YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 178 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 10.4 s]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) LLVM Symbolic Execution SCC
(7) SCC2IRS [SOUND, 256 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
(12) IntTRS
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IntTRS
(15) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(16) YES


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

(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
----------------------------------------

(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox2/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: true visibilityType: DEFAULT callingConvention: ccc
*BasicFunctionTypename: "Ack" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (m i32, n i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%3 = alloca i32, align 4
		store %m, %2
		store %n, %3
		%4 = load %2
		%5 = icmp eq %4 0
		br %5, %6, %9
	6:
		%7 = load %3
		%8 = add %7 1
		store %8, %1
		br %24
	9:
		%10 = load %3
		%11 = icmp eq %10 0
		br %11, %12, %16
	12:
		%13 = load %2
		%14 = sub %13 1
		%15 = call i32 @Ack(i32 %14, i32 1)
		store %15, %1
		br %24
	16:
		%17 = load %2
		%18 = sub %17 1
		%19 = load %2
		%20 = load %3
		%21 = sub %20 1
		%22 = call i32 @Ack(i32 %19, i32 %21)
		%23 = call i32 @Ack(i32 %18, i32 %22)
		store %23, %1
		br %24
	24:
		%25 = load %1
		ret %25

*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
		%r = 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
		%4 = load %x
		%5 = icmp slt %4 0
		br %5, %9, %6
	6:
		%7 = load %y
		%8 = icmp slt %7 0
		br %8, %9, %10
	9:
		store 0, %1
		br %15
	10:
		%11 = load %x
		%12 = load %y
		%13 = call i32 @Ack(i32 %11, i32 %12)
		store %13, %r
		%14 = load %r
		store %14, %1
		br %15
	15:
		%16 = load %1
		ret %16


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 1 SCC.
----------------------------------------

