details

property	value
status	complete
benchmark	LengthOfFiniteLists_nokinds_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	NTI_22
configuration	default
runtime (wallclock)	102.805165052 seconds
cpu usage	331.921468493
max memory	1.608515584E10

stage attributes

key	value
output-size	7590
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 ** The following rule was generated while unfolding the analyzed TRS: [iteration = 8] isNatList(n__cons(n__0,n__zeros)) -> isNatList(n__cons(n__0,n__zeros)) Let l be the left-hand side and r be the right-hand side of this rule. Let p = epsilon, theta1 = {} and theta2 = {}. We have r|p = isNatList(n__cons(n__0,n__zeros)) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = isNatList(n__cons(n__0,n__zeros)) loops 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 = [U11^#(tt,_0) -> length^#(activate(_0)), length^#(cons(_0,_1)) -> U11^#(and(isNatList(activate(_1)),n__isNat(_0)),activate(_1)), activate^#(n__length(_0)) -> length^#(activate(_0)), and^#(tt,_0) -> activate^#(_0), length^#(cons(_0,_1)) -> and^#(isNatList(activate(_1)),n__isNat(_0)), isNatList^#(n__cons(_0,_1)) -> and^#(isNat(activate(_0)),n__isNatList(activate(_1))), isNatIList^#(n__cons(_0,_1)) -> and^#(isNat(activate(_0)),n__isNatIList(activate(_1))), activate^#(n__isNatIList(_0)) -> isNatIList^#(_0), isNat^#(n__length(_0)) -> activate^#(_0), isNat^#(n__s(_0)) -> isNat^#(activate(_0)), isNatList^#(n__cons(_0,_1)) -> isNat^#(activate(_0)), isNat^#(n__length(_0)) -> isNatList^#(activate(_0)), activate^#(n__isNat(_0)) -> isNat^#(_0), isNatList^#(n__cons(_0,_1)) -> activate^#(_0), activate^#(n__isNatList(_0)) -> isNatList^#(_0), activate^#(n__length(_0)) -> activate^#(_0), activate^#(n__s(_0)) -> activate^#(_0), activate^#(n__cons(_0,_1)) -> activate^#(_0), length^#(cons(_0,_1)) -> activate^#(_1), length^#(cons(_0,_1)) -> activate^#(_1), isNatList^#(n__cons(_0,_1)) -> activate^#(_1), length^#(cons(_0,_1)) -> isNatList^#(activate(_1)), isNatIList^#(_0) -> isNatList^#(activate(_0)), isNatIList^#(n__cons(_0,_1)) -> activate^#(_1), isNatIList^#(n__cons(_0,_1)) -> activate^#(_0), isNatIList^#(_0) -> activate^#(_0), isNat^#(n__s(_0)) -> activate^#(_0), isNatIList^#(n__cons(_0,_1)) -> isNat^#(activate(_0)), U11^#(tt,_0) -> activate^#(_0)] TRS = {zeros -> cons(0,n__zeros), U11(tt,_0) -> s(length(activate(_0))), and(tt,_0) -> activate(_0), isNat(n__0) -> tt, isNat(n__length(_0)) -> isNatList(activate(_0)), isNat(n__s(_0)) -> isNat(activate(_0)), isNatIList(_0) -> isNatList(activate(_0)), isNatIList(n__zeros) -> tt, isNatIList(n__cons(_0,_1)) -> and(isNat(activate(_0)),n__isNatIList(activate(_1))), isNatList(n__nil) -> tt, isNatList(n__cons(_0,_1)) -> and(isNat(activate(_0)),n__isNatList(activate(_1))), length(nil) -> 0, length(cons(_0,_1)) -> U11(and(isNatList(activate(_1)),n__isNat(_0)),activate(_1)), zeros -> n__zeros, 0 -> n__0, length(_0) -> n__length(_0), s(_0) -> n__s(_0), cons(_0,_1) -> n__cons(_0,_1), isNatIList(_0) -> n__isNatIList(_0), nil -> n__nil, isNatList(_0) -> n__isNatList(_0), isNat(_0) -> n__isNat(_0), activate(n__zeros) -> zeros, activate(n__0) -> 0, activate(n__length(_0)) -> length(activate(_0)), activate(n__s(_0)) -> s(activate(_0)), activate(n__cons(_0,_1)) -> cons(activate(_0),_1), activate(n__isNatIList(_0)) -> isNatIList(_0), activate(n__nil) -> nil, activate(n__isNatList(_0)) -> isNatList(_0), activate(n__isNat(_0)) -> isNat(_0), activate(_0) -> _0} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... This DP problem is too complex! Aborting! ## Trying with lexicographic path orders... Too many argument filtering possibilities (165888)! Aborting! ## Trying with Knuth-Bendix orders... This DP problem is too complex! Aborting! 