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TRS Standard pair #516967777
details
property
value
status
complete
benchmark
list-sum-prod-assoc-append.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n183.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
0.263419151306 seconds
cpu usage
0.259965287
max memory
3.2079872E7
stage attributes
key
value
output-size
5402
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... ## 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 = [prod^#(cons(_0,_1)) -> prod^#(_1), prod^#(app(_0,_1)) -> prod^#(_0), prod^#(app(_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)), app(nil,_0) -> _0, app(cons(_0,_1),_2) -> cons(_0,app(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), sum(app(_0,_1)) -> +(sum(_0),sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1)), prod(app(_0,_1)) -> *(prod(_0),prod(_1))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [sum^#(cons(_0,_1)) -> sum^#(_1), sum^#(app(_0,_1)) -> sum^#(_0), sum^#(app(_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)), app(nil,_0) -> _0, app(cons(_0,_1),_2) -> cons(_0,app(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), sum(app(_0,_1)) -> +(sum(_0),sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1)), prod(app(_0,_1)) -> *(prod(_0),prod(_1))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [app^#(cons(_0,_1),_2) -> app^#(_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)), app(nil,_0) -> _0, app(cons(_0,_1),_2) -> cons(_0,app(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), sum(app(_0,_1)) -> +(sum(_0),sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1)), prod(app(_0,_1)) -> *(prod(_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)), app(nil,_0) -> _0, app(cons(_0,_1),_2) -> cons(_0,app(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), sum(app(_0,_1)) -> +(sum(_0),sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1)), prod(app(_0,_1)) -> *(prod(_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: {s:[0], sum:[0], *:[0, 1], app:[0, 1], cons:[0, 1], +:[0, 1], prod:[0], *^#:[0, 1]} and the precedence: * > [s, +], app > [s, sum, *, cons, +, prod], cons > [s, sum, *, +, prod], *^# > [s, *, +], + > [s], nil > [0, 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)), app(nil,_0) -> _0, app(cons(_0,_1),_2) -> cons(_0,app(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), sum(app(_0,_1)) -> +(sum(_0),sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1)), prod(app(_0,_1)) -> *(prod(_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: {s:[0], sum:[0], *:[0, 1], app:[0, 1], cons:[0, 1], +:[0, 1], prod:[0], +^#:[0, 1]} and the precedence: +^# > [s, +], * > [s, +], app > [s, sum, *, cons, +, prod], cons > [s, sum, *, +, prod], + > [s], nil > [0, 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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