20.55/6.29 YES 20.55/6.30 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 20.55/6.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.55/6.30 20.55/6.30 20.55/6.30 Termination of the given C Problem could be proven: 20.55/6.30 20.55/6.30 (0) C Problem 20.55/6.30 (1) CToLLVMProof [EQUIVALENT, 173 ms] 20.55/6.30 (2) LLVM problem 20.55/6.30 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1187 ms] 20.55/6.30 (4) LLVM Symbolic Execution Graph 20.55/6.30 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 20.55/6.30 (6) AND 20.55/6.30 (7) LLVM Symbolic Execution SCC 20.55/6.30 (8) SCC2IRS [SOUND, 63 ms] 20.55/6.30 (9) IntTRS 20.55/6.30 (10) IRS2T2 [EQUIVALENT, 0 ms] 20.55/6.30 (11) T2IntSys 20.55/6.30 (12) T2 [EQUIVALENT, 895 ms] 20.55/6.30 (13) YES 20.55/6.30 (14) LLVM Symbolic Execution SCC 20.55/6.30 (15) SCC2IRS [SOUND, 57 ms] 20.55/6.30 (16) IntTRS 20.55/6.30 (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] 20.55/6.30 (18) IntTRS 20.55/6.30 (19) PolynomialOrderProcessor [EQUIVALENT, 12 ms] 20.55/6.30 (20) YES 20.55/6.30 20.55/6.30 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (0) 20.55/6.30 Obligation: 20.55/6.30 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (1) CToLLVMProof (EQUIVALENT) 20.55/6.30 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (2) 20.55/6.30 Obligation: 20.55/6.30 LLVM Problem 20.55/6.30 20.55/6.30 Aliases: 20.55/6.30 20.55/6.30 Data layout: 20.55/6.30 20.55/6.30 "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" 20.55/6.30 20.55/6.30 Machine: 20.55/6.30 20.55/6.30 "x86_64-pc-linux-gnu" 20.55/6.30 20.55/6.30 Type definitions: 20.55/6.30 20.55/6.30 Global variables: 20.55/6.30 20.55/6.30 Function declarations and definitions: 20.55/6.30 20.55/6.30 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 20.55/6.30 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 20.55/6.30 0: 20.55/6.30 %1 = alloca i32, align 4 20.55/6.30 %N = alloca i32, align 4 20.55/6.30 %j = alloca i32, align 4 20.55/6.30 %i = alloca i32, align 4 20.55/6.30 store 0, %1 20.55/6.30 %2 = call i32 @__VERIFIER_nondet_int() 20.55/6.30 store %2, %N 20.55/6.30 %3 = load %N 20.55/6.30 store %3, %i 20.55/6.30 br %4 20.55/6.30 4: 20.55/6.30 %5 = load %i 20.55/6.30 %6 = icmp sgt %5 0 20.55/6.30 br %6, %7, %18 20.55/6.30 7: 20.55/6.30 %8 = load %N 20.55/6.30 store %8, %j 20.55/6.30 br %9 20.55/6.30 9: 20.55/6.30 %10 = load %j 20.55/6.30 %11 = icmp sgt %10 0 20.55/6.30 br %11, %12, %15 20.55/6.30 12: 20.55/6.30 %13 = load %j 20.55/6.30 %14 = add %13 -1 20.55/6.30 store %14, %j 20.55/6.30 br %9 20.55/6.30 15: 20.55/6.30 %16 = load %i 20.55/6.30 %17 = add %16 -1 20.55/6.30 store %17, %i 20.55/6.30 br %4 20.55/6.30 18: 20.55/6.30 ret 0 20.55/6.30 20.55/6.30 20.55/6.30 Analyze Termination of all function calls matching the pattern: 20.55/6.30 main() 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (3) LLVMToTerminationGraphProof (EQUIVALENT) 20.55/6.30 Constructed symbolic execution graph for LLVM program and proved memory safety. 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (4) 20.55/6.30 Obligation: 20.55/6.30 SE Graph 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (5) SymbolicExecutionGraphToSCCProof (SOUND) 20.55/6.30 Splitted symbolic execution graph to 2 SCCs. 