Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381713052
details
property
value
status
complete
benchmark
list-sum-prod-bin-assoc-distr-app.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n005.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.90556693077 seconds
cpu usage
4.572583784
max memory
2.85995008E8
stage attributes
key
value
output-size
15932
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 39 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) MRRProof [EQUIVALENT, 0 ms] (14) QDP (15) PisEmptyProof [EQUIVALENT, 0 ms] (16) YES (17) QDP (18) UsableRulesProof [EQUIVALENT, 0 ms] (19) QDP (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] (21) YES (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QDPSizeChangeProof [EQUIVALENT, 0 ms] (29) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 0(#) -> # +(x, #) -> x +(#, x) -> x +(0(x), 0(y)) -> 0(+(x, y)) +(0(x), 1(y)) -> 1(+(x, y)) +(1(x), 0(y)) -> 1(+(x, y)) +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) +(+(x, y), z) -> +(x, +(y, z)) *(#, x) -> # *(0(x), y) -> 0(*(x, y)) *(1(x), y) -> +(0(*(x, y)), y) *(*(x, y), z) -> *(x, *(y, z)) *(x, +(y, z)) -> +(*(x, y), *(x, z)) app(nil, l) -> l app(cons(x, l1), l2) -> cons(x, app(l1, l2)) sum(nil) -> 0(#) sum(cons(x, l)) -> +(x, sum(l)) sum(app(l1, l2)) -> +(sum(l1), sum(l2)) prod(nil) -> 1(#) prod(cons(x, l)) -> *(x, prod(l)) prod(app(l1, l2)) -> *(prod(l1), prod(l2)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: +^1(0(x), 0(y)) -> 0^1(+(x, y)) +^1(0(x), 0(y)) -> +^1(x, y) +^1(0(x), 1(y)) -> +^1(x, y) +^1(1(x), 0(y)) -> +^1(x, y) +^1(1(x), 1(y)) -> 0^1(+(+(x, y), 1(#))) +^1(1(x), 1(y)) -> +^1(+(x, y), 1(#)) +^1(1(x), 1(y)) -> +^1(x, y) +^1(+(x, y), z) -> +^1(x, +(y, z)) +^1(+(x, y), z) -> +^1(y, z) *^1(0(x), y) -> 0^1(*(x, y)) *^1(0(x), y) -> *^1(x, y) *^1(1(x), y) -> +^1(0(*(x, y)), y) *^1(1(x), y) -> 0^1(*(x, y))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472