/7.06 f_132(v7:0, v13:0, sum~cons_1~sum~cons_1~v446:0) -> f_236(v13:0, 1 + v446:0, v446:0, 1 + (1 + v446:0)) :|: v7:0 > 0 && v13:0 > -1 && v446:0 > -2 && sum~cons_1~sum~cons_1~v446:0 = 1 + (1 + v446:0) 23.62/7.06 f_132(x, x1, x2) -> f_132(1 + x3, x3, x4) :|: x3 > -2 && x4 > -1 && x > 0 && x1 = 1 + x3 && x2 = 0 23.62/7.06 f_236(x5, x6, x7, x8) -> f_132(1 + x9, x9, x10) :|: x10 > -1 && x9 > -2 && x5 = 1 + x9 && x6 = 0 && x7 = -1 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (10) IRS2T2 (EQUIVALENT) 23.62/7.06 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 23.62/7.06 23.62/7.06 (f_236_4,1) 23.62/7.06 (f_132_4,2) 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (11) 23.62/7.06 Obligation: 23.62/7.06 START: 0; 23.62/7.06 23.62/7.06 FROM: 0; 23.62/7.06 TO: 1; 23.62/7.06 23.62/7.06 FROM: 0; 23.62/7.06 TO: 2; 23.62/7.06 23.62/7.06 FROM: 1; 23.62/7.06 oldX0 := x0; 23.62/7.06 oldX1 := x1; 23.62/7.06 oldX2 := x2; 23.62/7.06 oldX3 := x3; 23.62/7.06 oldX4 := oldX2 - 1; 23.62/7.06 assume(oldX1 > 0 && oldX3 > 1 && oldX4 > -2 && oldX2 = 1 + oldX4); 23.62/7.06 x0 := oldX0; 23.62/7.06 x1 := 1 + oldX4; 23.62/7.06 x2 := oldX2 - 1; 23.62/7.06 x3 := oldX3; 23.62/7.06 TO: 1; 23.62/7.06 23.62/7.06 FROM: 2; 23.62/7.06 oldX0 := x0; 23.62/7.06 oldX1 := x1; 23.62/7.06 oldX2 := x2; 23.62/7.06 oldX3 := x3; 23.62/7.06 oldX4 := oldX2 - 2; 23.62/7.06 assume(oldX0 > 0 && oldX1 > -1 && oldX4 > -2 && oldX2 = 1 + (1 + oldX4)); 23.62/7.06 x0 := oldX1; 23.62/7.06 x1 := 1 + oldX4; 23.62/7.06 x2 := oldX2 - 2; 23.62/7.06 x3 := 1 + (1 + oldX4); 23.62/7.06 TO: 1; 23.62/7.06 23.62/7.06 FROM: 2; 23.62/7.06 oldX0 := x0; 23.62/7.06 oldX1 := x1; 23.62/7.06 oldX2 := x2; 23.62/7.06 oldX3 := x3; 23.62/7.06 oldX4 := oldX1 - 1; 23.62/7.06 oldX5 := nondet(); 23.62/7.06 oldX6 := nondet(); 23.62/7.06 assume(oldX4 > -2 && oldX5 > -1 && oldX0 > 0 && oldX1 = 1 + oldX4 && oldX2 = 0); 23.62/7.06 x0 := 1 + oldX4; 23.62/7.06 x1 := oldX1 - 1; 23.62/7.06 x2 := oldX5; 23.62/7.06 x3 := oldX6; 23.62/7.06 TO: 2; 23.62/7.06 23.62/7.06 FROM: 1; 23.62/7.06 oldX0 := x0; 23.62/7.06 oldX1 := x1; 23.62/7.06 oldX2 := x2; 23.62/7.06 oldX3 := x3; 23.62/7.06 oldX4 := oldX0 - 1; 23.62/7.06 oldX5 := nondet(); 23.62/7.06 oldX6 := nondet(); 23.62/7.06 assume(oldX5 > -1 && oldX4 > -2 && oldX0 = 1 + oldX4 && oldX1 = 0 && oldX2 = -1); 23.62/7.06 x0 := 1 + oldX4; 23.62/7.06 x1 := oldX0 - 1; 23.62/7.06 x2 := oldX5; 23.62/7.06 x3 := oldX6; 23.62/7.06 TO: 2; 23.62/7.06 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (12) T2 (EQUIVALENT) 23.62/7.06 Initially, performed program simplifications using lexicographic rank functions: 23.62/7.06 * Removed transitions 2, 5, 6, 14, 17, 18 using the following rank functions: 23.62/7.06 - Rank function 1: 23.62/7.06 RF for loc. 6: -1+3*x0 23.62/7.06 RF for loc. 7: 1+3*x1 23.62/7.06 RF for loc. 8: -1+3*x0 23.62/7.06 RF for loc. 12: 3*x1 23.62/7.06 Bound for (chained) transitions 17: 0 23.62/7.06 Bound for (chained) transitions 18: 0 23.62/7.06 - Rank function 2: 23.62/7.06 RF for loc. 6: 5+2*x2 23.62/7.06 RF for loc. 7: 1 23.62/7.06 RF for loc. 8: 4+2*x2 23.62/7.06 RF for loc. 12: 0 23.62/7.06 Bound for (chained) transitions 5: 4 23.62/7.06 Bound for (chained) transitions 6: 2 23.62/7.06 Bound for (chained) transitions 14: 1 23.62/7.06 - Rank function 3: 23.62/7.06 RF for loc. 6: 1 23.62/7.06 RF for loc. 8: 0 23.62/7.06 Bound for (chained) transitions 2: 1 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (13) 23.62/7.06 YES 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (14) 23.62/7.06 Obligation: 23.62/7.06 SCC 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (15) SCC2IRS (SOUND) 23.62/7.06 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 