details

property	value
status	complete
benchmark	from.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n080.star.cs.uiowa.edu
space	Mixed_HO_10

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.941406965256 seconds
cpu usage	1.794029942
max memory	7.3904128E7

stage attributes

key	value
output-size	10662
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: chain : [N -> N * list] --> list cons : [N * list] --> list false : [] --> B from : [N * list] --> list if : [B * list * list] --> list incch : [list] --> list lteq : [N * N] --> B nil : [] --> list o : [] --> N s : [N] --> N true : [] --> B Rules: if(true, x, y) => x if(false, x, y) => y lteq(s(x), o) => false lteq(o, x) => true lteq(s(x), s(y)) => lteq(x, y) from(x, nil) => nil from(x, cons(y, z)) => if(lteq(x, y), cons(y, z), from(x, z)) chain(f, nil) => nil chain(f, cons(x, y)) => cons(f x, chain(f, from(f x, y))) incch(x) => chain(/\y.s(y), x) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We observe that the rules contain a first-order subset: if(true, X, Y) => X if(false, X, Y) => Y lteq(s(X), o) => false lteq(o, X) => true lteq(s(X), s(Y)) => lteq(X, Y) from(X, nil) => nil from(X, cons(Y, Z)) => if(lteq(X, Y), cons(Y, Z), from(X, Z)) 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. According to the external first-order termination prover, this system is indeed terminating: || proof of resources/system.trs || # AProVE Commit ID: d84c10301d352dfd14de2104819581f4682260f5 fuhs 20130616 || || || Termination w.r.t. Q of the given QTRS could be proven: || || (0) QTRS || (1) QTRSRRRProof [EQUIVALENT] || (2) QTRS || (3) RisEmptyProof [EQUIVALENT] || (4) YES || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system: || The TRS R consists of the following rules: || || if(true, %X, %Y) -> %X || if(false, %X, %Y) -> %Y || lteq(s(%X), o) -> false || lteq(o, %X) -> true || lteq(s(%X), s(%Y)) -> lteq(%X, %Y) || from(%X, nil) -> nil || from(%X, cons(%Y, %Z)) -> if(lteq(%X, %Y), cons(%Y, %Z), from(%X, %Z)) || || Q is empty. || || ---------------------------------------- || || (1) QTRSRRRProof (EQUIVALENT) || Used ordering: || Quasi precedence: || from_2 > [if_3, cons_2] || from_2 > lteq_2 > [true, false, o] || from_2 > nil || || || Status: || if_3: multiset status || true: multiset status || false: multiset status || lteq_2: [2,1] || s_1: [1] || o: multiset status || from_2: multiset status popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to HRS union beta 16688