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TRS Standard pair #516966037
details
property
value
status
complete
benchmark
Ex4_7_37_Bor03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n087.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
0.481364011765 seconds
cpu usage
0.843201473
max memory
8.6593536E7
stage attributes
key
value
output-size
4651
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 = 0] from(_0) -> from(s(_0)) Let l be the left-hand side and r be the right-hand side of this rule. Let p = epsilon, theta1 = {} and theta2 = {_0->s(_0)}. We have r|p = from(s(_0)) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = from(_0) 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... ## 5 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [5 DP problems]: ## DP problem: Dependency pairs = [zWquot^#(cons(_0,_1),cons(_2,_3)) -> zWquot^#(_1,_3)] TRS = {from(_0) -> cons(_0,from(s(_0))), sel(0,cons(_0,_1)) -> _0, sel(s(_0),cons(_1,_2)) -> sel(_0,_2), minus(_0,0) -> 0, minus(s(_0),s(_1)) -> minus(_0,_1), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(minus(_0,_1),s(_1))), zWquot(_0,nil) -> nil, zWquot(nil,_0) -> nil, zWquot(cons(_0,_1),cons(_2,_3)) -> cons(quot(_0,_2),zWquot(_1,_3))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [quot^#(s(_0),s(_1)) -> quot^#(minus(_0,_1),s(_1))] TRS = {from(_0) -> cons(_0,from(s(_0))), sel(0,cons(_0,_1)) -> _0, sel(s(_0),cons(_1,_2)) -> sel(_0,_2), minus(_0,0) -> 0, minus(s(_0),s(_1)) -> minus(_0,_1), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(minus(_0,_1),s(_1))), zWquot(_0,nil) -> nil, zWquot(nil,_0) -> nil, zWquot(cons(_0,_1),cons(_2,_3)) -> cons(quot(_0,_2),zWquot(_1,_3))} ## 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. ## DP problem: Dependency pairs = [minus^#(s(_0),s(_1)) -> minus^#(_0,_1)] TRS = {from(_0) -> cons(_0,from(s(_0))), sel(0,cons(_0,_1)) -> _0, sel(s(_0),cons(_1,_2)) -> sel(_0,_2), minus(_0,0) -> 0, minus(s(_0),s(_1)) -> minus(_0,_1), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(minus(_0,_1),s(_1))), zWquot(_0,nil) -> nil, zWquot(nil,_0) -> nil, zWquot(cons(_0,_1),cons(_2,_3)) -> cons(quot(_0,_2),zWquot(_1,_3))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [sel^#(s(_0),cons(_1,_2)) -> sel^#(_0,_2)] TRS = {from(_0) -> cons(_0,from(s(_0))), sel(0,cons(_0,_1)) -> _0, sel(s(_0),cons(_1,_2)) -> sel(_0,_2), minus(_0,0) -> 0, minus(s(_0),s(_1)) -> minus(_0,_1), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(minus(_0,_1),s(_1))), zWquot(_0,nil) -> nil, zWquot(nil,_0) -> nil, zWquot(cons(_0,_1),cons(_2,_3)) -> cons(quot(_0,_2),zWquot(_1,_3))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [from^#(_0) -> from^#(s(_0))] TRS = {from(_0) -> cons(_0,from(s(_0))), sel(0,cons(_0,_1)) -> _0, sel(s(_0),cons(_1,_2)) -> sel(_0,_2), minus(_0,0) -> 0, minus(s(_0),s(_1)) -> minus(_0,_1), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(minus(_0,_1),s(_1))), zWquot(_0,nil) -> nil, zWquot(nil,_0) -> nil, zWquot(cons(_0,_1),cons(_2,_3)) -> cons(quot(_0,_2),zWquot(_1,_3))} ## 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. ## Some DP problems could not be proved finite. ## Now, we try to prove that one of these problems is infinite. ## Trying to find a loop (forward=true, backward=true, max=20) # max_depth=20, unfold_variables=false: # Iteration 0: success, found a loop, 1 unfolded rule generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = from^#(_0) -> from^#(s(_0)) [trans] is in U_IR^0. 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 = 36
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