(6)
Obligation:
SCC
----------------------------------------

(7) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 86 rulesP rules:
f_288(v93, v94, v108, v95, v96, v97, v98, v99, v100, v101, v102, v109, 0, v104, v105, 3, 1, 4) -> f_290(v93, v94, v108, v115, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, 0, v104, v105, 3, 1, 4) :|: 1 <= v115 && v116 = 3 + v115 && 4 <= v116
f_290(v93, v94, v108, v115, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, 0, v104, v105, 3, 1, 4) -> f_291(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) :|: 1 <= v117 && v118 = 3 + v117 && 4 <= v118
f_291(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) -> f_292(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) :|: TRUE
f_292(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) -> f_293(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) :|: TRUE
f_293(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) -> f_294(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) :|: 0 = 0
f_294(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) -> f_296(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) :|: v93 != 0 && 1 <= v104
f_296(v93, v94, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, 0, v104, v105, 3, 1, 4) -> f_298(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_298(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_300(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: TRUE
f_300(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_302(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_302(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_304(v93, 0, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: v94 = 0
f_302(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_305(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: v94 != 0
f_304(v93, 0, v108, v115, v117, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_307(v93, 0, v108, v115, v117, 1, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4) :|: 0 = 0
f_307(v93, 0, v108, v115, v117, 1, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4) -> f_310(v93, 0, v108, v115, v117, 1, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4) :|: TRUE
f_310(v93, 0, v108, v115, v117, 1, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4) -> f_313(v93, 0, v108, v115, v117, 1, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4) :|: 0 = 0
f_313(v93, 0, v108, v115, v117, 1, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4) -> f_316(v93, 0, v108, v115, v117, 1, v141, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4) :|: 1 + v141 = v93 && 0 <= v141
f_316(v93, 0, v108, v115, v117, 1, v141, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4) -> f_319(v141, 1, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 3, 4) :|: 0 = 0
f_319(v141, 1, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 3, 4) -> f_322(v141, 1, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 3, 4) :|: TRUE
f_322(v141, 1, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 3, 4) -> f_285(v141, 1, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_285(v93, v94, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) -> f_288(v93, v94, v108, v95, v96, v97, v98, v99, v100, v101, v102, v109, 0, v104, v105, 3, 1, 4) :|: 1 <= v108 && v109 = 3 + v108 && 4 <= v109
f_305(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_308(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_308(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_311(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: TRUE
f_311(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_314(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_314(v93, v94, v108, v115, v117, 0, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_317(v93, v94, v108, v115, v117, 0, v142, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 1 + v142 = v93 && 0 <= v142
f_317(v93, v94, v108, v115, v117, 0, v142, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_320(v93, v94, v108, v115, v117, 0, v142, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_320(v93, v94, v108, v115, v117, 0, v142, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_323(v93, v94, v108, v115, v117, 0, v142, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_323(v93, v94, v108, v115, v117, 0, v142, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_325(v93, v94, v108, v115, v117, 0, v142, v157, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 1 + v157 = v94 && 0 <= v157
f_325(v93, v94, v108, v115, v117, 0, v142, v157, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: 0 = 0
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_331(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, 3, 1, 4) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_474(v93, 0, v1084, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_520(v93, 0, v1355, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_564(v93, 0, v1655, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_619(v93, 0, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_678(v93, 0, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_689(v93, v157, v2360, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_735(v93, 0, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_788(v93, 0, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_796(v93, v157, v3017, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_844(v93, 0, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_853(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_891(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_918(v93, 0, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_928(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
f_328(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_958(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
f_331(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, 3, 1, 4) -> f_285(v93, v157, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_474(v93, 0, v1084, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_479(v93, 1, v108, v115, v117, 0, v142, v1084, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) :|: 0 = 0
f_479(v93, 1, v108, v115, v117, 0, v142, v1084, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) -> f_481(v142, v1084, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: 0 = 0
f_481(v142, v1084, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_483(v142, v1084, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: TRUE
f_483(v142, v1084, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_285(v142, v1084, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_520(v93, 0, v1355, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_529(v93, 1, v108, v115, v117, 0, v142, v1355, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) :|: 0 = 0
f_529(v93, 1, v108, v115, v117, 0, v142, v1355, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) -> f_535(v142, v1355, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: 0 = 0
f_535(v142, v1355, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_541(v142, v1355, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: TRUE
f_541(v142, v1355, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_285(v142, v1355, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_564(v93, 0, v1655, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_576(v93, 1, v108, v115, v117, 0, v142, v1655, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) :|: 0 = 0
