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TRS Standard pair #516967897
details
property
value
status
complete
benchmark
list-sum-prod-assoc.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n119.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
0.209022045135 seconds
cpu usage
0.23793237
max memory
3.090432E7
stage attributes
key
value
output-size
3975
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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,_1),_2) -> +(_0,+(_1,_2)), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), *(*(_0,_1),_2) -> *(_0,*(_1,_2)), 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,_1),_2) -> +(_0,+(_1,_2)), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), *(*(_0,_1),_2) -> *(_0,*(_1,_2)), 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), *^#(*(_0,_1),_2) -> *^#(_0,*(_1,_2)), *^#(*(_0,_1),_2) -> *^#(_1,_2)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), *(*(_0,_1),_2) -> *(_0,*(_1,_2)), 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... Failed! ## Trying with polynomial interpretations... This DP problem is too complex! Aborting! ## Trying with lexicographic path orders... The constraints are satisfied by the lexicographic path order using the argument filtering: {prod:[0], *:[0, 1], sum:[0], s:[0], cons:[0, 1], +:[0, 1], *^#:[0, 1]} and the precedence: * > [s, +], cons > [prod, sum, *, s, +], nil > [0, s], *^# > [*, s, +], + > [s] This DP problem is finite. ## DP problem: Dependency pairs = [+^#(s(_0),s(_1)) -> +^#(_0,_1), +^#(+(_0,_1),_2) -> +^#(_0,+(_1,_2)), +^#(+(_0,_1),_2) -> +^#(_1,_2)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), *(*(_0,_1),_2) -> *(_0,*(_1,_2)), 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... Failed! ## Trying with polynomial interpretations... This DP problem is too complex! Aborting! ## Trying with lexicographic path orders... The constraints are satisfied by the lexicographic path order using the argument filtering: {prod:[0], *:[0, 1], sum:[0], s:[0], cons:[0, 1], +:[0, 1], +^#:[0, 1]} and the precedence: * > [s, +], cons > [prod, sum, *, s, +], nil > [0, s], +^# > [s, +], + > [s] 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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