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (6) 20.55/6.30 Complex Obligation (AND) 20.55/6.30 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (7) 20.55/6.30 Obligation: 20.55/6.30 SCC 20.55/6.30 ---------------------------------------- 20.55/6.30 20.55/6.30 (8) SCC2IRS (SOUND) 20.55/6.30 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 20.55/6.30 Generated rules. Obtained 28 rulesP rules: 20.55/6.31 f_211(v231, v232, v233, v234, v235, v236, 1, v238, v240, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_212(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 1 + v247 = v238 && 0 <= v247 20.55/6.31 f_212(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_213(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: TRUE 20.55/6.31 f_213(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_214(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: TRUE 20.55/6.31 f_214(v231, v232, v233, v234, v235, v236, 1, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_215(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_215(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_216(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 0 < v247 && 2 <= v238 20.55/6.31 f_215(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_217(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) :|: v247 <= 0 && v238 = 1 && v247 = 0 && 0 = 0 20.55/6.31 f_216(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_218(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_218(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_220(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: TRUE 20.55/6.31 f_220(v231, v232, v233, v234, v235, v236, 1, v247, v238, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_210(v231, v232, v233, v234, v235, v236, 1, v247, v238, v247, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: TRUE 20.55/6.31 f_210(v231, v232, v233, v234, v235, v236, 1, v238, v239, v240, v241, v242, v243, v244, v245, 0, 3, 2, 4) -> f_211(v231, v232, v233, v234, v235, v236, 1, v238, v240, v241, v242, v243, v244, v245, 0, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_217(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) -> f_219(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_219(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) -> f_221(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) :|: TRUE 20.55/6.31 f_221(v231, v232, v233, v234, v235, v236, 1, 0, v241, v242, v243, v244, v245, 3, 2, 4) -> f_222(v231, v232, v233, v234, v235, v236, 1, 0, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_222(v231, v232, v233, v234, v235, v236, 1, 0, v242, v243, v244, v245, 3, 2, 4) -> f_223(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) :|: 1 + v297 = v236 && 0 <= v297 20.55/6.31 f_223(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) -> f_224(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) :|: TRUE 20.55/6.31 f_224(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) -> f_225(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) :|: TRUE 20.55/6.31 f_225(v231, v232, v233, v234, v235, v236, 1, 0, v297, v242, v243, v244, v245, 3, 2, 4) -> f_226(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_226(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_227(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: 0 < v297 && 2 <= v236 && 3 <= v235 20.55/6.31 f_227(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_229(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_229(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_231(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: TRUE 20.55/6.31 f_231(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_233(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_233(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_234(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: TRUE 20.55/6.31 f_234(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_235(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: TRUE 20.55/6.31 f_235(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) -> f_236(v231, v232, v233, v234, v235, v297, 1, 0, v236, v242, v243, v244, v245, 3, 2, 4) :|: TRUE 20.55/6.31 