f_576(v93, 1, v108, v115, v117, 0, v142, v1655, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) -> f_584(v142, v1655, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: 0 = 0
f_584(v142, v1655, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_596(v142, v1655, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: TRUE
f_596(v142, v1655, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_285(v142, v1655, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_619(v93, 0, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_635(v93, 1, v108, v115, v117, 0, v142, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) :|: 0 = 0
f_635(v93, 1, v108, v115, v117, 0, v142, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) -> f_647(v142, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: 0 = 0
f_647(v142, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_664(v142, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: TRUE
f_664(v142, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_285(v142, v1960, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_678(v93, 0, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_619(v93, 0, v1960, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_689(v93, v157, v2360, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_697(v93, v94, v108, v115, v117, 0, v142, v157, v2360, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_697(v93, v94, v108, v115, v117, 0, v142, v157, v2360, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_705(v142, v2360, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, v157, 3, 1, 4) :|: 0 = 0
f_705(v142, v2360, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, v157, 3, 1, 4) -> f_713(v142, v2360, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, 3, 1, 4) :|: TRUE
f_713(v142, v2360, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, 3, 1, 4) -> f_285(v142, v2360, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_735(v93, 0, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_751(v93, 1, v108, v115, v117, 0, v142, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) :|: 0 = 0
f_751(v93, 1, v108, v115, v117, 0, v142, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) -> f_763(v142, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: 0 = 0
f_763(v142, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_774(v142, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: TRUE
f_774(v142, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_285(v142, v2624, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_788(v93, 0, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_735(v93, 0, v2624, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_796(v93, v157, v3017, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_813(v93, v94, v108, v115, v117, 0, v142, v157, v3017, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_813(v93, v94, v108, v115, v117, 0, v142, v157, v3017, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_823(v142, v3017, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, v157, 3, 1, 4) :|: 0 = 0
f_823(v142, v3017, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, v157, 3, 1, 4) -> f_833(v142, v3017, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, 3, 1, 4) :|: TRUE
f_833(v142, v3017, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, 3, 1, 4) -> f_285(v142, v3017, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_844(v93, 0, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_863(v93, 1, v108, v115, v117, 0, v142, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) :|: 0 = 0
f_863(v93, 1, v108, v115, v117, 0, v142, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 4, 2) -> f_877(v142, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: 0 = 0
f_877(v142, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_900(v142, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) :|: TRUE
f_900(v142, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, 1, 3, 4, 2) -> f_285(v142, v3405, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_853(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_869(v93, v94, v108, v115, v117, 0, v142, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) :|: 0 = 0
f_869(v93, v94, v108, v115, v117, 0, v142, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v109, v116, v118, v104, v105, 3, 1, 4) -> f_882(v142, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, v157, 3, 1, 4) :|: 0 = 0
f_882(v142, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, v157, 3, 1, 4) -> f_905(v142, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, 3, 1, 4) :|: TRUE
f_905(v142, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v93, v94, 3, 1, 4) -> f_285(v142, v3508, v95, v96, v97, v98, v99, v100, v101, v102, 0, v104, v105, 3, 1, 4) :|: TRUE
f_891(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_853(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
f_918(v93, 0, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) -> f_844(v93, 0, v3405, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, v104, v105, 1, v142, 3, 4, 2) :|: TRUE
f_928(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_891(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
f_958(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) -> f_928(v93, v157, v3508, v95, v96, v97, v98, v99, v100, v101, v102, v108, v109, v115, v116, v117, v118, 0, v104, v105, v94, v142, 3, 1, 4) :|: TRUE
Combined rules. Obtained 3 rulesP rules:
f_288(1 + v141:0, 0, v108:0, v95:0, v96:0, v97:0, v98:0, v99:0, v100:0, v101:0, v102:0, v109:0, 0, v104:0, v105:0, 3, 1, 4) -> f_288(v141:0, 1, v108:1, v95:0, v96:0, v97:0, v98:0, v99:0, v100:0, v101:0, v102:0, 3 + v108:1, 0, v104:0, v105:0, 3, 1, 4) :|: v117:0 > 0 && v115:0 > 0 && v104:0 > 0 && v141:0 > -1 && v108:1 > 0
f_288(1 + v142:0, 1 + v157:0, v108:0, v95:0, v96:0, v97:0, v98:0, v99:0, v100:0, v101:0, v102:0, v109:0, 0, v104:0, v105:0, 3, 1, 4) -> f_288(v142:0, v1960:0, v108:1, v95:0, v96:0, v97:0, v98:0, v99:0, v100:0, v101:0, v102:0, 3 + v108:1, 0, v104:0, v105:0, 3, 1, 4) :|: v117:0 > 0 && v115:0 > 0 && v104:0 > 0 && v142:0 > -1 && v157:0 > -1 && v108:1 > 0
f_288(1 + v142:0, 1 + v157:0, v108:0, v95:0, v96:0, v97:0, v98:0, v99:0, v100:0, v101:0, v102:0, v109:0, 0, v104:0, v105:0, 3, 1, 4) -> f_288(1 + v142:0, v157:0, v108:1, v95:0, v96:0, v97:0, v98:0, v99:0, v100:0, v101:0, v102:0, 3 + v108:1, 0, v104:0, v105:0, 3, 1, 4) :|: v117:0 > 0 && v115:0 > 0 && v104:0 > 0 && v142:0 > -1 && v157:0 > -1 && v108:1 > 0
Filtered unneeded arguments:
   f_288(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_288(x1, x2, x14)
Removed division, modulo operations, cleaned up constraints. Obtained 3 rules.P rules:
f_288(sum~cons_1~v141:0, cons_0, v104:0) -> f_288(v141:0, 1, v104:0) :|: v104:0 > 0 && v141:0 > -1 && sum~cons_1~v141:0 = 1 + v141:0 && cons_0 = 0
f_288(sum~cons_1~v142:0, sum~cons_1~v157:0, v104:0) -> f_288(v142:0, v1960:0, v104:0) :|: v142:0 > -1 && v157:0 > -1 && v104:0 > 0 && sum~cons_1~v142:0 = 1 + v142:0 && sum~cons_1~v157:0 = 1 + v157:0
f_288(sum~cons_1~v142:0, sum~cons_1~v157:0, v104:0) -> f_288(1 + v142:0, v157:0, v104:0) :|: v142:0 > -1 && v157:0 > -1 && v104:0 > 0 && sum~cons_1~v142:0 = 1 + v142:0 && sum~cons_1~v157:0 = 1 + v157:0

