/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToLLVMProof [EQUIVALENT, 177 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 985 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 94 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 7 ms]
        (13) IntTRS
        (14) TerminationGraphProcessor [EQUIVALENT, 5 ms]
        (15) IntTRS
        (16) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (17) IntTRS
        (18) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (19) IntTRS
        (20) PolynomialOrderProcessor [EQUIVALENT, 4 ms]
        (21) YES
    (22) LLVM Symbolic Execution SCC
        (23) SCC2IRS [SOUND, 84 ms]
        (24) IntTRS
        (25) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (26) IntTRS
        (27) RankingReductionPairProof [EQUIVALENT, 4 ms]
        (28) 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
		store 0, %1
		br %2
	2:
		%3 = load %x
		%4 = icmp sge %3 0
		br %4, %5, %19
	5:
		%6 = load %y
		%7 = sub %6 1
		store %7, %y
		%8 = load %y
		%9 = icmp slt %8 0
		br %9, %10, %14
	10:
		%11 = load %x
		%12 = sub %11 1
		store %12, %x
		%13 = call i32 @__VERIFIER_nondet_int()
		store %13, %y
		br %14
	14:
		%15 = load %y
		%16 = icmp slt %15 0
		br %16, %17, %18
	17:
		br %19
	18:
		br %2
	19:
		%20 = load %1
		ret %20


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 55 rulesP rules:
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Combined rules. Obtained 4 rulesP rules:
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
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
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
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
Filtered unneeded arguments:
   f_236(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_236(x4, x6, x7, x10)
   f_132(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_132(x4, x8, x9)
Removed division, modulo operations, cleaned up constraints. Obtained 4 rules.P rules:
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
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)
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
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

----------------------------------------

(9)
Obligation:
Rules:
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
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)
f_132(x, x1, x2) -> f_132(1 + x3, x3, x4) :|: x3 > -2 && x4 > -1 && x > 0 && x1 = 1 + x3 && x2 = 0
f_236(x5, x6, x7, x8) -> f_132(1 + x9, x9, x10) :|: x10 > -1 && x9 > -2 && x5 = 1 + x9 && x6 = 0 && x7 = -1

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(10) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(11)
Obligation:
Rules:
f_132(x:0, sum~cons_1~x3:0, cons_0) -> f_132(1 + x3:0, x3:0, x4:0) :|: x3:0 > -2 && x4:0 > -1 && x:0 > 0 && sum~cons_1~x3:0 = 1 + x3:0 && cons_0 = 0
f_132(v7:0:0, v13:0:0, sum~cons_1~sum~cons_1~v446:0:0) -> f_236(v13:0:0, 1 + v446:0:0, v446:0:0, 1 + (1 + v446:0:0)) :|: v7:0:0 > 0 && v13:0:0 > -1 && v446:0:0 > -2 && sum~cons_1~sum~cons_1~v446:0:0 = 1 + (1 + v446:0:0)
f_236(v397:0:0, v400:0:0, sum~cons_1~v446:1:0, v403:0:0) -> f_236(v397:0:0, 1 + v446:1:0, v446:1:0, v403:0:0) :|: v400:0:0 > 0 && v403:0:0 > 1 && v446:1:0 > -2 && sum~cons_1~v446:1:0 = 1 + v446:1:0
f_236(x, x1, x2, x3) -> f_132(1 + x4, x4, x5) :|: x5 > -1 && x4 > -2 && x = 1 + x4 && x1 = 0 && x2 = -1

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_132(x, x1, x2)] = x1
[f_236(x3, x4, x5, x6)] = x3

The following rules are decreasing:
f_132(x:0, sum~cons_1~x3:0, cons_0) -> f_132(1 + x3:0, x3:0, x4:0) :|: x3:0 > -2 && x4:0 > -1 && x:0 > 0 && sum~cons_1~x3:0 = 1 + x3:0 && cons_0 = 0
f_236(x, x1, x2, x3) -> f_132(1 + x4, x4, x5) :|: x5 > -1 && x4 > -2 && x = 1 + x4 && x1 = 0 && x2 = -1
The following rules are bounded:
f_132(x:0, sum~cons_1~x3:0, cons_0) -> f_132(1 + x3:0, x3:0, x4:0) :|: x3:0 > -2 && x4:0 > -1 && x:0 > 0 && sum~cons_1~x3:0 = 1 + x3:0 && cons_0 = 0
f_132(v7:0:0, v13:0:0, sum~cons_1~sum~cons_1~v446:0:0) -> f_236(v13:0:0, 1 + v446:0:0, v446:0:0, 1 + (1 + v446:0:0)) :|: v7:0:0 > 0 && v13:0:0 > -1 && v446:0:0 > -2 && sum~cons_1~sum~cons_1~v446:0:0 = 1 + (1 + v446:0:0)
f_236(x, x1, x2, x3) -> f_132(1 + x4, x4, x5) :|: x5 > -1 && x4 > -2 && x = 1 + x4 && x1 = 0 && x2 = -1

