26.44/7.77 YES 26.44/7.78 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 26.44/7.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 26.44/7.78 26.44/7.78 26.44/7.78 Termination of the given C Problem could be proven: 26.44/7.78 26.44/7.78 (0) C Problem 26.44/7.78 (1) CToLLVMProof [EQUIVALENT, 175 ms] 26.44/7.78 (2) LLVM problem 26.44/7.78 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1268 ms] 26.44/7.78 (4) LLVM Symbolic Execution Graph 26.44/7.78 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 26.44/7.78 (6) LLVM Symbolic Execution SCC 26.44/7.78 (7) SCC2IRS [SOUND, 75 ms] 26.44/7.78 (8) IntTRS 26.44/7.78 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 26.44/7.78 (10) IntTRS 26.44/7.78 (11) PolynomialOrderProcessor [EQUIVALENT, 13 ms] 26.44/7.78 (12) AND 26.44/7.78 (13) IntTRS 26.44/7.78 (14) IntTRSCompressionProof [EQUIVALENT, 1 ms] 26.44/7.78 (15) IntTRS 26.44/7.78 (16) RankingReductionPairProof [EQUIVALENT, 37 ms] 26.44/7.78 (17) YES 26.44/7.78 (18) IntTRS 26.44/7.78 (19) IntTRSCompressionProof [EQUIVALENT, 2 ms] 26.44/7.78 (20) IntTRS 26.44/7.78 (21) PolynomialOrderProcessor [EQUIVALENT, 8 ms] 26.44/7.78 (22) IntTRS 26.44/7.78 (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] 26.44/7.78 (24) IntTRS 26.44/7.78 (25) RankingReductionPairProof [EQUIVALENT, 4 ms] 26.44/7.78 (26) YES 26.44/7.78 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (0) 26.44/7.78 Obligation: 26.44/7.78 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (1) CToLLVMProof (EQUIVALENT) 26.44/7.78 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (2) 26.44/7.78 Obligation: 26.44/7.78 LLVM Problem 26.44/7.78 26.44/7.78 Aliases: 26.44/7.78 26.44/7.78 Data layout: 26.44/7.78 26.44/7.78 "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" 26.44/7.78 26.44/7.78 Machine: 26.44/7.78 26.44/7.78 "x86_64-pc-linux-gnu" 26.44/7.78 26.44/7.78 Type definitions: 26.44/7.78 26.44/7.78 Global variables: 26.44/7.78 26.44/7.78 Function declarations and definitions: 26.44/7.78 26.44/7.78 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 26.44/7.78 *BasicFunctionTypename: "f" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 26.44/7.78 0: 26.44/7.78 %1 = alloca i32, align 4 26.44/7.78 %2 = alloca i32, align 4 26.44/7.78 %3 = alloca i32, align 4 26.44/7.78 store %x, %2 26.44/7.78 store %y, %3 26.44/7.78 %4 = load %3 26.44/7.78 %5 = icmp eq %4 0 26.44/7.78 br %5, %6, %8 26.44/7.78 6: 26.44/7.78 %7 = load %2 26.44/7.78 store %7, %1 26.44/7.78 br %21 26.44/7.78 8: 26.44/7.78 %9 = load %2 26.44/7.78 %10 = icmp eq %9 0 26.44/7.78 br %10, %11, %16 26.44/7.78 11: 26.44/7.78 %12 = load %3 26.44/7.78 %13 = load %3 26.44/7.78 %14 = sub %13 1 26.44/7.78 %15 = call i32 @f(i32 %12, i32 %14) 26.44/7.78 store %15, %1 26.44/7.78 br %21 26.44/7.78 16: 26.44/7.78 %17 = load %3 26.44/7.78 %18 = load %2 26.44/7.78 %19 = sub %18 1 26.44/7.78 %20 = call i32 @f(i32 %17, i32 %19) 26.44/7.78 store %20, %1 26.44/7.78 br %21 26.44/7.78 21: 26.44/7.78 %22 = load %1 26.44/7.78 ret %22 26.44/7.78 26.44/7.78 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 26.44/7.78 0: 26.44/7.78 %1 = alloca i32, align 4 