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Runti Compl Full Rewri 10127 pair #381902092
details
property
value
status
complete
benchmark
jones1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.0730340480804 seconds
cpu usage
0.24220746
max memory
3.1227904E7
stage attributes
key
value
output-size
3557
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: r1(y,z){y -> cons(x,y)} = r1(cons(x,y),z) ->^+ r1(y,cons(x,z)) = C[r1(y,cons(x,z)) = r1(y,z){z -> cons(x,z)}] ** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules ** Step 1.b:2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. cons_0(2,2) -> 1 cons_0(2,2) -> 2 cons_1(2,2) -> 1 cons_1(2,2) -> 3 cons_1(2,3) -> 1 cons_1(2,3) -> 3 empty_0() -> 1 empty_0() -> 2 empty_1() -> 1 empty_1() -> 3 r1_0(2,2) -> 1 r1_1(2,3) -> 1 rev_0(2) -> 1 2 -> 1 3 -> 1 ** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))
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