/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.c # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 162 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 1750 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) AND (7) LLVM Symbolic Execution SCC (8) SCC2IRS [SOUND, 40 ms] (9) IntTRS (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) YES (14) LLVM Symbolic Execution SCC (15) SCC2IRS [SOUND, 16 ms] (16) IntTRS (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IntTRS (19) RankingReductionPairProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: c file /export/starexec/sandbox/benchmark/theBenchmark.c ---------------------------------------- (1) CToLLVMProof (EQUIVALENT) Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. ---------------------------------------- (2) Obligation: LLVM Problem Aliases: Data layout: "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" Machine: "x86_64-pc-linux-gnu" Type definitions: Global variables: Function declarations and definitions: *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %x = alloca i32, align 4 %y = alloca i32, align 4 %oldx = alloca i32, align 4 store 0, %1 %2 = call i32 @__VERIFIER_nondet_int() store %2, %x %3 = call i32 @__VERIFIER_nondet_int() store %3, %y br %4 4: %5 = load %x %6 = icmp sge %5 0 br %6, %10, %7 7: %8 = load %y %9 = icmp sge %8 0 br %10 10: %11 = phi [1, %4], [%9, %7] br %11, %12, %18 12: %13 = load %x store %13, %oldx %14 = load %y %15 = sub %14 1 store %15, %x %16 = load %oldx %17 = sub %16 1 store %17, %y br %4 18: ret 0 Analyze Termination of all function calls matching the pattern: main() ---------------------------------------- (3) LLVMToTerminationGraphProof (EQUIVALENT) Constructed symbolic execution graph for LLVM program and proved memory safety. ---------------------------------------- (4) Obligation: SE Graph ---------------------------------------- (5) SymbolicExecutionGraphToSCCProof (SOUND) Splitted symbolic execution graph to 2 SCCs. ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: SCC ---------------------------------------- (8) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 33 rulesP rules: f_224(v405, v406, v407, v408, v409, v410, v411, 0, 1, v414, v415, v416, v417, v418, v419, v420, 3, 4) -> f_227(v405, v406, v407, v408, v409, v410, v411, 0, 1, v415, v414, v416, v417, v418, v419, v420, 3, 4) :|: 0 = 0 f_227(v405, v406, v407, v408, v409, v410, v411, 0, 1, v415, v414, v416, v417, v418, v419, v420, 3, 4) -> f_229(v405, v406, v407, v408, v409, v410, v411, 0, 1, v415, v414, v416, v417, v418, v419, v420, 3, 4) :|: TRUE f_229(v405, v406, v407, v408, v409, v410, v411, 0, 1, v415, v414, v416, v417, v418, v419, v420, 3, 4) -> f_230(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v414, v417, v418, v419, v420, 3, 4) :|: 0 = 0 f_230(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v414, v417, v418, v419, v420, 3, 4) -> f_231(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v414, v417, v418, v419, v420, 3, 4) :|: 1 + v556 = v416 && 0 <= 1 + v556 f_231(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v414, v417, v418, v419, v420, 3, 4) -> f_232(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v414, v417, v418, v419, v420, 3, 4) :|: TRUE f_232(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v414, v417, v418, v419, v420, 3, 4) -> f_233(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v417, v418, v419, v420, 3, 4) :|: 0 = 0 f_233(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v417, v418, v419, v420, 3, 4) -> f_234(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v558, v417, v418, v419, v420, 3, 4, 2) :|: 1 + v558 = v411 && 2 + v558 <= 0 f_234(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v558, v417, v418, v419, v420, 3, 4, 2) -> f_235(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v558, v417, v418, v419, v420, 3, 4, 2) :|: TRUE f_235(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v558, v417, v418, v419, v420, 3, 4, 2) -> f_236(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v558, v417, v418, v419, v420, 