details

property	value
status	complete
benchmark	ex1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	AProVE_10

run statistics

property	value
solver	NTI_22
configuration	default
runtime (wallclock)	0.386539936066 seconds
cpu usage	0.762876825
max memory	8.0961536E7

stage attributes

key	value
output-size	4503
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 pattern rule was generated by the strategy presented in Sect. 3 of [Emmes, Enger, Giesl, IJCAR'12]: [iteration = 4] cond(tt,_0,_1){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} -> cond(tt,s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} We apply Theorem 8 of [Emmes, Enger, Giesl, IJCAR'12] on this rule with m = 1, b = 1, pi = epsilon, sigma' = {} and mu' = {}. Hence the term cond(tt,s(0),s(_2)), 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... ## 2 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [2 DP problems]: ## DP problem: Dependency pairs = [f^#(_0,_1) -> cond^#(lt(_0,_1),_0,_1), cond^#(tt,_0,_1) -> f^#(s(_0),s(_1))] TRS = {f(_0,_1) -> cond(lt(_0,_1),_0,_1), cond(tt,_0,_1) -> f(s(_0),s(_1)), lt(0,_0) -> tt, lt(s(_0),s(_1)) -> lt(_0,_1)} ## 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 = [lt^#(s(_0),s(_1)) -> lt^#(_0,_1)] TRS = {f(_0,_1) -> cond(lt(_0,_1),_0,_1), cond(tt,_0,_1) -> f(s(_0),s(_1)), lt(0,_0) -> tt, lt(s(_0),s(_1)) -> lt(_0,_1)} ## Trying with homeomorphic embeddings... Success! 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 prove non-looping nontermination # Iteration 0: non-looping nontermination not proved, 2 unfolded rules generated. # Iteration 1: non-looping nontermination not proved, 6 unfolded rules generated. # Iteration 2: non-looping nontermination not proved, 17 unfolded rules generated. # Iteration 3: non-looping nontermination not proved, 46 unfolded rules generated. # Iteration 4: success, non-looping nontermination proved, 112 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. IR contains the dependency pair cond^#(tt,_0,_1) -> f^#(s(_0),s(_1)). We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair. ==> P0 = cond^#(tt,_0,_1){}^n{} -> f^#(s(_0),s(_1)){}^n{} is in U_IR^0. We apply (VI) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position epsilon using the pattern rule f(_0,_1){}^n{} -> cond(lt(_0,_1),_0,_1){}^n{} obtained from IR. ==> P1 = cond^#(tt,_0,_1){}^n{} -> cond(lt(s(_0),s(_1)),s(_0),s(_1)){}^n{} is in U_IR^1. We apply (VI) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the pattern rule lt(s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} -> lt(_2,_3){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} obtained from IR. ==> P2 = cond^#(tt,_0,_1){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} -> cond(lt(_2,_3),s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} is in U_IR^2. We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the rule lt(s(_0),s(_1)) -> lt(_0,_1) of IR. ==> P3 = cond^#(tt,_0,_1){_0->s(_0), _1->s(_1)}^n{_0->s(_2), _1->s(_3)} -> cond(lt(_2,_3),s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(_2), _1->s(_3)} is in U_IR^3. We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the rule lt(0,_0) -> tt of IR. ==> P4 = cond^#(tt,_0,_1){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} -> cond(tt,s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} is in U_IR^4. 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 = 485 popout

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