details

property	value
status	complete
benchmark	Ex24_GM04_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	NTI_23
configuration	default
runtime (wallclock)	0.38431096077 seconds
cpu usage	0.931324106
max memory	8.0314368E7

stage attributes

key	value
output-size	7255
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 ** * Certificate: a__f(c,g(c),mark(g(b))) is non-terminating * Description: The following rule R was generated while unfolding the dependency pairs of the analyzed TRS: [iteration = 9] a__f^#(c,g(c),mark(g(b))) -> a__f^#(c,g(c),mark(g(b))) Let l be the left-hand side and r be the right-hand side of R. Let p = epsilon, theta1 = {} and theta2 = {}. We have r|p = a__f^#(c,g(c),mark(g(b))) and theta2(theta1(l)) = theta1(r|p), i.e., l semi-unifies with r|p. So, the term theta1(l) = a__f(c,g(c),mark(g(b))) starts an infinite rewrite sequence 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 = [mark^#(g(_0)) -> mark^#(_0)] TRS = {a__f(_0,g(_0),_1) -> a__f(_1,_1,_1), a__g(b) -> c, a__b -> c, mark(f(_0,_1,_2)) -> a__f(_0,_1,_2), mark(g(_0)) -> a__g(mark(_0)), mark(b) -> a__b, mark(c) -> c, a__f(_0,_1,_2) -> f(_0,_1,_2), a__g(_0) -> g(_0), a__b -> b} ## DP Processor: homeomorphic embeddings. Using no argument filtering, i.e., applying the processor to the full problem only. Success, finiteness proved! This DP problem is finite. ## DP problem: Dependency pairs = [a__f^#(_0,g(_0),_1) -> a__f^#(_1,_1,_1)] TRS = {a__f(_0,g(_0),_1) -> a__f(_1,_1,_1), a__g(b) -> c, a__b -> c, mark(f(_0,_1,_2)) -> a__f(_0,_1,_2), mark(g(_0)) -> a__g(mark(_0)), mark(b) -> a__b, mark(c) -> c, a__f(_0,_1,_2) -> f(_0,_1,_2), a__g(_0) -> g(_0), a__b -> b} ## DP Processor: homeomorphic embeddings. Using no argument filtering, i.e., applying the processor to the full problem only. Failed! ## DP Processor: lexicographic path orders. Using no argument filtering, i.e., applying the processor to the full problem only. Failed! ## DP Processor: polynomial interpretations. Using no argument filtering, i.e., applying the processor to the full problem only. This DP problem is too complex (25 coefficients to instantiate)! Aborting! Failed! ## DP Processor: Knuth-Bendix orders. Using no argument filtering, i.e., applying the processor to the full problem only. Failed! All the DP processors have failed! 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. ## DP Processor: [Payet, LOPSTR'18] + [Payet, Non-termination in TRS and LP] (forward=true, backward=false, max=-1). # max_depth=2, unfold_variables=false: # Iteration 0: infiniteness not proved, 1 unfolded rule generated. # Iteration 1: infiniteness not proved, 1 unfolded rule generated. # Iteration 2: infiniteness not proved, 0 unfolded rule generated. Could not prove infiniteness! # max_depth=2, unfold_variables=true: # Iteration 0: infiniteness not proved, 1 unfolded rule generated. # Iteration 1: infiniteness not proved, 1 unfolded rule generated. # Iteration 2: infiniteness not proved, 7 unfolded rules generated. # Iteration 3: infiniteness not proved, 11 unfolded rules generated. # Iteration 4: infiniteness not proved, 2 unfolded rules generated. # Iteration 5: infiniteness not proved, 0 unfolded rule generated. Could not prove infiniteness! # max_depth=3, unfold_variables=false: # Iteration 0: infiniteness not proved, 1 unfolded rule generated. # Iteration 1: infiniteness not proved, 1 unfolded rule generated. # Iteration 2: infiniteness not proved, 0 unfolded rule generated. Could not prove infiniteness! # max_depth=3, unfold_variables=true: # Iteration 0: infiniteness not proved, 1 unfolded rule generated. # Iteration 1: infiniteness not proved, 1 unfolded rule generated. # Iteration 2: infiniteness not proved, 10 unfolded rules generated. # Iteration 3: infiniteness not proved, 20 unfolded rules generated. # Iteration 4: infiniteness not proved, 14 unfolded rules generated. # Iteration 5: infiniteness not proved, 20 unfolded rules generated. # Iteration 6: infiniteness not proved, 22 unfolded rules generated. # Iteration 7: infiniteness not proved, 27 unfolded rules generated. # Iteration 8: infiniteness not proved, 32 unfolded rules generated. # Iteration 9: success, loop found, 20 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = a__f^#(_0,g(_0),_1) -> a__f^#(_1,_1,_1) [trans] is in U_IR^0. We build a unit triple from L0. ==> L1 = a__f^#(_0,g(_0),_1) -> a__f^#(_1,_1,_1) [unit] is in U_IR^1. Let p1 = [0]. We unfold the rule of L1 forwards at position p1 with the rule mark(g(_0)) -> a__g(mark(_0)). ==> L2 = a__f^#(_0,g(_0),mark(g(_1))) -> a__f^#(a__g(mark(_1)),mark(g(_1)),mark(g(_1))) [unit] is in U_IR^2. Let p2 = [0, 0]. We unfold the rule of L2 forwards at position p2 with the rule mark(b) -> a__b. popout

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all output return to TRS Standard