3, 4, 2) :|: TRUE f_236(v405, v406, v407, v408, v409, v410, v411, 0, 1, v416, v556, v558, v417, v418, v419, v420, 3, 4, 2) -> f_237(v405, v406, v407, v408, v409, v410, v411, 0, v416, 1, v556, v558, v417, v418, v419, v420, 3, 2, 4) :|: TRUE f_237(v560, v561, v562, v563, v564, v565, v566, 0, v568, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) -> f_238(v560, v561, v562, v563, v564, v565, v570, 0, v568, 1, v566, v571, v572, v573, v574, v575, 3, 2, 4) :|: 0 = 0 f_238(v560, v561, v562, v563, v564, v565, v570, 0, v568, 1, v566, v571, v572, v573, v574, v575, 3, 2, 4) -> f_239(v560, v561, v562, v563, v564, v565, v570, 0, v568, 1, v566, v571, v572, v573, v574, v575, 3, 2, 4) :|: 0 <= v570 && 1 <= v568 f_239(v560, v561, v562, v563, v564, v565, v570, 0, v568, 1, v566, v571, v572, v573, v574, v575, 3, 2, 4) -> f_241(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) :|: 0 = 0 f_241(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) -> f_243(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) :|: 0 = 0 f_243(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) -> f_245(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) :|: TRUE f_245(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) -> f_247(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) :|: 0 = 0 f_247(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) -> f_249(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) :|: TRUE f_249(v560, v561, v562, v563, v564, v565, v570, 1, v568, v566, v571, v572, v573, v574, v575, 0, 3, 2, 4) -> f_252(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v566, v572, v573, v574, v575, 0, 3, 2, 4) :|: 0 = 0 f_252(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v566, v572, v573, v574, v575, 0, 3, 2, 4) -> f_254(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v566, v572, v573, v574, v575, 0, 3, 2, 4) :|: 1 + v714 = v571 && 3 + v714 <= 0 f_254(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v566, v572, v573, v574, v575, 0, 3, 2, 4) -> f_255(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v566, v572, v573, v574, v575, 0, 3, 2, 4) :|: TRUE f_255(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v566, v572, v573, v574, v575, 0, 3, 2, 4) -> f_256(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v572, v573, v574, v575, 0, 3, 2, 4) :|: 0 = 0 f_256(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v572, v573, v574, v575, 0, 3, 2, 4) -> f_257(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v716, v572, v573, v574, v575, 0, 3, 2, 4) :|: 1 + v716 = v570 && 0 <= 1 + v716 f_257(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v716, v572, v573, v574, v575, 0, 3, 2, 4) -> f_258(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v716, v572, v573, v574, v575, 0, 3, 2, 4) :|: TRUE f_258(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v716, v572, v573, v574, v575, 0, 3, 2, 4) -> f_259(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v716, v572, v573, v574, v575, 0, 3, 2, 4) :|: TRUE f_259(v560, v561, v562, v563, v564, v565, v570, 1, v568, v571, v714, v716, v572, v573, v574, v575, 0, 3, 2, 4) -> f_260(v560, v561, v562, v563, v564, v565, v714, 1, v568, v570, v571, v716, v572, v573, v574, v575, 0, 3, 2, 4) :|: 0 = 0 f_260(v560, v561, v562, v563, v564, v565, v714, 1, v568, v570, v571, v716, v572, v573, v574, v575, 0, 3, 2, 4) -> f_261(v560, v561, v562, v563, v564, v565, v714, 0, v568, 1, v570, v571, v716, v572, v573, v574, v575, 3, 2, 4) :|: 0 = 0 f_261(v560, v561, v562, v563, v564, v565, v714, 0, v568, 1, v570, v571, v716, v572, v573, v574, v575, 3, 2, 4) -> f_262(v560, v561, v562, v563, v564, v565, v714, 0, v568, 1, v570, v571, v716, v572, v573, v574, v575, 3, 2, 4) :|: TRUE f_262(v560, v561, v562, v563, v564, v565, v714, 0, v568, 1, v570, v571, v716, v572, v573, v574, v575, 3, 2, 4) -> f_263(v560, v561, v562, v563, v564, v565, v714, 0, v716, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) :|: 0 = 0 f_263(v560, v561, v562, v563, v564, v565, v714, 0, v716, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) -> f_264(v560, v561, v562, v563, v564, v565, v714, 