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TRS Standard pair #516961457
details
property
value
status
complete
benchmark
ExIntrod_Zan97_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
1.65325713158 seconds
cpu usage
3.26008771
max memory
4.20483072E8
stage attributes
key
value
output-size
3628
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] fact(_0) -> fact(p(_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->p(_0)}. We have r|p = fact(p(_0)) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = fact(_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... ## 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 = [fact^#(_0) -> fact^#(p(_0))] TRS = {fact(_0) -> if(zero(_0),n__s(0),n__prod(_0,fact(p(_0)))), add(0,_0) -> _0, add(s(_0),_1) -> s(add(_0,_1)), prod(0,_0) -> 0, prod(s(_0),_1) -> add(_1,prod(_0,_1)), if(true,_0,_1) -> activate(_0), if(false,_0,_1) -> activate(_1), zero(0) -> true, zero(s(_0)) -> false, p(s(_0)) -> _0, s(_0) -> n__s(_0), prod(_0,_1) -> n__prod(_0,_1), activate(n__s(_0)) -> s(_0), activate(n__prod(_0,_1)) -> prod(_0,_1), activate(_0) -> _0} ## 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 = [prod^#(s(_0),_1) -> prod^#(_0,_1)] TRS = {fact(_0) -> if(zero(_0),n__s(0),n__prod(_0,fact(p(_0)))), add(0,_0) -> _0, add(s(_0),_1) -> s(add(_0,_1)), prod(0,_0) -> 0, prod(s(_0),_1) -> add(_1,prod(_0,_1)), if(true,_0,_1) -> activate(_0), if(false,_0,_1) -> activate(_1), zero(0) -> true, zero(s(_0)) -> false, p(s(_0)) -> _0, s(_0) -> n__s(_0), prod(_0,_1) -> n__prod(_0,_1), activate(n__s(_0)) -> s(_0), activate(n__prod(_0,_1)) -> prod(_0,_1), activate(_0) -> _0} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [add^#(s(_0),_1) -> add^#(_0,_1)] TRS = {fact(_0) -> if(zero(_0),n__s(0),n__prod(_0,fact(p(_0)))), add(0,_0) -> _0, add(s(_0),_1) -> s(add(_0,_1)), prod(0,_0) -> 0, prod(s(_0),_1) -> add(_1,prod(_0,_1)), if(true,_0,_1) -> activate(_0), if(false,_0,_1) -> activate(_1), zero(0) -> true, zero(s(_0)) -> false, p(s(_0)) -> _0, s(_0) -> n__s(_0), prod(_0,_1) -> n__prod(_0,_1), activate(n__s(_0)) -> s(_0), activate(n__prod(_0,_1)) -> prod(_0,_1), activate(_0) -> _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 find a loop (forward=true, backward=false, max=-1) # max_depth=4, 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 = fact^#(_0) -> fact^#(p(_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 = 2
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