details

property	value
status	complete
benchmark	Ex4_DLMMU04_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n003.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	NTI_23
configuration	default
runtime (wallclock)	1.80171084404 seconds
cpu usage	6.458528586
max memory	7.003136E8

stage attributes

key	value
output-size	7808
starexec-result	"NO"

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO ** BEGIN proof argument ** * Certificate: isNatIList(n__cons(_0,n__zeros)) is non-terminating * Description: The following rule R was generated while unfolding the dependency pairs of the analyzed TRS: [iteration = 4] isNatIList^#(n__cons(_0,n__zeros)) -> isNatIList^#(n__cons(0,n__zeros)) Let l be the left-hand side and r be the right-hand side of R. Let p = epsilon, theta1 = {} and theta2 = {_0->0}. We have r|p = isNatIList^#(n__cons(0,n__zeros)) and theta2(theta1(l)) = theta1(r|p), i.e., l semi-unifies with r|p. So, the term theta1(l) = isNatIList(n__cons(_0,n__zeros)) starts an infinite rewrite sequence w.r.t. the analyzed TRS. ** END proof argument ** ** BEGIN proof description ** ## Searching for a generalized rewrite rule (a rule whose right-hand side contains a variable that does not occur in the left-hand side)... No generalized rewrite rule found! ## Applying the DP framework... ## 1 initial DP problem to solve. ## First, we try to decompose this problem into smaller problems. ## Round 1 [1 DP problem]: ## DP problem: Dependency pairs = [isNatIList^#(_0) -> isNatList^#(activate(_0)), isNatIList^#(n__cons(_0,_1)) -> isNatIList^#(activate(_1)), isNatList^#(n__take(_0,_1)) -> isNatIList^#(activate(_1)), isNat^#(n__length(_0)) -> isNatList^#(activate(_0)), isNat^#(n__s(_0)) -> isNat^#(activate(_0)), isNatIList^#(n__cons(_0,_1)) -> isNat^#(activate(_0)), take^#(0,_0) -> isNatIList^#(_0), activate^#(n__take(_0,_1)) -> take^#(activate(_0),activate(_1)), isNat^#(n__s(_0)) -> activate^#(_0), isNatList^#(n__cons(_0,_1)) -> isNat^#(activate(_0)), isNatList^#(n__cons(_0,_1)) -> isNatList^#(activate(_1)), length^#(cons(_0,_1)) -> isNatList^#(activate(_1)), uLength^#(tt,_0) -> length^#(activate(_0)), length^#(cons(_0,_1)) -> uLength^#(and(isNat(_0),isNatList(activate(_1))),activate(_1)), activate^#(n__length(_0)) -> length^#(activate(_0)), activate^#(n__s(_0)) -> activate^#(_0), activate^#(n__length(_0)) -> activate^#(_0), activate^#(n__cons(_0,_1)) -> activate^#(_0), activate^#(n__take(_0,_1)) -> activate^#(_0), activate^#(n__take(_0,_1)) -> activate^#(_1), uLength^#(tt,_0) -> activate^#(_0), length^#(cons(_0,_1)) -> activate^#(_1), length^#(cons(_0,_1)) -> activate^#(_1), uTake2^#(tt,_0,_1,_2) -> activate^#(_2), uTake2^#(tt,_0,_1,_2) -> activate^#(_0), uTake2^#(tt,_0,_1,_2) -> activate^#(_1), take^#(s(_0),cons(_1,_2)) -> uTake2^#(and(isNat(_0),and(isNat(_1),isNatIList(activate(_2)))),_0,_1,activate(_2)), take^#(s(_0),cons(_1,_2)) -> activate^#(_2), take^#(s(_0),cons(_1,_2)) -> activate^#(_2), isNatList^#(n__take(_0,_1)) -> activate^#(_1), isNatList^#(n__take(_0,_1)) -> activate^#(_0), isNatList^#(n__cons(_0,_1)) -> activate^#(_1), isNatList^#(n__cons(_0,_1)) -> activate^#(_0), isNatIList^#(n__cons(_0,_1)) -> activate^#(_1), isNatIList^#(n__cons(_0,_1)) -> activate^#(_0), isNat^#(n__length(_0)) -> activate^#(_0), length^#(cons(_0,_1)) -> isNat^#(_0), take^#(s(_0),cons(_1,_2)) -> isNat^#(_1), take^#(s(_0),cons(_1,_2)) -> isNat^#(_0), isNatList^#(n__take(_0,_1)) -> isNat^#(activate(_0)), isNatIList^#(_0) -> activate^#(_0), take^#(s(_0),cons(_1,_2)) -> isNatIList^#(activate(_2))] TRS = {and(tt,_0) -> _0, isNatIList(_0) -> isNatList(activate(_0)), isNat(n__0) -> tt, isNat(n__s(_0)) -> isNat(activate(_0)), isNat(n__length(_0)) -> isNatList(activate(_0)), isNatIList(n__zeros) -> tt, isNatIList(n__cons(_0,_1)) -> and(isNat(activate(_0)),isNatIList(activate(_1))), isNatList(n__nil) -> tt, isNatList(n__cons(_0,_1)) -> and(isNat(activate(_0)),isNatList(activate(_1))), isNatList(n__take(_0,_1)) -> and(isNat(activate(_0)),isNatIList(activate(_1))), zeros -> cons(0,n__zeros), take(0,_0) -> uTake1(isNatIList(_0)), uTake1(tt) -> nil, take(s(_0),cons(_1,_2)) -> uTake2(and(isNat(_0),and(isNat(_1),isNatIList(activate(_2)))),_0,_1,activate(_2)), uTake2(tt,_0,_1,_2) -> cons(activate(_1),n__take(activate(_0),activate(_2))), length(cons(_0,_1)) -> uLength(and(isNat(_0),isNatList(activate(_1))),activate(_1)), uLength(tt,_0) -> s(length(activate(_0))), 0 -> n__0, s(_0) -> n__s(_0), length(_0) -> n__length(_0), zeros -> n__zeros, cons(_0,_1) -> n__cons(_0,_1), nil -> n__nil, take(_0,_1) -> n__take(_0,_1), activate(n__0) -> 0, activate(n__s(_0)) -> s(activate(_0)), activate(n__length(_0)) -> length(activate(_0)), activate(n__zeros) -> zeros, activate(n__cons(_0,_1)) -> cons(activate(_0),_1), activate(n__nil) -> nil, activate(n__take(_0,_1)) -> take(activate(_0),activate(_1)), activate(_0) -> _0} ## DP Processor: homeomorphic embeddings. Using no argument filtering, i.e., applying the processor to the full problem only. Failed! ## DP Processor: lexicographic path orders. Using no argument filtering, i.e., applying the processor to the full problem only. This DP problem is too complex (31 symbols to deal with)! Aborting! Failed! ## DP Processor: polynomial interpretations. Using no argument filtering, i.e., applying the processor to the full problem only. This DP problem is too complex! Aborting! Failed! ## DP Processor: Knuth-Bendix orders. Using no argument filtering, i.e., applying the processor to the full problem only. This DP problem is too complex (23 weights to instantiate)! Aborting! Failed! All the DP processors have failed! Don't know whether this DP problem is finite. ## A DP problem could not be proved finite. ## Now, we try to prove that this problem is infinite. ## DP Processor: [Payet, LOPSTR'18] + [Payet, Non-termination in TRS and LP] (forward=true, backward=false, max=-1). # max_depth=5, unfold_variables=false: # Iteration 0: infiniteness not proved, 42 unfolded rules generated. # Iteration 1: infiniteness not proved, 428 unfolded rules generated. # Iteration 2: infiniteness not proved, 2644 unfolded rules generated. # Iteration 3: infiniteness not proved, 14312 unfolded rules generated. # Iteration 4: success, loop found, 3007 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = isNatIList^#(n__cons(_0,_1)) -> isNatIList^#(activate(_1)) [trans] is in U_IR^0. D = isNatIList^#(n__cons(_0,_1)) -> isNat^#(activate(_0)) is a dependency pair of IR. We build a composed triple from L0 and D. ==> L1 = [isNatIList^#(n__cons(_0,_1)) -> isNatIList^#(activate(_1)), isNatIList^#(n__cons(_2,_3)) -> isNat^#(activate(_2))] [comp] is in U_IR^1. Let p1 = [0]. We unfold the first rule of L1 forwards at position p1 with the rule activate(n__zeros) -> zeros. ==> L2 = [isNatIList^#(n__cons(_0,n__zeros)) -> isNatIList^#(zeros), isNatIList^#(n__cons(_1,_2)) -> isNat^#(activate(_1))] [comp] is in U_IR^2. Let p2 = [0]. We unfold the first rule of L2 forwards at position p2 with the rule zeros -> cons(0,n__zeros). ==> L3 = [isNatIList^#(n__cons(_0,n__zeros)) -> isNatIList^#(cons(0,n__zeros)), isNatIList^#(n__cons(_1,_2)) -> isNat^#(activate(_1))] [comp] is in U_IR^3. Let p3 = [0]. We unfold the first rule of L3 forwards at position p3 with the rule cons(_0,_1) -> n__cons(_0,_1). ==> L4 = [isNatIList^#(n__cons(_0,n__zeros)) -> isNatIList^#(n__cons(0,n__zeros)), isNatIList^#(n__cons(_1,_2)) -> isNat^#(activate(_1))] [comp] is in U_IR^4. This DP problem is infinite. Proof run on Linux version 3.10.0-1160.62.1.el7.x86_64 for amd64 using Java version 1.8.0_322 ** END proof description ** Total number of generated unfolded rules = 45438 popout

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all output return to TRS Standard