TRS Standard pair #615303603

details

property	value
status	complete
benchmark	thiemann05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n026.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	2.70123505592 seconds
cpu usage	7.921213064
max memory	4.21646336E8

stage attributes

key	value
output-size	19355
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) TransformationProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) DependencyGraphProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) TransformationProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) TransformationProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) TransformationProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) QDPOrderProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) DependencyGraphProof [EQUIVALENT, 0 ms]
        (32) TRUE


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   isLeaf(leaf) -> true
   isLeaf(cons(u, v)) -> false
   left(cons(u, v)) -> u
   right(cons(u, v)) -> v
   concat(leaf, y) -> y
   concat(cons(u, v), y) -> cons(u, concat(v, y))
   less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v)
   if1(b, true, u, v) -> false
   if1(b, false, u, v) -> if2(b, u, v)
   if2(true, u, v) -> true
   if2(false, u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))

Q is empty.

----------------------------------------

(1) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   isLeaf(leaf) -> true
   isLeaf(cons(u, v)) -> false
   left(cons(u, v)) -> u
   right(cons(u, v)) -> v
   concat(leaf, y) -> y
   concat(cons(u, v), y) -> cons(u, concat(v, y))
   less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v)
   if1(b, true, u, v) -> false
   if1(b, false, u, v) -> if2(b, u, v)
   if2(true, u, v) -> true
   if2(false, u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))

The set Q consists of the following terms:

   isLeaf(leaf)
   isLeaf(cons(x0, x1))
   left(cons(x0, x1))
   right(cons(x0, x1))
   concat(leaf, x0)
   concat(cons(x0, x1), x2)

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