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TRS Standard pair #487069420
details
property
value
status
complete
benchmark
Ex3_3_25_Bor03_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
NTI-TC20-firstrun
configuration
Default 200
runtime (wallclock)
1.08018 seconds
cpu usage
3.24718
user time
3.03587
system time
0.211306
max virtual memory
3.5398796E7
max residence set size
605152.0
stage attributes
key
value
starexec-result
NO
output
NO Prover = TRS(tech=GUIDED_UNF_TRIPLES, nb_unfoldings=unlimited, unfold_variables=false, max_nb_coefficients=12, max_nb_unfolded_rules=-1, strategy=LEFTMOST_NE) ** BEGIN proof argument ** The following rule was generated while unfolding the analyzed TRS: [iteration = 5] activate(n__zWadr(cons(_0,_1),n__prefix(_2))) -> activate(n__zWadr(_2,n__prefix(_2))) Let l be the left-hand side and r be the right-hand side of this rule. Let p = epsilon, theta1 = {_2->cons(_3,_4)} and theta2 = {_1->_4, _0->_3}. We have r|p = activate(n__zWadr(_2,n__prefix(_2))) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = activate(n__zWadr(cons(_0,_1),n__prefix(cons(_3,_4)))) loops 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 = [app^#(cons(_0,_1),_2) -> activate^#(_1), activate^#(n__app(_0,_1)) -> app^#(activate(_0),activate(_1)), zWadr^#(cons(_0,_1),cons(_2,_3)) -> app^#(_2,cons(_0,n__nil)), activate^#(n__zWadr(_0,_1)) -> zWadr^#(activate(_0),activate(_1)), activate^#(n__app(_0,_1)) -> activate^#(_0), activate^#(n__app(_0,_1)) -> activate^#(_1), activate^#(n__from(_0)) -> activate^#(_0), activate^#(n__s(_0)) -> activate^#(_0), activate^#(n__zWadr(_0,_1)) -> activate^#(_0), activate^#(n__zWadr(_0,_1)) -> activate^#(_1), activate^#(n__prefix(_0)) -> activate^#(_0), zWadr^#(cons(_0,_1),cons(_2,_3)) -> activate^#(_3), zWadr^#(cons(_0,_1),cons(_2,_3)) -> activate^#(_1)] TRS = {app(nil,_0) -> _0, app(cons(_0,_1),_2) -> cons(_0,n__app(activate(_1),_2)), from(_0) -> cons(_0,n__from(n__s(_0))), zWadr(nil,_0) -> nil, zWadr(_0,nil) -> nil, zWadr(cons(_0,_1),cons(_2,_3)) -> cons(app(_2,cons(_0,n__nil)),n__zWadr(activate(_1),activate(_3))), prefix(_0) -> cons(nil,n__zWadr(_0,n__prefix(_0))), app(_0,_1) -> n__app(_0,_1), from(_0) -> n__from(_0), s(_0) -> n__s(_0), nil -> n__nil, zWadr(_0,_1) -> n__zWadr(_0,_1), prefix(_0) -> n__prefix(_0), activate(n__app(_0,_1)) -> app(activate(_0),activate(_1)), activate(n__from(_0)) -> from(activate(_0)), activate(n__s(_0)) -> s(activate(_0)), activate(n__nil) -> nil, activate(n__zWadr(_0,_1)) -> zWadr(activate(_0),activate(_1)), activate(n__prefix(_0)) -> prefix(activate(_0)), activate(_0) -> _0} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... Too many coefficients (37)! Aborting! ## Trying with lexicographic path orders... Too many argument filtering possibilities (31104)! Aborting! ## Trying to prove nontermination by unfolding the dependency pairs with the rules of the TRS # max_depth=3, unfold_variables=false: # Iteration 0: nontermination not detected, 13 unfolded rules generated. # Iteration 1: nontermination not detected, 172 unfolded rules generated. # Iteration 2: nontermination not detected, 537 unfolded rules generated. # Iteration 3: nontermination not detected, 168 unfolded rules generated. # Iteration 4: nontermination not detected, 517 unfolded rules generated. # Iteration 5: nontermination detected, 833 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = activate^#(n__zWadr(_0,_1)) -> zWadr^#(activate(_0),activate(_1)) [trans] is in U_IR^0. D = zWadr^#(cons(_0,_1),cons(_2,_3)) -> activate^#(_3) is a dependency pair of IR. We build a composed triple from L0 and D. ==> L1 = [activate^#(n__zWadr(_0,_1)) -> zWadr^#(activate(_0),activate(_1)), zWadr^#(cons(_2,_3),cons(_4,_5)) -> activate^#(_5)] [comp] is in U_IR^1. Let p1 = [0]. We unfold the first rule of L1 forwards at position p1 with the rule activate(_0) -> _0. ==> L2 = [activate^#(n__zWadr(_0,_1)) -> zWadr^#(_0,activate(_1)), zWadr^#(cons(_2,_3),cons(_4,_5)) -> activate^#(_5)] [comp] is in U_IR^2. Let p2 = [1]. We unfold the first rule of L2 forwards at position p2 with the rule activate(n__prefix(_0)) -> prefix(activate(_0)). ==> L3 = [activate^#(n__zWadr(_0,n__prefix(_1))) -> zWadr^#(_0,prefix(activate(_1))), zWadr^#(cons(_2,_3),cons(_4,_5)) -> activate^#(_5)] [comp] is in U_IR^3. Let p3 = [1, 0]. We unfold the first rule of L3 forwards at position p3 with the rule activate(_0) -> _0. ==> L4 = [activate^#(n__zWadr(_0,n__prefix(_1))) -> zWadr^#(_0,prefix(_1)), zWadr^#(cons(_2,_3),cons(_4,_5)) -> activate^#(_5)] [comp] is in U_IR^4. Let p4 = [1]. We unfold the first rule of L4 forwards at position p4 with the rule prefix(_0) -> cons(nil,n__zWadr(_0,n__prefix(_0))). ==> L5 = activate^#(n__zWadr(cons(_0,_1),n__prefix(_2))) -> activate^#(n__zWadr(_2,n__prefix(_2))) [trans] is in U_IR^5. This DP problem is infinite. ** END proof description ** Proof stopped at iteration 5 Number of unfolded rules generated by this proof = 2240 Number of unfolded rules generated by all the parallel proofs = 9864
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