/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 174 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 13.6 s]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 2 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 115 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 67 ms]
        (16) IntTRS
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 7 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: "subxy" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%3 = alloca i32, align 4
		%x_ref = alloca *i32, align 8
		%y_ref = alloca *i32, align 8
		%z = alloca *i32, align 8
		%i = alloca *i32, align 8
		store %x, %2
		store %y, %3
		%4 = alloca i8, numElementsLit: 4
		%5 = bitcast *i8 %4 to *i32
		store %5, %x_ref
		%6 = alloca i8, numElementsLit: 4
		%7 = bitcast *i8 %6 to *i32
		store %7, %y_ref
		%8 = alloca i8, numElementsLit: 4
		%9 = bitcast *i8 %8 to *i32
		store %9, %z
		%10 = alloca i8, numElementsLit: 4
		%11 = bitcast *i8 %10 to *i32
		store %11, %i
		%12 = load %2
		%13 = load %x_ref
		store %12, %13
		%14 = load %3
		%15 = load %y_ref
		store %14, %15
		%16 = load %z
		store 0, %16
		%17 = load %x_ref
		%18 = load %17
		%19 = load %i
		store %18, %19
		%20 = load %y_ref
		%21 = load %20
		%22 = icmp sle %21 0
		br %22, %27, %23
	23:
		%24 = load %x_ref
		%25 = load %24
		%26 = icmp sle %25 0
		br %26, %27, %28
	27:
		store 0, %1
		br %57
	28:
		br %29
	29:
		%30 = load %i
		%31 = load %30
		%32 = icmp sgt %31 0
		br %32, %33, %40
	33:
		%34 = load %i
		%35 = load %34
		%36 = add %35 -1
		store %36, %34
		%37 = load %z
		%38 = load %37
		%39 = add %38 1
		store %39, %37
		br %29
	40:
		br %41
	41:
		%42 = load %i
		%43 = load %42
		%44 = load %y_ref
		%45 = load %44
		%46 = icmp slt %43 %45
		br %46, %47, %54
	47:
		%48 = load %i
		%49 = load %48
		%50 = add %49 1
		store %50, %48
		%51 = load %z
		%52 = load %51
		%53 = add %52 -1
		store %53, %51
		br %41
	54:
		%55 = load %z
		%56 = load %55
		store %56, %1
		br %57
	57:
		%58 = load %1
		ret %58