26.44/7.78 %x = alloca i32, align 4 26.44/7.78 %y = alloca i32, align 4 26.44/7.78 store 0, %1 26.44/7.78 %2 = call i32 @__VERIFIER_nondet_int() 26.44/7.78 store %2, %x 26.44/7.78 %3 = call i32 @__VERIFIER_nondet_int() 26.44/7.78 store %3, %y 26.44/7.78 %4 = load %x 26.44/7.78 %5 = icmp sge %4 0 26.44/7.78 br %5, %6, %13 26.44/7.78 6: 26.44/7.78 %7 = load %y 26.44/7.78 %8 = icmp sge %7 0 26.44/7.78 br %8, %9, %13 26.44/7.78 9: 26.44/7.78 %10 = load %x 26.44/7.78 %11 = load %y 26.44/7.78 %12 = call i32 @f(i32 %10, i32 %11) 26.44/7.78 br %13 26.44/7.78 13: 26.44/7.78 ret 0 26.44/7.78 26.44/7.78 26.44/7.78 Analyze Termination of all function calls matching the pattern: 26.44/7.78 main() 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (3) LLVMToTerminationGraphProof (EQUIVALENT) 26.44/7.78 Constructed symbolic execution graph for LLVM program and proved memory safety. 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (4) 26.44/7.78 Obligation: 26.44/7.78 SE Graph 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (5) SymbolicExecutionGraphToSCCProof (SOUND) 26.44/7.78 Splitted symbolic execution graph to 1 SCC. 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (6) 26.44/7.78 Obligation: 26.44/7.78 SCC 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (7) SCC2IRS (SOUND) 26.44/7.78 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 26.44/7.78 Generated rules. Obtained 28 rulesP rules: 26.44/7.78 f_210(v50, v51, v52, v53, 3, 0, 1, 4) -> f_211(v50, v51, v52, v54, v53, v55, 3, 0, 1, 4) :|: 1 <= v54 && v55 = 3 + v54 && 4 <= v55 26.44/7.78 f_211(v50, v51, v52, v54, v53, v55, 3, 0, 1, 4) -> f_212(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: 1 <= v56 && v57 = 3 + v56 && 4 <= v57 26.44/7.78 f_212(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_213(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: TRUE 26.44/7.78 f_213(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_214(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: TRUE 26.44/7.78 f_214(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_215(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: 0 = 0 26.44/7.78 f_215(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_217(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) :|: v51 != 0 26.44/7.78 f_217(v50, v51, v52, v54, v56, v53, v55, v57, 3, 0, 1, 4) -> f_219(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0 26.44/7.78 f_219(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_221(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: TRUE 26.44/7.78 f_221(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_223(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0 26.44/7.78 f_223(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_225(0, v51, v52, v54, v56, v53, v55, v57, 3, 1, 4) :|: v50 = 0 26.44/7.78 f_223(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_226(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: v50 != 0 26.44/7.78 f_225(0, v51, v52, v54, v56, v53, v55, v57, 3, 1, 4) -> f_228(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) :|: 0 = 0 26.44/7.78 