0, v716, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) :|: 0 <= v716 && 1 <= v570 f_264(v560, v561, v562, v563, v564, v565, v714, 0, v716, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) -> f_266(v560, v561, v562, v563, v564, v565, v714, 0, v716, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) :|: 0 = 0 f_266(v560, v561, v562, v563, v564, v565, v714, 0, v716, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) -> f_268(v560, v561, v562, v563, v564, v565, v714, 0, v716, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) :|: 0 = 0 f_268(v560, v561, v562, v563, v564, v565, v714, 0, v716, 1, v570, v571, v572, v573, v574, v575, 3, 2, 4) -> f_220(v560, v561, v562, v563, v564, v565, v714, 0, 1, v570, v571, v716, v572, v573, v574, v575, 3, 4) :|: TRUE f_220(v405, v406, v407, v408, v409, v410, v411, 0, 1, v414, v415, v416, v417, v418, v419, v420, 3, 4) -> f_224(v405, v406, v407, v408, v409, v410, v411, 0, 1, v414, v415, v416, v417, v418, v419, v420, 3, 4) :|: TRUE Combined rules. Obtained 1 rulesP rules: f_224(v405:0, v406:0, v407:0, v408:0, v409:0, v410:0, 1 + (1 + v714:0), 0, 1, v414:0, v415:0, 1 + (1 + v716:0), v417:0, v418:0, v419:0, v420:0, 3, 4) -> f_224(v405:0, v406:0, v407:0, v408:0, v409:0, v410:0, v714:0, 0, 1, 1 + v716:0, 1 + v714:0, v716:0, v417:0, v418:0, v419:0, v420:0, 3, 4) :|: v716:0 > -1 && v714:0 < -2 Filtered unneeded arguments: f_224(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_224(x7, x12) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_224(sum~cons_1~sum~cons_1~v714:0, sum~cons_1~sum~cons_1~v716:0) -> f_224(v714:0, v716:0) :|: v716:0 > -1 && v714:0 < -2 && sum~cons_1~sum~cons_1~v714:0 = 1 + (1 + v714:0) && sum~cons_1~sum~cons_1~v716:0 = 1 + (1 + v716:0) ---------------------------------------- (9) Obligation: Rules: f_224(sum~cons_1~sum~cons_1~v714:0, sum~cons_1~sum~cons_1~v716:0) -> f_224(v714:0, v716:0) :|: v716:0 > -1 && v714:0 < -2 && sum~cons_1~sum~cons_1~v714:0 = 1 + (1 + v714:0) && sum~cons_1~sum~cons_1~v716:0 = 1 + (1 + v716:0) ---------------------------------------- (10) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (11) Obligation: Rules: f_224(sum~cons_1~sum~cons_1~v714:0:0, sum~cons_1~sum~cons_1~v716:0:0) -> f_224(v714:0:0, v716:0:0) :|: v716:0:0 > -1 && v714:0:0 < -2 && sum~cons_1~sum~cons_1~v714:0:0 = 1 + (1 + v714:0:0) && sum~cons_1~sum~cons_1~v716:0:0 = 1 + (1 + v716:0:0) ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f_224(x, x1)] = -4 - 2*x + 3*x1 The following rules are decreasing: f_224(sum~cons_1~sum~cons_1~v714:0:0, sum~cons_1~sum~cons_1~v716:0:0) -> f_224(v714:0:0, v716:0:0) :|: v716:0:0 > -1 && v714:0:0 < -2 && sum~cons_1~sum~cons_1~v714:0:0 = 1 + (1 + v714:0:0) && sum~cons_1~sum~cons_1~v716:0:0 = 1 + (1 + v716:0:0) The following rules are bounded: f_224(sum~cons_1~sum~cons_1~v714:0:0, sum~cons_1~sum~cons_1~v716:0:0) -> f_224(v714:0:0, v716:0:0) :|: v716:0:0 > -1 && v714:0:0 < -2 && sum~cons_1~sum~cons_1~v714:0:0 = 1 + (1 + v714:0:0) && sum~cons_1~sum~cons_1~v716:0:0 = 1 + (1 + v716:0:0) ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: SCC ---------------------------------------- (15) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 15 rulesP rules: f_182(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) -> f_184(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) :|: 0 <= v218 && 1 <= v217 f_184(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) -> f_187(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) :|: 0 = 0 f_187(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) -> f_190(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) :|: 0 = 0 f_190(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) -> f_193(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) :|: TRUE f_193(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) -> f_196(v209, v210, v211, v212, v213, v214, v218, 1, v217, v215, v219, v220, v221, v222, v223, 0, 3, 4) :|: 0 = 0 f_196(v209, v210, v211, v212, v213, v214, v218, 