TRS Standard pair #516964690

details

property	value
status	complete
benchmark	enno.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.6996049881 seconds
cpu usage	7.335143797
max memory	5.19757824E8

stage attributes

key	value
output-size	20681
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 2 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QDPOrderProof [EQUIVALENT, 42 ms]
        (34) QDP
        (35) DependencyGraphProof [EQUIVALENT, 0 ms]
        (36) TRUE


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

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

   lt(0, s(X)) -> true
   lt(s(X), 0) -> false
   lt(s(X), s(Y)) -> lt(X, Y)
   append(nil, Y) -> Y
   append(add(N, X), Y) -> add(N, append(X, Y))
   split(N, nil) -> pair(nil, nil)
   split(N, add(M, Y)) -> f_1(split(N, Y), N, M, Y)
   f_1(pair(X, Z), N, M, Y) -> f_2(lt(N, M), N, M, Y, X, Z)
   f_2(true, N, M, Y, X, Z) -> pair(X, add(M, Z))
   f_2(false, N, M, Y, X, Z) -> pair(add(M, X), Z)
   qsort(nil) -> nil
   qsort(add(N, X)) -> f_3(split(N, X), N, X)
   f_3(pair(Y, Z), N, X) -> append(qsort(Y), add(X, qsort(Z)))

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:

   lt(0, s(X)) -> true
   lt(s(X), 0) -> false
   lt(s(X), s(Y)) -> lt(X, Y)
   append(nil, Y) -> Y
   append(add(N, X), Y) -> add(N, append(X, Y))
   split(N, nil) -> pair(nil, nil)
   split(N, add(M, Y)) -> f_1(split(N, Y), N, M, Y)
   f_1(pair(X, Z), N, M, Y) -> f_2(lt(N, M), N, M, Y, X, Z)
   f_2(true, N, M, Y, X, Z) -> pair(X, add(M, Z))
   f_2(false, N, M, Y, X, Z) -> pair(add(M, X), Z)
   qsort(nil) -> nil
   qsort(add(N, X)) -> f_3(split(N, X), N, X)
   f_3(pair(Y, Z), N, X) -> append(qsort(Y), add(X, qsort(Z)))

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