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(13)
Obligation:
Rules:
f_132(v7:0:0, v13:0:0, sum~cons_1~sum~cons_1~v446:0:0) -> f_236(v13:0:0, 1 + v446:0:0, v446:0:0, 1 + (1 + v446:0:0)) :|: v7:0:0 > 0 && v13:0:0 > -1 && v446:0:0 > -2 && sum~cons_1~sum~cons_1~v446:0:0 = 1 + (1 + v446:0:0)
f_236(v397:0:0, v400:0:0, sum~cons_1~v446:1:0, v403:0:0) -> f_236(v397:0:0, 1 + v446:1:0, v446:1:0, v403:0:0) :|: v400:0:0 > 0 && v403:0:0 > 1 && v446:1:0 > -2 && sum~cons_1~v446:1:0 = 1 + v446:1:0

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(14) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

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(15)
Obligation:
Rules:
f_236(v397:0:0, v400:0:0, sum~cons_1~v446:1:0, v403:0:0) -> f_236(v397:0:0, 1 + v446:1:0, v446:1:0, v403:0:0) :|: v400:0:0 > 0 && v403:0:0 > 1 && v446:1:0 > -2 && sum~cons_1~v446:1:0 = 1 + v446:1:0

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(16) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(17)
Obligation:
Rules:
f_236(v397:0:0:0, v400:0:0:0, sum~cons_1~v446:1:0:0, v403:0:0:0) -> f_236(v397:0:0:0, 1 + v446:1:0:0, v446:1:0:0, v403:0:0:0) :|: v400:0:0:0 > 0 && v403:0:0:0 > 1 && v446:1:0:0 > -2 && sum~cons_1~v446:1:0:0 = 1 + v446:1:0:0

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(18) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f_236(x1, x2, x3, x4) -> f_236(x2, x3, x4)

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(19)
Obligation:
Rules:
f_236(v400:0:0:0, sum~cons_1~v446:1:0:0, v403:0:0:0) -> f_236(1 + v446:1:0:0, v446:1:0:0, v403:0:0:0) :|: v400:0:0:0 > 0 && v403:0:0:0 > 1 && v446:1:0:0 > -2 && sum~cons_1~v446:1:0:0 = 1 + v446:1:0:0

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(20) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_236(x, x1, x2)] = x1

The following rules are decreasing:
f_236(v400:0:0:0, sum~cons_1~v446:1:0:0, v403:0:0:0) -> f_236(1 + v446:1:0:0, v446:1:0:0, v403:0:0:0) :|: v400:0:0:0 > 0 && v403:0:0:0 > 1 && v446:1:0:0 > -2 && sum~cons_1~v446:1:0:0 = 1 + v446:1:0:0
The following rules are bounded:
f_236(v400:0:0:0, sum~cons_1~v446:1:0:0, v403:0:0:0) -> f_236(1 + v446:1:0:0, v446:1:0:0, v403:0:0:0) :|: v400:0:0:0 > 0 && v403:0:0:0 > 1 && v446:1:0:0 > -2 && sum~cons_1~v446:1:0:0 = 1 + v446:1:0:0

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(21)
YES

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(22)
Obligation:
SCC
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(23) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 15 rulesP rules:
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Combined rules. Obtained 1 rulesP rules:
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
Filtered unneeded arguments:
   f_117(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f_117(x7)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_117(sum~cons_1~v17:0) -> f_117(v17:0) :|: v17:0 > -1 && sum~cons_1~v17:0 = 1 + v17:0

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(24)
Obligation:
Rules:
f_117(sum~cons_1~v17:0) -> f_117(v17:0) :|: v17:0 > -1 && sum~cons_1~v17:0 = 1 + v17:0

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(25) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(26)
Obligation:
Rules:
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

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(27) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_117 ] = f_117_1

The following rules are decreasing:
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

The following rules are bounded:
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


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(28)
YES