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. ## Trying to find a loop (forward=true, backward=false, max=-1) # max_depth=4, unfold_variables=false: # Iteration 0: no loop found, 29 unfolded rules generated. # Iteration 1: no loop found, 257 unfolded rules generated. # Iteration 2: no loop found, 1480 unfolded rules generated. # Iteration 3: no loop found, 5100 unfolded rules generated. # Iteration 4: no loop found, 15305 unfolded rules generated. # Iteration 5: no loop found, 45610 unfolded rules generated. # Iteration 6: no loop found, 142419 unfolded rules generated. # Iteration 7: no loop found, 393313 unfolded rules generated. # Iteration 8: success, found a loop, 402726 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = isNatList^#(n__cons(_0,_1)) -> and^#(isNat(activate(_0)),n__isNatList(activate(_1))) [trans] is in U_IR^0. D = and^#(tt,_0) -> activate^#(_0) is a dependency pair of IR. We build a composed triple from L0 and D. ==> L1 = [isNatList^#(n__cons(_0,_1)) -> and^#(isNat(activate(_0)),n__isNatList(activate(_1))), and^#(tt,_2) -> activate^#(_2)] [comp] is in U_IR^1. Let p1 = [0, 0]. We unfold the first rule of L1 forwards at position p1 with the rule activate(_0) -> _0. ==> L2 = [isNatList^#(n__cons(_0,_1)) -> and^#(isNat(_0),n__isNatList(activate(_1))), and^#(tt,_2) -> activate^#(_2)] [comp] is in U_IR^2. Let p2 = [0]. We unfold the first rule of L2 forwards at position p2 with the rule isNat(n__0) -> tt. ==> L3 = [isNatList^#(n__cons(n__0,_0)) -> and^#(tt,n__isNatList(activate(_0))), and^#(tt,_1) -> activate^#(_1)] [comp] is in U_IR^3. Let p3 = [1, 0]. We unfold the first rule of L3 forwards at position p3 with the rule activate(n__zeros) -> zeros. ==> L4 = [isNatList^#(n__cons(n__0,n__zeros)) -> and^#(tt,n__isNatList(zeros)), and^#(tt,_0) -> activate^#(_0)] [comp] is in U_IR^4. Let p4 = [1, 0]. We unfold the first rule of L4 forwards at position p4 with the rule zeros -> cons(0,n__zeros). ==> L5 = [isNatList^#(n__cons(n__0,n__zeros)) -> and^#(tt,n__isNatList(cons(0,n__zeros))), and^#(tt,_0) -> activate^#(_0)] [comp] is in U_IR^5. Let p5 = [1, 0]. We unfold the first rule of L5 forwards at position p5 with the rule cons(_0,_1) -> n__cons(_0,_1). ==> L6 = [isNatList^#(n__cons(n__0,n__zeros)) -> and^#(tt,n__isNatList(n__cons(0,n__zeros))), and^#(tt,_0) -> activate^#(_0)] [comp] is in U_IR^6. Let p6 = [1, 0, 0]. We unfold the first rule of L6 forwards at position p6 with the rule 0 -> n__0. ==> L7 = isNatList^#(n__cons(n__0,n__zeros)) -> activate^#(n__isNatList(n__cons(n__0,n__zeros))) [trans] is in U_IR^7. D = activate^#(n__isNatList(_0)) -> isNatList^#(_0) is a dependency pair of IR. We build a composed triple from L7 and D. ==> L8 = isNatList^#(n__cons(n__0,n__zeros)) -> isNatList^#(n__cons(n__0,n__zeros)) [trans] is in U_IR^8. This DP problem is infinite. Proof run on Linux version 3.10.0-1160.25.1.el7.x86_64 for amd64 using Java version 1.8.0_292 ** END proof description ** Total number of generated unfolded rules = 2878736 popout

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all output return to TRS Standard