23.62/7.06 Generated rules. Obtained 15 rulesP rules: 23.62/7.06 f_117(v1, v3, v5, v7, 1, v9, v11, 0, v2, v4, v6, 3, 4) -> f_119(v1, v3, v5, v7, 1, v9, v11, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_119(v1, v3, v5, v7, 1, v9, v11, 0, v2, v4, v6, 3, 4) -> f_121(v1, v3, v5, v7, 1, v9, v11, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_121(v1, v3, v5, v7, 1, v9, v11, 0, v2, v4, v6, 3, 4) -> f_124(v1, v3, v5, v7, 1, v11, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_124(v1, v3, v5, v7, 1, v11, 0, v2, v4, v6, 3, 4) -> f_127(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: 1 + v17 = v11 && 0 <= 1 + v17 23.62/7.06 f_127(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_130(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_130(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_133(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_133(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_137(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: 0 <= v17 && 1 <= v11 23.62/7.06 f_137(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_141(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_141(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_145(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_145(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_149(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_149(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_153(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 f_153(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_156(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_156(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_159(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_159(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) -> f_115(v1, v3, v5, v7, 1, v11, v17, 0, v2, v4, v6, 3, 4) :|: TRUE 23.62/7.06 f_115(v1, v3, v5, v7, 1, v9, v11, 0, v2, v4, v6, 3, 4) -> f_117(v1, v3, v5, v7, 1, v9, v11, 0, v2, v4, v6, 3, 4) :|: 0 = 0 23.62/7.06 Combined rules. Obtained 1 rulesP rules: 23.62/7.06 f_117(v1:0, v3:0, v5:0, v7:0, 1, v9:0, 1 + v17:0, 0, v2:0, v4:0, v6:0, 3, 4) -> f_117(v1:0, v3:0, v5:0, v7:0, 1, 1 + v17:0, v17:0, 0, v2:0, v4:0, v6:0, 3, 4) :|: v17:0 > -1 23.62/7.06 Filtered unneeded arguments: 23.62/7.06 f_117(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f_117(x7) 23.62/7.06 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 23.62/7.06 f_117(sum~cons_1~v17:0) -> f_117(v17:0) :|: v17:0 > -1 && sum~cons_1~v17:0 = 1 + v17:0 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (16) 23.62/7.06 Obligation: 23.62/7.06 Rules: 23.62/7.06 f_117(sum~cons_1~v17:0) -> f_117(v17:0) :|: v17:0 > -1 && sum~cons_1~v17:0 = 1 + v17:0 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (17) IntTRSCompressionProof (EQUIVALENT) 23.62/7.06 Compressed rules. 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (18) 23.62/7.06 Obligation: 23.62/7.06 Rules: 23.62/7.06 f_117(sum~cons_1~v17:0:0) -> f_117(v17:0:0) :|: v17:0:0 > -1 && sum~cons_1~v17:0:0 = 1 + v17:0:0 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (19) PolynomialOrderProcessor (EQUIVALENT) 23.62/7.06 Found the following polynomial interpretation: 23.62/7.06 [f_117(x)] = x 23.62/7.06 23.62/7.06 The following rules are decreasing: 23.62/7.06 f_117(sum~cons_1~v17:0:0) -> f_117(v17:0:0) :|: v17:0:0 > -1 && sum~cons_1~v17:0:0 = 1 + v17:0:0 23.62/7.06 The following rules are bounded: 23.62/7.06 f_117(sum~cons_1~v17:0:0) -> f_117(v17:0:0) :|: v17:0:0 > -1 && sum~cons_1~v17:0:0 = 1 + v17:0:0 23.62/7.06 23.62/7.06 ---------------------------------------- 23.62/7.06 23.62/7.06 (20) 23.62/7.06 YES 23.79/7.11 EOF