*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
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %x
		%3 = call i32 @__VERIFIER_nondet_int()
		store %3, %y
		%4 = load %x
		%5 = load %y
		%6 = call i32 @subxy(i32 %4, i32 %5)
		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 17 rulesP rules:
f_705(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v780, v781, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) -> f_706(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) :|: 0 = 0
f_706(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) -> f_707(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) :|: 0 = 0
f_707(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) -> f_708(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) :|: 0 = 0
f_708(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) -> f_709(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: v781 < v764 && 2 <= v764
f_709(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_711(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: 0 = 0
f_711(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_713(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: TRUE
f_713(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_715(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: 0 = 0
f_715(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v780, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_717(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: 0 = 0
f_717(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_719(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: v818 = 1 + v781 && 2 <= v818
f_719(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_721(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: TRUE
f_721(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_723(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: 0 = 0
f_723(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_725(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: 0 = 0
f_725(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_727(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v821, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: 1 + v821 = v783
f_727(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v821, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_728(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v821, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: TRUE
f_728(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v821, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_729(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v821, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) :|: TRUE
f_729(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v821, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 2, 4, 8) -> f_704(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v781, v818, v783, v821, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) :|: TRUE
f_704(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v780, v781, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) -> f_705(v763, v764, v765, v766, v767, v768, v769, v770, v771, v772, v773, v774, v775, 0, 1, v778, v779, v780, v781, v782, v783, v784, v787, v785, v788, v786, v789, v790, v791, v792, v793, v794, v795, v796, v797, v798, v799, v800, 3, 7, 4, 8) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_705(v763:0, v764:0, v765:0, v766:0, v767:0, v768:0, v769:0, v770:0, v771:0, v772:0, v773:0, v774:0, v775:0, 0, 1, v778:0, v779:0, v780:0, v781:0, v782:0, 1 + v821:0, v784:0, v787:0, v785:0, v788:0, v786:0, v789:0, v790:0, v791:0, v792:0, v793:0, v794:0, v795:0, v796:0, v797:0, v798:0, v799:0, v800:0, 3, 7, 4, 8) -> f_705(v763:0, v764:0, v765:0, v766:0, v767:0, v768:0, v769:0, v770:0, v771:0, v772:0, v773:0, v774:0, v775:0, 0, 1, v778:0, v779:0, v781:0, 1 + v781:0, 1 + v821:0, v821:0, v784:0, v787:0, v785:0, v788:0, v786:0, v789:0, v790:0, v791:0, v792:0, v793:0, v794:0, v795:0, v796:0, v797:0, v798:0, v799:0, v800:0, 3, 7, 4, 8) :|: v764:0 > 1 && v781:0 > 0 && v781:0 < v764:0
Filtered unneeded arguments:
   f_705(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42) -> f_705(x2, x19, x21)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_705(v764:0, v781:0, sum~cons_1~v821:0) -> f_705(v764:0, 1 + v781:0, v821:0) :|: v781:0 > 0 && v781:0 < v764:0 && v764:0 > 1 && sum~cons_1~v821:0 = 1 + v821:0

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

(9)
Obligation:
Rules:
f_705(v764:0, v781:0, sum~cons_1~v821:0) -> f_705(v764:0, 1 + v781:0, v821:0) :|: v781:0 > 0 && v781:0 < v764:0 && v764:0 > 1 && sum~cons_1~v821:0 = 1 + v821:0

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

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

(11)
Obligation:
Rules:
f_705(v764:0:0, v781:0:0, sum~cons_1~v821:0:0) -> f_705(v764:0:0, 1 + v781:0:0, v821:0:0) :|: v781:0:0 > 0 && v781:0:0 < v764:0:0 && v764:0:0 > 1 && sum~cons_1~v821:0:0 = 1 + v821:0:0

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_705(x, x1, x2)] = -1 + x - x1

The following rules are decreasing:
f_705(v764:0:0, v781:0:0, sum~cons_1~v821:0:0) -> f_705(v764:0:0, 1 + v781:0:0, v821:0:0) :|: v781:0:0 > 0 && v781:0:0 < v764:0:0 && v764:0:0 > 1 && sum~cons_1~v821:0:0 = 1 + v821:0:0
The following rules are bounded:
f_705(v764:0:0, v781:0:0, sum~cons_1~v821:0:0) -> f_705(v764:0:0, 1 + v781:0:0, v821:0:0) :|: v781:0:0 > 0 && v781:0:0 < v764:0:0 && v764:0:0 > 1 && sum~cons_1~v821:0:0 = 1 + v821:0:0

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(13)
YES

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(14)
Obligation:
SCC
----------------------------------------

