details

property	value
status	complete
benchmark	isNat.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n185.star.cs.uiowa.edu
space	AProVE_10

run statistics

property	value
solver	NTI-TC20-firstrun
configuration	Default 200
runtime (wallclock)	0.4698 seconds
cpu usage	1.35822
user time	1.28434
system time	0.073884
max virtual memory	113188.0
max residence set size	114368.0

stage attributes

key	value
starexec-result	NO

output

NO Prover = TRS(tech=PATTERN_RULES, nb_unfoldings=unlimited, max_nb_unfolded_rules=200) ** BEGIN proof argument ** The following pattern rule was generated by the strategy presented in Sect. 3 of [Emmes, Enger, Giesl, IJCAR'12]: [iteration = 2] f(tt,s(_0)){_0->s(_0)}^n{_0->0} -> f(tt,s(s(_0))){_0->s(_0)}^n{_0->0} 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 f(tt,s(0)), 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... ## Round 1: ## DP problem: Dependency pairs = [f^#(tt,_0) -> f^#(isNat(_0),s(_0))] TRS = {f(tt,_0) -> f(isNat(_0),s(_0)), isNat(s(_0)) -> isNat(_0), isNat(0) -> tt} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... Failed! ## Trying with lexicographic path orders... Failed! ## Trying to prove nontermination by unfolding the dependency pairs with the rules of the TRS # Iteration 0: nontermination not detected, 1 unfolded rule generated. # Iteration 1: nontermination not detected, 5 unfolded rules generated. # Iteration 2: nontermination detected, 14 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. IR contains the dependency pair f^#(tt,_0) -> f^#(isNat(_0),s(_0)). We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair. ==> P0 = f^#(tt,_0){}^n{} -> f^#(isNat(_0),s(_0)){}^n{} is in U_IR^0. We apply (VI) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the pattern rule isNat(s(_0)){_0->s(_0)}^n{_0->_1} -> isNat(_1){_0->s(_0)}^n{_0->_1} obtained from IR. ==> P1 = f^#(tt,s(_0)){_0->s(_0)}^n{_0->_1} -> f^#(isNat(_1),s(s(_0))){_0->s(_0)}^n{_0->_1} is in U_IR^1. We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the rule isNat(0) -> tt of IR. ==> P2 = f^#(tt,s(_0)){_0->s(_0)}^n{_0->0} -> f^#(tt,s(s(_0))){_0->s(_0)}^n{_0->0} is in U_IR^2. This DP problem is infinite. ** END proof description ** Proof stopped at iteration 2 Number of unfolded rules generated by this proof = 20 Number of unfolded rules generated by all the parallel proofs = 263 popout

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