f_228(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) -> f_231(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) :|: TRUE 26.44/7.78 f_231(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) -> f_234(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) :|: 0 = 0 26.44/7.78 f_234(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) -> f_237(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) :|: 0 = 0 26.44/7.78 f_237(0, v51, v52, v54, v56, 1, v53, v55, v57, 3, 4) -> f_240(0, v51, v52, v54, v56, 1, v72, v53, v55, v57, 3, 4) :|: 1 + v72 = v51 && 0 <= v72 26.44/7.78 f_240(0, v51, v52, v54, v56, 1, v72, v53, v55, v57, 3, 4) -> f_242(v51, v72, v52, v53, v54, v55, v56, v57, 0, 1, 3, 4) :|: 0 = 0 26.44/7.78 f_242(v51, v72, v52, v53, v54, v55, v56, v57, 0, 1, 3, 4) -> f_244(v51, v72, v52, v53, v54, v55, v56, v57, 0, 3, 1, 4) :|: TRUE 26.44/7.78 f_244(v51, v72, v52, v53, v54, v55, v56, v57, 0, 3, 1, 4) -> f_209(v51, v72, 0) :|: TRUE 26.44/7.78 f_209(v50, v51, 0) -> f_210(v50, v51, v52, v53, 3, 0, 1, 4) :|: 1 <= v52 && v53 = 3 + v52 && 4 <= v53 26.44/7.78 f_226(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_229(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0 26.44/7.78 f_229(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_232(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: TRUE 26.44/7.78 f_232(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_235(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0 26.44/7.78 f_235(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_238(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) :|: 0 = 0 26.44/7.78 f_238(v50, v51, v52, v54, v56, 0, v53, v55, v57, 3, 1, 4) -> f_241(v50, v51, v52, v54, v56, 0, v73, v53, v55, v57, 3, 1, 4) :|: 1 + v73 = v50 && 0 <= v73 26.44/7.78 f_241(v50, v51, v52, v54, v56, 0, v73, v53, v55, v57, 3, 1, 4) -> f_243(v51, v73, v52, v53, v54, v55, v56, v57, v50, 0, 3, 1, 4) :|: 0 = 0 26.44/7.78 f_243(v51, v73, v52, v53, v54, v55, v56, v57, v50, 0, 3, 1, 4) -> f_245(v51, v73, v52, v53, v54, v55, v56, v57, v50, 3, 1, 4, 0) :|: TRUE 26.44/7.78 f_245(v51, v73, v52, v53, v54, v55, v56, v57, v50, 3, 1, 4, 0) -> f_209(v51, v73, 0) :|: TRUE 26.44/7.78 Combined rules. Obtained 3 rulesP rules: 26.44/7.78 f_210(0, 1 + v72:0, v52:0, v53:0, 3, 0, 1, 4) -> f_210(1 + v72:0, v72:0, v52:1, 3 + v52:1, 3, 0, 1, 4) :|: v56:0 > 0 && v54:0 > 0 && v72:0 > -1 && v52:1 > 0 26.44/7.78 f_210(1 + v73:0, v51:0, v52:0, v53:0, 3, 0, 1, 4) -> f_210(v51:0, v73:0, v52:1, 3 + v52:1, 3, 0, 1, 4) :|: v56:0 > 0 && v54:0 > 0 && v51:0 < 0 && v73:0 > -1 && v52:1 > 0 26.44/7.78 f_210(1 + v73:0, v51:0, v52:0, v53:0, 3, 0, 1, 4) -> f_210(v51:0, v73:0, v52:1, 3 + v52:1, 3, 0, 1, 4) :|: v56:0 > 0 && v54:0 > 0 && v51:0 > 0 && v73:0 > -1 && v52:1 > 0 26.44/7.78 Filtered unneeded arguments: 26.44/7.78 f_210(x1, x2, x3, x4, x5, x6, x7, x8) -> f_210(x1, x2) 26.44/7.78 Removed division, modulo operations, cleaned up constraints. Obtained 3 rules.P rules: 26.44/7.78 f_210(cons_0, sum~cons_1~v72:0) -> f_210(1 + v72:0, v72:0) :|: v72:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0 = 1 + v72:0 26.44/7.78 f_210(sum~cons_1~v73:0, v51:0) -> f_210(v51:0, v73:0) :|: v51:0 < 0 && v73:0 > -1 && sum~cons_1~v73:0 = 1 + v73:0 26.44/7.78 f_210(sum~cons_1~v73:0, v51:0) -> f_210(v51:0, v73:0) :|: v51:0 > 0 && v73:0 > -1 && sum~cons_1~v73:0 = 1 + v73:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (8) 26.44/7.78 Obligation: 26.44/7.78 Rules: 26.44/7.78 f_210(cons_0, sum~cons_1~v72:0) -> f_210(1 + v72:0, v72:0) :|: v72:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0 = 1 + v72:0 26.44/7.78 f_210(sum~cons_1~v73:0, v51:0) -> f_210(v51:0, v73:0) :|: v51:0 < 0 && v73:0 > -1 && sum~cons_1~v73:0 = 1 + v73:0 26.44/7.78 f_210(x, x1) -> f_210(x1, x2) :|: x1 > 0 && x2 > -1 && x = 1 + x2 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (9) IntTRSCompressionProof (EQUIVALENT) 26.44/7.78 Compressed rules. 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (10) 26.44/7.78 Obligation: 26.44/7.78 Rules: 26.44/7.78 f_210(cons_0, sum~cons_1~v72:0:0) -> f_210(1 + v72:0:0, v72:0:0) :|: v72:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0 = 1 + v72:0:0 26.44/7.78 f_210(sum~cons_1~x2:0, x1:0) -> f_210(x1:0, x2:0) :|: x1:0 > 0 && x2:0 > -1 && sum~cons_1~x2:0 = 1 + x2:0 26.44/7.78 f_210(sum~cons_1~v73:0:0, v51:0:0) -> f_210(v51:0:0, v73:0:0) :|: v51:0:0 < 0 && v73:0:0 > -1 && sum~cons_1~v73:0:0 = 1 + v73:0:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (11) PolynomialOrderProcessor (EQUIVALENT) 26.44/7.78 Found the following polynomial interpretation: 26.44/7.78 [f_210(x, x1)] = -4 - 2*x - 3*x*x1 + 2*x^2 + x1 + 2*x1^2 26.44/7.78 26.44/7.78 The following rules are decreasing: 26.44/7.78 f_210(cons_0, sum~cons_1~v72:0:0) -> f_210(1 + v72:0:0, v72:0:0) :|: v72:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0 = 1 + v72:0:0 26.44/7.78 The following rules are bounded: 26.44/7.78 f_210(sum~cons_1~v73:0:0, v51:0:0) -> f_210(v51:0:0, v73:0:0) :|: v51:0:0 < 0 && v73:0:0 > -1 && sum~cons_1~v73:0:0 = 1 + v73:0:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (12) 26.44/7.78 Complex Obligation (AND) 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (13) 26.44/7.78 Obligation: 26.44/7.78 Rules: 26.44/7.78 f_210(sum~cons_1~x2:0, x1:0) -> f_210(x1:0, x2:0) :|: x1:0 > 0 && x2:0 > -1 && sum~cons_1~x2:0 = 1 + x2:0 26.44/7.78 f_210(sum~cons_1~v73:0:0, v51:0:0) -> f_210(v51:0:0, v73:0:0) :|: v51:0:0 < 0 && v73:0:0 > -1 && sum~cons_1~v73:0:0 = 1 + v73:0:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (14) IntTRSCompressionProof (EQUIVALENT) 26.44/7.78 Compressed rules. 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (15) 26.44/7.78 Obligation: 26.44/7.78 Rules: 26.44/7.78 f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0 26.44/7.78 f_210(sum~cons_1~v73:0:0:0, v51:0:0:0) -> f_210(v51:0:0:0, v73:0:0:0) :|: v51:0:0:0 < 0 && v73:0:0:0 > -1 && sum~cons_1~v73:0:0:0 = 1 + v73:0:0:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (16) RankingReductionPairProof (EQUIVALENT) 26.44/7.78 Interpretation: 26.44/7.78 [ f_210 ] = 1/2*f_210_2 + 1/2*f_210_1 + 1/2*f_210_2^2 + 1/2*f_210_1^2 26.44/7.78 26.44/7.78 The following rules are decreasing: 26.44/7.78 f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0 26.44/7.78 f_210(sum~cons_1~v73:0:0:0, v51:0:0:0) -> f_210(v51:0:0:0, v73:0:0:0) :|: v51:0:0:0 < 0 && v73:0:0:0 > -1 && sum~cons_1~v73:0:0:0 = 1 + v73:0:0:0 26.44/7.78 26.44/7.78 The following rules are bounded: 26.44/7.78 f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0 26.44/7.78 f_210(sum~cons_1~v73:0:0:0, v51:0:0:0) -> f_210(v51:0:0:0, v73:0:0:0) :|: v51:0:0:0 < 0 && v73:0:0:0 > -1 && sum~cons_1~v73:0:0:0 = 1 + v73:0:0:0 26.44/7.78 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (17) 26.44/7.78 YES 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (18) 26.44/7.78 Obligation: 26.44/7.78 Rules: 26.44/7.78 f_210(cons_0, sum~cons_1~v72:0:0) -> f_210(1 + v72:0:0, v72:0:0) :|: v72:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0 = 1 + v72:0:0 26.44/7.78 f_210(sum~cons_1~x2:0, x1:0) -> f_210(x1:0, x2:0) :|: x1:0 > 0 && x2:0 > -1 && sum~cons_1~x2:0 = 1 + x2:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (19) IntTRSCompressionProof (EQUIVALENT) 26.44/7.78 Compressed rules. 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (20) 26.44/7.78 Obligation: 26.44/7.78 Rules: 26.44/7.78 f_210(cons_0, sum~cons_1~v72:0:0:0) -> f_210(1 + v72:0:0:0, v72:0:0:0) :|: v72:0:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0:0 = 1 + v72:0:0:0 26.44/7.78 f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (21) PolynomialOrderProcessor (EQUIVALENT) 26.44/7.78 Found the following polynomial interpretation: 26.44/7.78 [f_210(x, x1)] = -2*x - x*x1 + x^2 + x1^2 26.44/7.78 26.44/7.78 The following rules are decreasing: 26.44/7.78 f_210(cons_0, sum~cons_1~v72:0:0:0) -> f_210(1 + v72:0:0:0, v72:0:0:0) :|: v72:0:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0:0 = 1 + v72:0:0:0 26.44/7.78 The following rules are bounded: 26.44/7.78 f_210(cons_0, sum~cons_1~v72:0:0:0) -> f_210(1 + v72:0:0:0, v72:0:0:0) :|: v72:0:0:0 > -1 && cons_0 = 0 && sum~cons_1~v72:0:0:0 = 1 + v72:0:0:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (22) 26.44/7.78 Obligation: 26.44/7.78 Rules: 26.44/7.78 f_210(sum~cons_1~x2:0:0, x1:0:0) -> f_210(x1:0:0, x2:0:0) :|: x1:0:0 > 0 && x2:0:0 > -1 && sum~cons_1~x2:0:0 = 1 + x2:0:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (23) IntTRSCompressionProof (EQUIVALENT) 26.44/7.78 Compressed rules. 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (24) 26.44/7.78 Obligation: 26.44/7.78 Rules: 26.44/7.78 f_210(sum~cons_1~x2:0:0:0, x1:0:0:0) -> f_210(x1:0:0:0, x2:0:0:0) :|: x1:0:0:0 > 0 && x2:0:0:0 > -1 && sum~cons_1~x2:0:0:0 = 1 + x2:0:0:0 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (25) RankingReductionPairProof (EQUIVALENT) 26.44/7.78 Interpretation: 26.44/7.78 [ f_210 ] = f_210_2 + f_210_1 26.44/7.78 26.44/7.78 The following rules are decreasing: 26.44/7.78 f_210(sum~cons_1~x2:0:0:0, x1:0:0:0) -> f_210(x1:0:0:0, x2:0:0:0) :|: x1:0:0:0 > 0 && x2:0:0:0 > -1 && sum~cons_1~x2:0:0:0 = 1 + x2:0:0:0 26.44/7.78 26.44/7.78 The following rules are bounded: 26.44/7.78 f_210(sum~cons_1~x2:0:0:0, x1:0:0:0) -> f_210(x1:0:0:0, x2:0:0:0) :|: x1:0:0:0 > 0 && x2:0:0:0 > -1 && sum~cons_1~x2:0:0:0 = 1 + x2:0:0:0 26.44/7.78 26.44/7.78 26.44/7.78 ---------------------------------------- 26.44/7.78 26.44/7.78 (26) 26.44/7.78 YES 26.76/7.87 EOF