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Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270377
details
property
value
status
complete
benchmark
h07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Hamana_Kikuchi_18
run statistics
property
value
solver
Wanda 2.1c
configuration
default
runtime (wallclock)
11.2193 seconds
cpu usage
11.9623
user time
11.0231
system time
0.93923
max virtual memory
7562056.0
max residence set size
968288.0
stage attributes
key
value
starexec-result
YES
output
11.80/11.13 YES 11.80/11.15 We consider the system theBenchmark. 11.80/11.15 11.80/11.15 Alphabet: 11.80/11.15 11.80/11.15 0 : [] --> N 11.80/11.15 even : [] --> N -> N -> B 11.80/11.15 false : [] --> B 11.80/11.15 g : [] --> N -> B 11.80/11.15 h : [] --> N -> (N -> B) -> N -> B 11.80/11.15 not : [] --> B -> B 11.80/11.15 rec : [] --> (N -> (N -> B) -> N -> B) -> B -> N -> B 11.80/11.15 true : [] --> B 11.80/11.15 11.80/11.15 Rules: 11.80/11.15 11.80/11.15 rec f (i 0) => i 11.80/11.15 g x => true 11.80/11.15 h x f y => not (f y) 11.80/11.15 not true => false 11.80/11.15 not false => true 11.80/11.15 even x y => rec h (g x) y 11.80/11.15 11.80/11.15 Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term. 11.80/11.15 11.80/11.15 We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0). This leads to the following AFSM: 11.80/11.15 11.80/11.15 Alphabet: 11.80/11.15 11.80/11.15 0 : [] --> N 11.80/11.15 even : [N] --> N -> B 11.80/11.15 false : [] --> B 11.80/11.15 g : [] --> N -> B 11.80/11.15 h : [] --> N -> (N -> B) -> N -> B 11.80/11.15 not : [B] --> B 11.80/11.15 rec : [N -> (N -> B) -> N -> B * B] --> N -> B 11.80/11.15 true : [] --> B 11.80/11.15 ~AP1 : [N -> B * N] --> B 11.80/11.15 11.80/11.15 Rules: 11.80/11.15 11.80/11.15 rec(F, ~AP1(G, 0)) => G 11.80/11.15 g X => true 11.80/11.15 h X F Y => not(~AP1(F, Y)) 11.80/11.15 not(true) => false 11.80/11.15 not(false) => true 11.80/11.15 even(X) Y => ~AP1(rec(h, g X), Y) 11.80/11.15 rec(F, even(X) 0) => even(X) 11.80/11.15 rec(F, g 0) => g 11.80/11.15 rec(F, h X G 0) => h X G 11.80/11.15 ~AP1(F, X) => F X 11.80/11.15 11.80/11.15 We observe that the rules contain a first-order subset: 11.80/11.15 11.80/11.15 g X => true 11.80/11.15 not(true) => false 11.80/11.15 not(false) => true 11.80/11.15 11.80/11.15 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. 11.80/11.15 11.80/11.15 According to the external first-order termination prover, this system is indeed Ce-terminating: 11.80/11.15 11.80/11.15 || proof of resources/system.trs 11.80/11.15 || # AProVE Commit ID: d84c10301d352dfd14de2104819581f4682260f5 fuhs 20130616 11.80/11.15 || 11.80/11.15 || 11.80/11.15 || Termination w.r.t. Q of the given QTRS could be proven: 11.80/11.15 || 11.80/11.15 || (0) QTRS 11.80/11.15 || (1) QTRSRRRProof [EQUIVALENT] 11.80/11.15 || (2) QTRS 11.80/11.15 || (3) RisEmptyProof [EQUIVALENT] 11.80/11.15 || (4) YES 11.80/11.15 || 11.80/11.15 || 11.80/11.15 || ---------------------------------------- 11.80/11.15 || 11.80/11.15 || (0) 11.80/11.15 || Obligation: 11.80/11.15 || Q restricted rewrite system: 11.80/11.15 || The TRS R consists of the following rules: 11.80/11.15 || 11.80/11.15 || g(%X) -> true 11.80/11.15 || not(true) -> false 11.80/11.15 || not(false) -> true 11.80/11.15 || ~PAIR(%X, %Y) -> %X 11.80/11.15 || ~PAIR(%X, %Y) -> %Y 11.80/11.15 || 11.80/11.15 || Q is empty. 11.80/11.15 || 11.80/11.15 || ---------------------------------------- 11.80/11.15 || 11.80/11.15 || (1) QTRSRRRProof (EQUIVALENT) 11.80/11.15 || Used ordering: 11.80/11.15 || Knuth-Bendix order [KBO] with precedence:not_1 > ~PAIR_2 > false > g_1 > true 11.80/11.15 || 11.80/11.15 || and weight map: 11.80/11.15 || 11.80/11.15 || true=2 11.80/11.15 || false=2
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