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TRS Standard pair #487074047
details
property
value
status
complete
benchmark
list-sum-prod-assoc-append.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n178.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.775974 seconds
cpu usage
1.73401
user time
1.41405
system time
0.319959
max virtual memory
1766196.0
max residence set size
72864.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) *(*(x,y),z) -> *(x,*(y,z)) app(nil(),l) -> l app(cons(x,l1),l2) -> cons(x,app(l1,l2)) sum(nil()) -> 0() sum(cons(x,l)) -> +(x,sum(l)) sum(app(l1,l2)) -> +(sum(l1),sum(l2)) prod(nil()) -> s(0()) prod(cons(x,l)) -> *(x,prod(l)) prod(app(l1,l2)) -> *(prod(l1),prod(l2)) Proof: DP Processor: DPs: +#(s(x),s(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) *#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> *#(x,y) *#(s(x),s(y)) -> +#(*(x,y),+(x,y)) *#(*(x,y),z) -> *#(y,z) *#(*(x,y),z) -> *#(x,*(y,z)) app#(cons(x,l1),l2) -> app#(l1,l2) sum#(cons(x,l)) -> sum#(l) sum#(cons(x,l)) -> +#(x,sum(l)) sum#(app(l1,l2)) -> sum#(l2) sum#(app(l1,l2)) -> sum#(l1) sum#(app(l1,l2)) -> +#(sum(l1),sum(l2)) prod#(cons(x,l)) -> prod#(l) prod#(cons(x,l)) -> *#(x,prod(l)) prod#(app(l1,l2)) -> prod#(l2) prod#(app(l1,l2)) -> prod#(l1) prod#(app(l1,l2)) -> *#(prod(l1),prod(l2)) TRS: +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) *(*(x,y),z) -> *(x,*(y,z)) app(nil(),l) -> l app(cons(x,l1),l2) -> cons(x,app(l1,l2)) sum(nil()) -> 0() sum(cons(x,l)) -> +(x,sum(l)) sum(app(l1,l2)) -> +(sum(l1),sum(l2)) prod(nil()) -> s(0()) prod(cons(x,l)) -> *(x,prod(l)) prod(app(l1,l2)) -> *(prod(l1),prod(l2)) TDG Processor: DPs: +#(s(x),s(y)) -> +#(x,y) +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(x,+(y,z)) *#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> *#(x,y) *#(s(x),s(y)) -> +#(*(x,y),+(x,y)) *#(*(x,y),z) -> *#(y,z) *#(*(x,y),z) -> *#(x,*(y,z)) app#(cons(x,l1),l2) -> app#(l1,l2) sum#(cons(x,l)) -> sum#(l) sum#(cons(x,l)) -> +#(x,sum(l)) sum#(app(l1,l2)) -> sum#(l2) sum#(app(l1,l2)) -> sum#(l1) sum#(app(l1,l2)) -> +#(sum(l1),sum(l2)) prod#(cons(x,l)) -> prod#(l) prod#(cons(x,l)) -> *#(x,prod(l)) prod#(app(l1,l2)) -> prod#(l2) prod#(app(l1,l2)) -> prod#(l1) prod#(app(l1,l2)) -> *#(prod(l1),prod(l2)) TRS: +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) *(*(x,y),z) -> *(x,*(y,z)) app(nil(),l) -> l app(cons(x,l1),l2) -> cons(x,app(l1,l2)) sum(nil()) -> 0() sum(cons(x,l)) -> +(x,sum(l)) sum(app(l1,l2)) -> +(sum(l1),sum(l2)) prod(nil()) -> s(0()) prod(cons(x,l)) -> *(x,prod(l)) prod(app(l1,l2)) -> *(prod(l1),prod(l2)) graph: prod#(cons(x,l)) -> prod#(l) -> prod#(app(l1,l2)) -> *#(prod(l1),prod(l2))
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