Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270593
details
property
value
status
complete
benchmark
Applicative_05__mapDivMinus.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n136.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda 2.1c
configuration
default
runtime (wallclock)
0.96074 seconds
cpu usage
2.12202
user time
1.98174
system time
0.140278
max virtual memory
7019232.0
max residence set size
131764.0
stage attributes
key
value
starexec-result
YES
output
1.90/0.95 YES 1.90/0.95 We consider the system theBenchmark. 1.90/0.95 1.90/0.95 Alphabet: 1.90/0.95 1.90/0.95 0 : [] --> c 1.90/0.95 cons : [a * b] --> b 1.90/0.95 div : [c * c] --> c 1.90/0.95 map : [a -> a * b] --> b 1.90/0.95 minus : [c * c] --> c 1.90/0.95 nil : [] --> b 1.90/0.95 s : [c] --> c 1.90/0.95 1.90/0.95 Rules: 1.90/0.95 1.90/0.95 map(f, nil) => nil 1.90/0.95 map(f, cons(x, y)) => cons(f x, map(f, y)) 1.90/0.95 minus(x, 0) => x 1.90/0.95 minus(s(x), s(y)) => minus(x, y) 1.90/0.95 div(0, s(x)) => 0 1.90/0.95 div(s(x), s(y)) => s(div(minus(x, y), s(y))) 1.90/0.95 1.90/0.95 This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). 1.90/0.95 1.90/0.95 We observe that the rules contain a first-order subset: 1.90/0.95 1.90/0.95 minus(X, 0) => X 1.90/0.95 minus(s(X), s(Y)) => minus(X, Y) 1.90/0.95 div(0, s(X)) => 0 1.90/0.95 div(s(X), s(Y)) => s(div(minus(X, Y), s(Y))) 1.90/0.95 1.90/0.95 Moreover, the system is orthogonal. 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 terminating when seen as a many-sorted first-order TRS. 1.90/0.95 1.90/0.95 According to the external first-order termination prover, this system is indeed terminating: 1.90/0.95 1.90/0.95 || proof of resources/system.trs 1.90/0.95 || # AProVE Commit ID: d84c10301d352dfd14de2104819581f4682260f5 fuhs 20130616 1.90/0.95 || 1.90/0.95 || 1.90/0.95 || Termination w.r.t. Q of the given QTRS could be proven: 1.90/0.95 || 1.90/0.95 || (0) QTRS 1.90/0.95 || (1) Overlay + Local Confluence [EQUIVALENT] 1.90/0.95 || (2) QTRS 1.90/0.95 || (3) DependencyPairsProof [EQUIVALENT] 1.90/0.95 || (4) QDP 1.90/0.95 || (5) DependencyGraphProof [EQUIVALENT] 1.90/0.95 || (6) AND 1.90/0.95 || (7) QDP 1.90/0.95 || (8) UsableRulesProof [EQUIVALENT] 1.90/0.95 || (9) QDP 1.90/0.95 || (10) QReductionProof [EQUIVALENT] 1.90/0.95 || (11) QDP 1.90/0.95 || (12) QDPSizeChangeProof [EQUIVALENT] 1.90/0.95 || (13) YES 1.90/0.95 || (14) QDP 1.90/0.95 || (15) UsableRulesProof [EQUIVALENT] 1.90/0.95 || (16) QDP 1.90/0.95 || (17) QReductionProof [EQUIVALENT] 1.90/0.95 || (18) QDP 1.90/0.95 || (19) QDPOrderProof [EQUIVALENT] 1.90/0.95 || (20) QDP 1.90/0.95 || (21) PisEmptyProof [EQUIVALENT] 1.90/0.95 || (22) YES 1.90/0.95 || 1.90/0.95 || 1.90/0.95 || ---------------------------------------- 1.90/0.95 || 1.90/0.95 || (0) 1.90/0.95 || Obligation: 1.90/0.95 || Q restricted rewrite system: 1.90/0.95 || The TRS R consists of the following rules: 1.90/0.95 || 1.90/0.95 || minus(%X, 0) -> %X 1.90/0.95 || minus(s(%X), s(%Y)) -> minus(%X, %Y) 1.90/0.95 || div(0, s(%X)) -> 0 1.90/0.95 || div(s(%X), s(%Y)) -> s(div(minus(%X, %Y), s(%Y))) 1.90/0.95 || 1.90/0.95 || Q is empty. 1.90/0.95 || 1.90/0.95 || ---------------------------------------- 1.90/0.95 || 1.90/0.95 || (1) Overlay + Local Confluence (EQUIVALENT) 1.90/0.95 || The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 1.90/0.95 || ---------------------------------------- 1.90/0.95 || 1.90/0.95 || (2) 1.90/0.95 || Obligation: 1.90/0.95 || Q restricted rewrite system: 1.90/0.95 || The TRS R consists of the following rules: 1.90/0.95 || 1.90/0.95 || minus(%X, 0) -> %X 1.90/0.95 || minus(s(%X), s(%Y)) -> minus(%X, %Y) 1.90/0.95 || div(0, s(%X)) -> 0 1.90/0.95 || div(s(%X), s(%Y)) -> s(div(minus(%X, %Y), s(%Y))) 1.90/0.95 || 1.90/0.95 || The set Q consists of the following terms: 1.90/0.95 || 1.90/0.95 || minus(x0, 0) 1.90/0.95 || minus(s(x0), s(x1))
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
