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TRS Standard pair #516961072
details
property
value
status
complete
benchmark
ttt1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n064.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
0.257065057755 seconds
cpu usage
0.269803777
max memory
4.2172416E7
stage attributes
key
value
output-size
3332
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 rule was generated while unfolding the analyzed TRS: [iteration = 3] f(cons(s(a),_0),s(b),cons(s(a),_0)) -> f(cons(s(a),_0),_0,cons(s(a),_0)) Let l be the left-hand side and r be the right-hand side of this rule. Let p = epsilon, theta1 = {_0->s(b)} and theta2 = {}. We have r|p = f(cons(s(a),_0),_0,cons(s(a),_0)) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = f(cons(s(a),s(b)),s(b),cons(s(a),s(b))) 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... ## 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 = [g^#(f(s(_0),s(_1),_2)) -> g^#(f(_0,_1,_2))] TRS = {f(s(a),s(b),_0) -> f(_0,_0,_0), g(f(s(_0),s(_1),_2)) -> g(f(_0,_1,_2)), cons(_0,_1) -> _0, cons(_0,_1) -> _1} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [f^#(s(a),s(b),_0) -> f^#(_0,_0,_0)] TRS = {f(s(a),s(b),_0) -> f(_0,_0,_0), g(f(s(_0),s(_1),_2)) -> g(f(_0,_1,_2)), cons(_0,_1) -> _0, cons(_0,_1) -> _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. ## A DP problem could not be proved finite. ## Now, we try to prove that this problem is infinite. ## Trying to find a loop (forward=true, backward=true, max=20) # max_depth=20, unfold_variables=false: # Iteration 0: no loop found, 1 unfolded rule generated. # Iteration 1: no loop found, 1 unfolded rule generated. # Iteration 2: no loop found, 6 unfolded rules generated. # Iteration 3: success, found a loop, 10 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = f^#(s(a),s(b),_0) -> f^#(_0,_0,_0) [trans] is in U_IR^0. We build a unit triple from L0. ==> L1 = f^#(s(a),s(b),_0) -> f^#(_0,_0,_0) [unit] is in U_IR^1. Let p1 = [0]. We unfold the rule of L1 backwards at position p1 with the rule cons(_0,_1) -> _0. ==> L2 = f^#(cons(s(a),_0),s(b),cons(s(a),_0)) -> f^#(cons(s(a),_0),cons(s(a),_0),cons(s(a),_0)) [unit] is in U_IR^2. Let p2 = [1]. We unfold the rule of L2 forwards at position p2 with the rule cons(_0,_1) -> _1. ==> L3 = f^#(cons(s(a),_0),s(b),cons(s(a),_0)) -> f^#(cons(s(a),_0),_0,cons(s(a),_0)) [unit] is in U_IR^3. 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 = 23
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