(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 15 rulesP rules:
f_516(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v260, 1, v262, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 4, 8) -> f_517(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 4, 8) :|: 0 = 0
f_517(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 4, 8) -> f_518(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: 0 < v262 && 2 <= v260 && 2 <= v246
f_518(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_520(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: 0 = 0
f_520(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_522(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: TRUE
f_522(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_524(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: 0 = 0
f_524(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v260, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_526(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: 0 = 0
f_526(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_528(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: 1 + v282 = v262 && 0 <= v282
f_528(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_530(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: TRUE
f_530(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_532(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: 0 = 0
f_532(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_534(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: 0 = 0
f_534(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_536(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v284, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: v284 = 1 + v264 && 2 <= v284
f_536(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v284, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_538(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v284, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: TRUE
f_538(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v284, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_540(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v284, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) :|: TRUE
f_540(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v284, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 2, 4, 8) -> f_515(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v262, 1, v282, v264, v284, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 4, 8) :|: TRUE
f_515(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v260, 1, v262, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 4, 8) -> f_516(v246, v247, v248, v249, v250, v251, v252, v253, v254, v255, v256, v257, v258, 0, v260, 1, v262, v263, v264, v265, v268, v266, v269, v267, v270, v271, v272, v273, v274, v275, v276, v277, v278, v279, v280, v281, 3, 7, 4, 8) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_516(v246:0, v247:0, v248:0, v249:0, v250:0, v251:0, v252:0, v253:0, v254:0, v255:0, v256:0, v257:0, v258:0, 0, v260:0, 1, 1 + v282:0, v263:0, v264:0, v265:0, v268:0, v266:0, v269:0, v267:0, v270:0, v271:0, v272:0, v273:0, v274:0, v275:0, v276:0, v277:0, v278:0, v279:0, v280:0, v281:0, 3, 7, 4, 8) -> f_516(v246:0, v247:0, v248:0, v249:0, v250:0, v251:0, v252:0, v253:0, v254:0, v255:0, v256:0, v257:0, v258:0, 0, 1 + v282:0, 1, v282:0, v264:0, 1 + v264:0, v265:0, v268:0, v266:0, v269:0, v267:0, v270:0, v271:0, v272:0, v273:0, v274:0, v275:0, v276:0, v277:0, v278:0, v279:0, v280:0, v281:0, 3, 7, 4, 8) :|: v260:0 > 1 && v282:0 > -1 && v246:0 > 1 && v264:0 > 0
Filtered unneeded arguments:
   f_516(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40) -> f_516(x1, x15, x17, x19)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_516(v246:0, v260:0, sum~cons_1~v282:0, v264:0) -> f_516(v246:0, 1 + v282:0, v282:0, 1 + v264:0) :|: v282:0 > -1 && v260:0 > 1 && v264:0 > 0 && v246:0 > 1 && sum~cons_1~v282:0 = 1 + v282:0

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(16)
Obligation:
Rules:
f_516(v246:0, v260:0, sum~cons_1~v282:0, v264:0) -> f_516(v246:0, 1 + v282:0, v282:0, 1 + v264:0) :|: v282:0 > -1 && v260:0 > 1 && v264:0 > 0 && v246:0 > 1 && sum~cons_1~v282:0 = 1 + v282:0

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(17) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(18)
Obligation:
Rules:
f_516(v246:0:0, v260:0:0, sum~cons_1~v282:0:0, v264:0:0) -> f_516(v246:0:0, 1 + v282:0:0, v282:0:0, 1 + v264:0:0) :|: v264:0:0 > 0 && v246:0:0 > 1 && v260:0:0 > 1 && v282:0:0 > -1 && sum~cons_1~v282:0:0 = 1 + v282:0:0

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(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_516 ] = f_516_3

The following rules are decreasing:
f_516(v246:0:0, v260:0:0, sum~cons_1~v282:0:0, v264:0:0) -> f_516(v246:0:0, 1 + v282:0:0, v282:0:0, 1 + v264:0:0) :|: v264:0:0 > 0 && v246:0:0 > 1 && v260:0:0 > 1 && v282:0:0 > -1 && sum~cons_1~v282:0:0 = 1 + v282:0:0

The following rules are bounded:
f_516(v246:0:0, v260:0:0, sum~cons_1~v282:0:0, v264:0:0) -> f_516(v246:0:0, 1 + v282:0:0, v282:0:0, 1 + v264:0:0) :|: v264:0:0 > 0 && v246:0:0 > 1 && v260:0:0 > 1 && v282:0:0 > -1 && sum~cons_1~v282:0:0 = 1 + v282:0:0


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(20)
YES