details

property	value
status	complete
benchmark	enger-nonloop-toOne.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n032.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	NTI_22
configuration	default
runtime (wallclock)	9.97804307938 seconds
cpu usage	10.587629548
max memory	5.45140736E8

stage attributes

key	value
output-size	4553
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 = 4] f(tt,s(s(_0))){_0->s(_0)}^n{_0->0} -> f(tt,s(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(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... ## 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 = [f^#(tt,_0) -> f^#(eq(toOne(_0),s(0)),s(_0))] TRS = {f(tt,_0) -> f(eq(toOne(_0),s(0)),s(_0)), eq(s(_0),s(_1)) -> eq(_0,_1), eq(0,0) -> tt, toOne(s(s(_0))) -> toOne(s(_0)), toOne(s(0)) -> s(0)} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... Failed! ## 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 = [toOne^#(s(s(_0))) -> toOne^#(s(_0))] TRS = {f(tt,_0) -> f(eq(toOne(_0),s(0)),s(_0)), eq(s(_0),s(_1)) -> eq(_0,_1), eq(0,0) -> tt, toOne(s(s(_0))) -> toOne(s(_0)), toOne(s(0)) -> s(0)} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [eq^#(s(_0),s(_1)) -> eq^#(_0,_1)] TRS = {f(tt,_0) -> f(eq(toOne(_0),s(0)),s(_0)), eq(s(_0),s(_1)) -> eq(_0,_1), eq(0,0) -> tt, toOne(s(s(_0))) -> toOne(s(_0)), toOne(s(0)) -> s(0)} ## 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, 1 unfolded rule generated. # Iteration 1: non-looping nontermination not proved, 5 unfolded rules generated. # Iteration 2: non-looping nontermination not proved, 16 unfolded rules generated. # Iteration 3: non-looping nontermination not proved, 43 unfolded rules generated. # Iteration 4: success, non-looping nontermination proved, 98 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. IR contains the dependency pair f^#(tt,_0) -> f^#(eq(toOne(_0),s(0)),s(_0)). We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair. ==> P0 = f^#(tt,_0){}^n{} -> f^#(eq(toOne(_0),s(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, 0] using the pattern rule toOne(s(s(_0))){_0->s(_0)}^n{_0->_1} -> toOne(s(_1)){_0->s(_0)}^n{_0->_1} obtained from IR. ==> P1 = f^#(tt,s(s(_0))){_0->s(_0)}^n{_0->_1} -> f^#(eq(toOne(s(_1)),s(0)),s(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, 0] using the rule toOne(s(0)) -> s(0) of IR. ==> P2 = f^#(tt,s(s(_0))){_0->s(_0)}^n{_0->0} -> f^#(eq(s(0),s(0)),s(s(s(_0)))){_0->s(_0)}^n{_0->0} is in U_IR^2. We apply (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the rule eq(s(_0),s(_1)) -> eq(_0,_1) of IR. ==> P3 = f^#(tt,s(s(_0))){_0->s(_0)}^n{_0->0} -> f^#(eq(0,0),s(s(s(_0)))){_0->s(_0)}^n{_0->0} is in U_IR^3. We apply (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the rule eq(0,0) -> tt of IR. ==> P4 = f^#(tt,s(s(_0))){_0->s(_0)}^n{_0->0} -> f^#(tt,s(s(s(_0)))){_0->s(_0)}^n{_0->0} 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 = 482 popout

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