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TRS Standard pair #516961917
details
property
value
status
complete
benchmark
Ex1_Luc04b_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n066.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
0.622103214264 seconds
cpu usage
1.194067464
max memory
1.42225408E8
stage attributes
key
value
output-size
3829
starexec-result
NO
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- NO ** BEGIN proof argument ** The following pattern rule was generated by the strategy presented in Sect. 3 of [Emmes, Enger, Giesl, IJCAR'12]: [iteration = 0] nats{}^n{} -> nats{}^n{} We apply Theorem 8 of [Emmes, Enger, Giesl, IJCAR'12] on this rule with m = 1, b = 0, pi = epsilon, sigma' = {} and mu' = {}. Hence the term nats, obtained from instantiating n with 0 in the left-hand side of the rule, starts an infinite derivation 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... ## 3 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [3 DP problems]: ## DP problem: Dependency pairs = [pairs^# -> odds^#, odds^# -> pairs^#] TRS = {nats -> cons(0,n__incr(nats)), pairs -> cons(0,n__incr(odds)), odds -> incr(pairs), incr(cons(_0,_1)) -> cons(s(_0),n__incr(activate(_1))), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> activate(_1), incr(_0) -> n__incr(_0), activate(n__incr(_0)) -> incr(_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... Failed! ## Trying with Knuth-Bendix orders... Failed! Don't know whether this DP problem is finite. ## DP problem: Dependency pairs = [incr^#(cons(_0,_1)) -> activate^#(_1), activate^#(n__incr(_0)) -> incr^#(_0)] TRS = {nats -> cons(0,n__incr(nats)), pairs -> cons(0,n__incr(odds)), odds -> incr(pairs), incr(cons(_0,_1)) -> cons(s(_0),n__incr(activate(_1))), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> activate(_1), incr(_0) -> n__incr(_0), activate(n__incr(_0)) -> incr(_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... Failed! ## Trying with Knuth-Bendix orders... Failed! Don't know whether this DP problem is finite. ## DP problem: Dependency pairs = [nats^# -> nats^#] TRS = {nats -> cons(0,n__incr(nats)), pairs -> cons(0,n__incr(odds)), odds -> incr(pairs), incr(cons(_0,_1)) -> cons(s(_0),n__incr(activate(_1))), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> activate(_1), incr(_0) -> n__incr(_0), activate(n__incr(_0)) -> incr(_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... Failed! ## Trying with Knuth-Bendix orders... Failed! Don't know whether this DP problem is finite. ## Some DP problems could not be proved finite. ## Now, we try to prove that one of these problems is infinite. ## Trying to prove non-looping nontermination # Iteration 0: success, non-looping nontermination proved, 1 unfolded rule generated. Here is the successful unfolding. Let IR be the TRS under analysis. IR contains the dependency pair nats^# -> nats^#. We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair. ==> P0 = nats^#{}^n{} -> nats^#{}^n{} is in U_IR^0. 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 = 13
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