f_236(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) -> f_237(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_237(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) -> f_238(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_238(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) -> f_239(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) :|: TRUE 20.55/6.31 f_239(v327, v328, v329, v330, v331, v332, 1, 0, v335, v336, v337, v338, v339, 3, 2, 4) -> f_210(v327, v328, v329, v330, v331, v332, 1, v331, 1, 0, v335, v336, v337, v338, v339, 0, 3, 2, 4) :|: TRUE 20.55/6.31 Combined rules. Obtained 2 rulesP rules: 20.55/6.31 f_211(v231:0, v232:0, v233:0, v234:0, v235:0, v236:0, 1, 1 + v247:0, v240:0, v241:0, v242:0, v243:0, v244:0, v245:0, 0, 3, 2, 4) -> f_211(v231:0, v232:0, v233:0, v234:0, v235:0, v236:0, 1, v247:0, v247:0, v241:0, v242:0, v243:0, v244:0, v245:0, 0, 3, 2, 4) :|: v247:0 > 0 20.55/6.31 f_211(v231:0, v232:0, v233:0, v234:0, v235:0, 1 + v297:0, 1, 1, v240:0, v241:0, v242:0, v243:0, v244:0, v245:0, 0, 3, 2, 4) -> f_211(v231:0, v232:0, v233:0, v234:0, v235:0, v297:0, 1, v235:0, 0, 1 + v297:0, v242:0, v243:0, v244:0, v245:0, 0, 3, 2, 4) :|: v297:0 > 0 && v235:0 > 2 20.55/6.31 Filtered unneeded arguments: 20.55/6.31 f_211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_211(x5, x6, x8) 20.55/6.31 Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules: 20.55/6.31 f_211(v235:0, v236:0, sum~cons_1~v247:0) -> f_211(v235:0, v236:0, v247:0) :|: v247:0 > 0 && sum~cons_1~v247:0 = 1 + v247:0 20.55/6.31 f_211(v235:0, sum~cons_1~v297:0, cons_1) -> f_211(v235:0, v297:0, v235:0) :|: v297:0 > 0 && v235:0 > 2 && sum~cons_1~v297:0 = 1 + v297:0 && cons_1 = 1 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (9) 20.55/6.31 Obligation: 20.55/6.31 Rules: 20.55/6.31 f_211(v235:0, v236:0, sum~cons_1~v247:0) -> f_211(v235:0, v236:0, v247:0) :|: v247:0 > 0 && sum~cons_1~v247:0 = 1 + v247:0 20.55/6.31 f_211(x, x1, x2) -> f_211(x, x3, x) :|: x3 > 0 && x > 2 && x1 = 1 + x3 && x2 = 1 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (10) IRS2T2 (EQUIVALENT) 20.55/6.31 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 20.55/6.31 20.55/6.31 (f_211_3,1) 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (11) 20.55/6.31 Obligation: 20.55/6.31 START: 0; 20.55/6.31 20.55/6.31 FROM: 0; 20.55/6.31 TO: 1; 20.55/6.31 20.55/6.31 FROM: 1; 20.55/6.31 oldX0 := x0; 20.55/6.31 oldX1 := x1; 20.55/6.31 oldX2 := x2; 20.55/6.31 oldX3 := oldX2 - 1; 20.55/6.31 assume(oldX3 > 0 && oldX2 = 1 + oldX3); 20.55/6.31 x0 := oldX0; 20.55/6.31 x1 := oldX1; 20.55/6.31 x2 := oldX2 - 1; 20.55/6.31 TO: 1; 20.55/6.31 20.55/6.31 FROM: 1; 20.55/6.31 oldX0 := x0; 20.55/6.31 oldX1 := x1; 20.55/6.31 oldX2 := x2; 20.55/6.31 oldX3 := oldX1 - 1; 20.55/6.31 assume(oldX3 > 0 && oldX0 > 2 && oldX1 = 1 + oldX3 && oldX2 = 1); 20.55/6.31 x0 := oldX0; 20.55/6.31 x1 := oldX1 - 1; 20.55/6.31 x2 := oldX0; 20.55/6.31 TO: 1; 20.55/6.31 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (12) T2 (EQUIVALENT) 20.55/6.31 Initially, performed program simplifications using lexicographic rank functions: 20.55/6.31 * Removed transitions 1, 4, 5 using the following rank functions: 20.55/6.31 - Rank function 1: 20.55/6.31 RF for loc. 5: x1 20.55/6.31 RF for loc. 6: x1 20.55/6.31 Bound for (chained) transitions 5: 2 20.55/6.31 - Rank function 2: 20.55/6.31 RF for loc. 5: 1+2*x2 20.55/6.31 RF for loc. 6: 2*x2 20.55/6.31 Bound for (chained) transitions 4: 4 20.55/6.31 - Rank function 3: 20.55/6.31 RF for loc. 5: 1 20.55/6.31 RF for loc. 6: 0 20.55/6.31 Bound for (chained) transitions 1: 1 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (13) 20.55/6.31 YES 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (14) 