1, v217, v215, v219, v220, v221, v222, v223, 0, 3, 4) -> f_200(v209, v210, v211, v212, v213, v214, v218, 1, v217, v215, v219, v220, v221, v222, v223, 0, 3, 4) :|: TRUE f_200(v209, v210, v211, v212, v213, v214, v218, 1, v217, v215, v219, v220, v221, v222, v223, 0, 3, 4) -> f_204(v209, v210, v211, v212, v213, v214, v218, 1, v219, v215, v220, v221, v222, v223, 0, 3, 4) :|: 0 = 0 f_204(v209, v210, v211, v212, v213, v214, v218, 1, v219, v215, v220, v221, v222, v223, 0, 3, 4) -> f_208(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v215, v220, v221, v222, v223, 0, 3, 4, 2) :|: 1 + v343 = v219 && 0 <= 2 + v343 f_208(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v215, v220, v221, v222, v223, 0, 3, 4, 2) -> f_213(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v215, v220, v221, v222, v223, 0, 3, 4, 2) :|: TRUE f_213(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v215, v220, v221, v222, v223, 0, 3, 4, 2) -> f_217(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v220, v221, v222, v223, 0, 3, 4, 2) :|: 0 = 0 f_217(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v220, v221, v222, v223, 0, 3, 4, 2) -> f_223(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v498, v220, v221, v222, v223, 0, 3, 4, 2) :|: 1 + v498 = v218 && 0 <= 1 + v498 f_223(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v498, v220, v221, v222, v223, 0, 3, 4, 2) -> f_226(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v498, v220, v221, v222, v223, 0, 3, 4, 2) :|: TRUE f_226(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v498, v220, v221, v222, v223, 0, 3, 4, 2) -> f_228(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v498, v220, v221, v222, v223, 0, 3, 4, 2) :|: TRUE f_228(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v498, v220, v221, v222, v223, 0, 3, 4, 2) -> f_180(v209, v210, v211, v212, v213, v214, v218, 1, v219, v343, v498, v220, v221, v222, v223, 0, 3, 4) :|: TRUE f_180(v209, v210, v211, v212, v213, v214, v215, 1, v217, v218, v219, v220, v221, v222, v223, 0, 3, 4) -> f_182(v209, v210, v211, v212, v213, v214, v218, 1, v215, v217, v219, v220, v221, v222, v223, 0, 3, 4) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_182(v209:0, v210:0, v211:0, v212:0, v213:0, v214:0, 1 + v498:0, 1, v215:0, v217:0, 1 + v343:0, v220:0, v221:0, v222:0, v223:0, 0, 3, 4) -> f_182(v209:0, v210:0, v211:0, v212:0, v213:0, v214:0, v343:0, 1, 1 + v498:0, 1 + v343:0, v498:0, v220:0, v221:0, v222:0, v223:0, 0, 3, 4) :|: v217:0 > 0 && v498:0 > -2 && v343:0 > -3 Filtered unneeded arguments: f_182(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_182(x7, x10, x11) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_182(sum~cons_1~v498:0, v217:0, sum~cons_1~v343:0) -> f_182(v343:0, 1 + v343:0, v498:0) :|: v498:0 > -2 && v343:0 > -3 && v217:0 > 0 && sum~cons_1~v498:0 = 1 + v498:0 && sum~cons_1~v343:0 = 1 + v343:0 ---------------------------------------- (16) Obligation: Rules: f_182(sum~cons_1~v498:0, v217:0, sum~cons_1~v343:0) -> f_182(v343:0, 1 + v343:0, v498:0) :|: v498:0 > -2 && v343:0 > -3 && v217:0 > 0 && sum~cons_1~v498:0 = 1 + v498:0 && sum~cons_1~v343:0 = 1 + v343:0 ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f_182(sum~cons_1~v498:0:0, v217:0:0, sum~cons_1~v343:0:0) -> f_182(v343:0:0, 1 + v343:0:0, v498:0:0) :|: v498:0:0 > -2 && v343:0:0 > -3 && v217:0:0 > 0 && sum~cons_1~v498:0:0 = 1 + v498:0:0 && sum~cons_1~v343:0:0 = 1 + v343:0:0 ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_182 ] = 1/2*f_182_1 + 1/2*f_182_3 The following rules are decreasing: f_182(sum~cons_1~v498:0:0, v217:0:0, sum~cons_1~v343:0:0) -> f_182(v343:0:0, 1 + v343:0:0, v498:0:0) :|: v498:0:0 > -2 && v343:0:0 > -3 && v217:0:0 > 0 && sum~cons_1~v498:0:0 = 1 + v498:0:0 && sum~cons_1~v343:0:0 = 1 + v343:0:0 The following rules are bounded: f_182(sum~cons_1~v498:0:0, v217:0:0, sum~cons_1~v343:0:0) -> f_182(v343:0:0, 1 + v343:0:0, v498:0:0) :|: v498:0:0 > -2 && v343:0:0 > -3 && v217:0:0 > 0 && sum~cons_1~v498:0:0 = 1 + v498:0:0 && sum~cons_1~v343:0:0 = 1 + v343:0:0 ---------------------------------------- (20) YES