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TRS Standard pair #516967872
details
property
value
status
complete
benchmark
list-sum-prod.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
0.225191831589 seconds
cpu usage
0.202937561
max memory
3.325952E7
stage attributes
key
value
output-size
2703
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES ** BEGIN proof argument ** All the DP problems were proved finite. As all the involved DP processors are sound, the TRS under analysis terminates. ** 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... ## 4 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [4 DP problems]: ## DP problem: Dependency pairs = [prod^#(cons(_0,_1)) -> prod^#(_1)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [sum^#(cons(_0,_1)) -> sum^#(_1)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [*^#(s(_0),s(_1)) -> *^#(_0,_1)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [+^#(s(_0),s(_1)) -> +^#(_0,_1)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## All the DP problems were proved finite. As all the involved DP processors are sound, the TRS under analysis terminates. 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 = 0
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