20.55/6.31 Obligation: 20.55/6.31 SCC 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (15) SCC2IRS (SOUND) 20.55/6.31 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 20.55/6.31 Generated rules. Obtained 9 rulesP rules: 20.55/6.31 f_145(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 4) -> f_146(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) :|: 0 < v41 && 2 <= v40 && 2 <= v38 20.55/6.31 f_146(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) -> f_148(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_148(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) -> f_150(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) :|: TRUE 20.55/6.31 f_150(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 2, 4) -> f_152(v34, v35, v36, v37, v38, 1, v41, v42, v43, v44, v45, 0, 3, 2, 4) :|: 0 = 0 20.55/6.31 f_152(v34, v35, v36, v37, v38, 1, v41, v42, v43, v44, v45, 0, 3, 2, 4) -> f_154(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) :|: 1 + v47 = v41 && 0 <= v47 20.55/6.31 f_154(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) -> f_156(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) :|: TRUE 20.55/6.31 f_156(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) -> f_158(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) :|: TRUE 20.55/6.31 f_158(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 2, 4) -> f_144(v34, v35, v36, v37, v38, 1, v41, v47, v42, v43, v44, v45, 0, 3, 4) :|: TRUE 20.55/6.31 f_144(v34, v35, v36, v37, v38, 1, v40, v41, v42, v43, v44, v45, 0, 3, 4) -> f_145(v34, v35, v36, v37, v38, 1, v41, v40, v42, v43, v44, v45, 0, 3, 4) :|: 0 = 0 20.55/6.31 Combined rules. Obtained 1 rulesP rules: 20.55/6.31 f_145(v34:0, v35:0, v36:0, v37:0, v38:0, 1, 1 + v47:0, v40:0, v42:0, v43:0, v44:0, v45:0, 0, 3, 4) -> f_145(v34:0, v35:0, v36:0, v37:0, v38:0, 1, v47:0, 1 + v47:0, v42:0, v43:0, v44:0, v45:0, 0, 3, 4) :|: v40:0 > 1 && v47:0 > -1 && v38:0 > 1 20.55/6.31 Filtered unneeded arguments: 20.55/6.31 f_145(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_145(x5, x7, x8) 20.55/6.31 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 20.55/6.31 f_145(v38:0, sum~cons_1~v47:0, v40:0) -> f_145(v38:0, v47:0, 1 + v47:0) :|: v47:0 > -1 && v38:0 > 1 && v40:0 > 1 && sum~cons_1~v47:0 = 1 + v47:0 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (16) 20.55/6.31 Obligation: 20.55/6.31 Rules: 20.55/6.31 f_145(v38:0, sum~cons_1~v47:0, v40:0) -> f_145(v38:0, v47:0, 1 + v47:0) :|: v47:0 > -1 && v38:0 > 1 && v40:0 > 1 && sum~cons_1~v47:0 = 1 + v47:0 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (17) IntTRSCompressionProof (EQUIVALENT) 20.55/6.31 Compressed rules. 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (18) 20.55/6.31 Obligation: 20.55/6.31 Rules: 20.55/6.31 f_145(v38:0:0, sum~cons_1~v47:0:0, v40:0:0) -> f_145(v38:0:0, v47:0:0, 1 + v47:0:0) :|: v47:0:0 > -1 && v38:0:0 > 1 && v40:0:0 > 1 && sum~cons_1~v47:0:0 = 1 + v47:0:0 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (19) PolynomialOrderProcessor (EQUIVALENT) 20.55/6.31 Found the following polynomial interpretation: 20.55/6.31 [f_145(x, x1, x2)] = x1 20.55/6.31 20.55/6.31 The following rules are decreasing: 20.55/6.31 f_145(v38:0:0, sum~cons_1~v47:0:0, v40:0:0) -> f_145(v38:0:0, v47:0:0, 1 + v47:0:0) :|: v47:0:0 > -1 && v38:0:0 > 1 && v40:0:0 > 1 && sum~cons_1~v47:0:0 = 1 + v47:0:0 20.55/6.31 The following rules are bounded: 20.55/6.31 f_145(v38:0:0, sum~cons_1~v47:0:0, v40:0:0) -> f_145(v38:0:0, v47:0:0, 1 + v47:0:0) :|: v47:0:0 > -1 && v38:0:0 > 1 && v40:0:0 > 1 && sum~cons_1~v47:0:0 = 1 + v47:0:0 20.55/6.31 20.55/6.31 ---------------------------------------- 20.55/6.31 20.55/6.31 (20) 20.55/6.31 YES 20.80/6.37 EOF