TRS Context Sensitive pair #516978813

details

property	value
status	complete
benchmark	Ex1_2_AEL03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.08195090294 seconds
cpu usage	5.579595309
max memory	4.80251904E8

stage attributes

key	value
output-size	17853
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given CSR could be proven:

(0) CSR
(1) CSRInnermostProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSDPSubtermProof [EQUIVALENT, 1 ms]
        (9) QCSDP
        (10) PIsEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QCSDP
        (13) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (14) QCSDP
        (15) PIsEmptyProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QCSDP
        (18) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (19) QCSDP
        (20) PIsEmptyProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QCSDP
        (23) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (24) QCSDP
        (25) PIsEmptyProof [EQUIVALENT, 0 ms]
        (26) YES


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

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   from(X) -> cons(X, from(s(X)))
   2ndspos(0, Z) -> rnil
   2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z))
   2ndsneg(0, Z) -> rnil
   2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, Z))
   pi(X) -> 2ndspos(X, from(0))
   plus(0, Y) -> Y
   plus(s(X), Y) -> s(plus(X, Y))
   times(0, Y) -> 0
   times(s(X), Y) -> plus(Y, times(X, Y))
   square(X) -> times(X, X)

The replacement map contains the following entries:

from: {1}
cons: {1}
s: {1}
2ndspos: {1, 2}
0: empty set
rnil: empty set
rcons: {1, 2}
posrecip: {1}
2ndsneg: {1, 2}
negrecip: {1}
pi: {1}
plus: {1, 2}
times: {1, 2}
square: {1}

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

(1) CSRInnermostProof (EQUIVALENT)
The CSR is orthogonal. By [CS_Inn] we can switch to innermost.
----------------------------------------

(2)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   from(X) -> cons(X, from(s(X)))
   2ndspos(0, Z) -> rnil
   2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z))
   2ndsneg(0, Z) -> rnil
   2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, Z))
   pi(X) -> 2ndspos(X, from(0))
   plus(0, Y) -> Y
   plus(s(X), Y) -> s(plus(X, Y))
   times(0, Y) -> 0
   times(s(X), Y) -> plus(Y, times(X, Y))
   square(X) -> times(X, X)

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