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(8)
Obligation:
Rules:
f_288(sum~cons_1~v141:0, cons_0, v104:0) -> f_288(v141:0, 1, v104:0) :|: v104:0 > 0 && v141:0 > -1 && sum~cons_1~v141:0 = 1 + v141:0 && cons_0 = 0
f_288(x, x1, x2) -> f_288(x3, x4, x2) :|: x3 > -1 && x5 > -1 && x2 > 0 && x = 1 + x3 && x1 = 1 + x5
f_288(x6, x7, x8) -> f_288(1 + x9, x10, x8) :|: x9 > -1 && x10 > -1 && x8 > 0 && x6 = 1 + x9 && x7 = 1 + x10

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f_288(sum~cons_1~v141:0:0, cons_0, v104:0:0) -> f_288(v141:0:0, 1, v104:0:0) :|: v104:0:0 > 0 && v141:0:0 > -1 && sum~cons_1~v141:0:0 = 1 + v141:0:0 && cons_0 = 0
f_288(sum~cons_1~x9:0, sum~cons_1~x10:0, x8:0) -> f_288(1 + x9:0, x10:0, x8:0) :|: x9:0 > -1 && x10:0 > -1 && x8:0 > 0 && sum~cons_1~x9:0 = 1 + x9:0 && sum~cons_1~x10:0 = 1 + x10:0
f_288(sum~cons_1~x3:0, sum~cons_1~x5:0, x2:0) -> f_288(x3:0, x4:0, x2:0) :|: x3:0 > -1 && x5:0 > -1 && x2:0 > 0 && sum~cons_1~x3:0 = 1 + x3:0 && sum~cons_1~x5:0 = 1 + x5:0

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_288 ] = f_288_1

The following rules are decreasing:
f_288(sum~cons_1~v141:0:0, cons_0, v104:0:0) -> f_288(v141:0:0, 1, v104:0:0) :|: v104:0:0 > 0 && v141:0:0 > -1 && sum~cons_1~v141:0:0 = 1 + v141:0:0 && cons_0 = 0
f_288(sum~cons_1~x3:0, sum~cons_1~x5:0, x2:0) -> f_288(x3:0, x4:0, x2:0) :|: x3:0 > -1 && x5:0 > -1 && x2:0 > 0 && sum~cons_1~x3:0 = 1 + x3:0 && sum~cons_1~x5:0 = 1 + x5:0

The following rules are bounded:
f_288(sum~cons_1~v141:0:0, cons_0, v104:0:0) -> f_288(v141:0:0, 1, v104:0:0) :|: v104:0:0 > 0 && v141:0:0 > -1 && sum~cons_1~v141:0:0 = 1 + v141:0:0 && cons_0 = 0
f_288(sum~cons_1~x9:0, sum~cons_1~x10:0, x8:0) -> f_288(1 + x9:0, x10:0, x8:0) :|: x9:0 > -1 && x10:0 > -1 && x8:0 > 0 && sum~cons_1~x9:0 = 1 + x9:0 && sum~cons_1~x10:0 = 1 + x10:0
f_288(sum~cons_1~x3:0, sum~cons_1~x5:0, x2:0) -> f_288(x3:0, x4:0, x2:0) :|: x3:0 > -1 && x5:0 > -1 && x2:0 > 0 && sum~cons_1~x3:0 = 1 + x3:0 && sum~cons_1~x5:0 = 1 + x5:0


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(12)
Obligation:
Rules:
f_288(sum~cons_1~x9:0, sum~cons_1~x10:0, x8:0) -> f_288(1 + x9:0, x10:0, x8:0) :|: x9:0 > -1 && x10:0 > -1 && x8:0 > 0 && sum~cons_1~x9:0 = 1 + x9:0 && sum~cons_1~x10:0 = 1 + x10:0

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f_288(sum~cons_1~x9:0:0, sum~cons_1~x10:0:0, x8:0:0) -> f_288(1 + x9:0:0, x10:0:0, x8:0:0) :|: x9:0:0 > -1 && x10:0:0 > -1 && x8:0:0 > 0 && sum~cons_1~x9:0:0 = 1 + x9:0:0 && sum~cons_1~x10:0:0 = 1 + x10:0:0

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(15) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_288(x, x1, x2)] = x1

The following rules are decreasing:
f_288(sum~cons_1~x9:0:0, sum~cons_1~x10:0:0, x8:0:0) -> f_288(1 + x9:0:0, x10:0:0, x8:0:0) :|: x9:0:0 > -1 && x10:0:0 > -1 && x8:0:0 > 0 && sum~cons_1~x9:0:0 = 1 + x9:0:0 && sum~cons_1~x10:0:0 = 1 + x10:0:0
The following rules are bounded:
f_288(sum~cons_1~x9:0:0, sum~cons_1~x10:0:0, x8:0:0) -> f_288(1 + x9:0:0, x10:0:0, x8:0:0) :|: x9:0:0 > -1 && x10:0:0 > -1 && x8:0:0 > 0 && sum~cons_1~x9:0:0 = 1 + x9:0:0 && sum~cons_1~x10:0:0 = 1 + x10:0:0

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(16)
YES