Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270699
details
property
value
status
complete
benchmark
Applicative_first_order_05__13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n155.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda 2.1c
configuration
default
runtime (wallclock)
13.5623 seconds
cpu usage
35.5346
user time
34.4664
system time
1.06817
max virtual memory
7110092.0
max residence set size
1594056.0
stage attributes
key
value
starexec-result
YES
output
35.41/13.55 YES 35.41/13.56 We consider the system theBenchmark. 35.41/13.56 35.41/13.56 Alphabet: 35.41/13.56 35.41/13.56 !facplus : [a * a] --> a 35.41/13.56 !factimes : [a * a] --> a 35.41/13.56 cons : [c * d] --> d 35.41/13.56 false : [] --> b 35.41/13.56 filter : [c -> b * d] --> d 35.41/13.56 filter2 : [b * c -> b * c * d] --> d 35.41/13.56 map : [c -> c * d] --> d 35.41/13.56 nil : [] --> d 35.41/13.56 true : [] --> b 35.41/13.56 35.41/13.56 Rules: 35.41/13.56 35.41/13.56 !factimes(x, !facplus(y, z)) => !facplus(!factimes(x, y), !factimes(x, z)) 35.41/13.56 !factimes(!facplus(x, y), z) => !facplus(!factimes(z, x), !factimes(z, y)) 35.41/13.56 !factimes(!factimes(x, y), z) => !factimes(x, !factimes(y, z)) 35.41/13.56 !facplus(!facplus(x, y), z) => !facplus(x, !facplus(y, z)) 35.41/13.56 map(f, nil) => nil 35.41/13.56 map(f, cons(x, y)) => cons(f x, map(f, y)) 35.41/13.56 filter(f, nil) => nil 35.41/13.56 filter(f, cons(x, y)) => filter2(f x, f, x, y) 35.41/13.56 filter2(true, f, x, y) => cons(x, filter(f, y)) 35.41/13.56 filter2(false, f, x, y) => filter(f, y) 35.41/13.56 35.41/13.56 This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). 35.41/13.56 35.41/13.56 We observe that the rules contain a first-order subset: 35.41/13.56 35.41/13.56 !factimes(X, !facplus(Y, Z)) => !facplus(!factimes(X, Y), !factimes(X, Z)) 35.41/13.56 !factimes(!facplus(X, Y), Z) => !facplus(!factimes(Z, X), !factimes(Z, Y)) 35.41/13.56 !factimes(!factimes(X, Y), Z) => !factimes(X, !factimes(Y, Z)) 35.41/13.56 !facplus(!facplus(X, Y), Z) => !facplus(X, !facplus(Y, Z)) 35.41/13.56 35.41/13.56 Moreover, the system is finitely branching. Thus, by [Kop12, Thm. 7.55], we may omit all first-order dependency pairs from the dependency pair problem (DP(R), R) if this first-order part is Ce-terminating when seen as a many-sorted first-order TRS. 35.41/13.56 35.41/13.56 According to the external first-order termination prover, this system is indeed Ce-terminating: 35.41/13.56 35.41/13.56 || proof of resources/system.trs 35.41/13.56 || # AProVE Commit ID: d84c10301d352dfd14de2104819581f4682260f5 fuhs 20130616 35.41/13.56 || 35.41/13.56 || 35.41/13.56 || Termination w.r.t. Q of the given QTRS could be proven: 35.41/13.56 || 35.41/13.56 || (0) QTRS 35.41/13.56 || (1) DependencyPairsProof [EQUIVALENT] 35.41/13.56 || (2) QDP 35.41/13.56 || (3) DependencyGraphProof [EQUIVALENT] 35.41/13.56 || (4) AND 35.41/13.56 || (5) QDP 35.41/13.56 || (6) UsableRulesProof [EQUIVALENT] 35.41/13.56 || (7) QDP 35.41/13.56 || (8) QDPSizeChangeProof [EQUIVALENT] 35.41/13.56 || (9) YES 35.41/13.56 || (10) QDP 35.41/13.56 || (11) QDPOrderProof [EQUIVALENT] 35.41/13.56 || (12) QDP 35.41/13.56 || (13) QDPSizeChangeProof [EQUIVALENT] 35.41/13.56 || (14) YES 35.41/13.56 || 35.41/13.56 || 35.41/13.56 || ---------------------------------------- 35.41/13.56 || 35.41/13.56 || (0) 35.41/13.56 || Obligation: 35.41/13.56 || Q restricted rewrite system: 35.41/13.56 || The TRS R consists of the following rules: 35.41/13.56 || 35.41/13.56 || !factimes(%X, !facplus(%Y, %Z)) -> !facplus(!factimes(%X, %Y), !factimes(%X, %Z)) 35.41/13.56 || !factimes(!facplus(%X, %Y), %Z) -> !facplus(!factimes(%Z, %X), !factimes(%Z, %Y)) 35.41/13.56 || !factimes(!factimes(%X, %Y), %Z) -> !factimes(%X, !factimes(%Y, %Z)) 35.41/13.56 || !facplus(!facplus(%X, %Y), %Z) -> !facplus(%X, !facplus(%Y, %Z)) 35.41/13.56 || ~PAIR(%X, %Y) -> %X 35.41/13.56 || ~PAIR(%X, %Y) -> %Y 35.41/13.56 || 35.41/13.56 || Q is empty. 35.41/13.56 || 35.41/13.56 || ---------------------------------------- 35.41/13.56 || 35.41/13.56 || (1) DependencyPairsProof (EQUIVALENT) 35.41/13.56 || Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 35.41/13.56 || ---------------------------------------- 35.41/13.56 || 35.41/13.56 || (2) 35.41/13.56 || Obligation: 35.41/13.56 || Q DP problem: 35.41/13.56 || The TRS P consists of the following rules: 35.41/13.56 || 35.41/13.56 || !FACTIMES(%X, !facplus(%Y, %Z)) -> !FACPLUS(!factimes(%X, %Y), !factimes(%X, %Z)) 35.41/13.56 || !FACTIMES(%X, !facplus(%Y, %Z)) -> !FACTIMES(%X, %Y) 35.41/13.56 || !FACTIMES(%X, !facplus(%Y, %Z)) -> !FACTIMES(%X, %Z) 35.41/13.56 || !FACTIMES(!facplus(%X, %Y), %Z) -> !FACPLUS(!factimes(%Z, %X), !factimes(%Z, %Y)) 35.41/13.56 || !FACTIMES(!facplus(%X, %Y), %Z) -> !FACTIMES(%Z, %X) 35.41/13.56 || !FACTIMES(!facplus(%X, %Y), %Z) -> !FACTIMES(%Z, %Y) 35.41/13.56 || !FACTIMES(!factimes(%X, %Y), %Z) -> !FACTIMES(%X, !factimes(%Y, %Z)) 35.41/13.56 || !FACTIMES(!factimes(%X, %Y), %Z) -> !FACTIMES(%Y, %Z) 35.41/13.56 || !FACPLUS(!facplus(%X, %Y), %Z) -> !FACPLUS(%X, !facplus(%Y, %Z))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10
